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Pinpointing thermal tolerance thresholds for commercially important species, such as aquaculture finfish, under acute and chronic thermal stress is becoming increasingly relevant in the context of climate change. While experimental research, traditionally quantified by the determination of the Critical Thermal Maximum (CTmax), offers valuable insights, it is necessary to further develop appropriate tools to provide predictions and shed light on the underlying mechanisms of thermal tolerance. Bioenergetic models have long been used to study the effects of temperature on fish metabolism under chronic, but rarely under acute, scales. In this study, we present a modelling approach based on the Dynamic Energy Budget (DEB) theory that describes the tolerance limits of fish under acute thermal stress in bioenergetics terms. It adopts the notion of an energy-dependent tolerance to stress and defines acute tolerance limits at the intersection of fundamental energy fluxes, namely those relating to the mobilization of energy and to maintenance costs. To showcase this approach, DEB models for two finfish, the European sea bass (Dicentrarchus labrax) and the meagre (Argyrosomus regius) were used to run acute thermal challenge simulations and study shifts in the critical temperature achieved by the fish. The results suggest that the model can adequately capture the general tolerance patterns observed experimentally for the two species as well as pinpoint the parameters that may influence them. In particular, the simulations showed a positive relation between acclimation temperature and tolerance while the opposite stands for the body size of the fish, with smaller fish achieving higher critical temperatures than their larger counterparts. Also, tolerance limits were affected by the state of internal reserves, with well-fed fish exhibiting higher values. Finally, the potential application of this modelling approach on higher taxonomic scales was evaluated, by running simulations on species belonging to major fish orders. The preliminary results suggest that the method can capture differences among groups that are consistent with literature, suggesting it may be a realistic mechanistic approach for studying thermal tolerance in ectotherms.

In the oligotrophic, phosphorus (P)-limited Eastern Mediterranean Sea (EMS), grazing on heterotrophic bacteria (HB) by pigmented nanoflagellates (PNF) through mixotrophy is a significant source of bacterial mortality and is P-dependent. Heterotrophic nanoflagellates (HNF) are also important consumers of HB. However, there is still no conceptual framework describing the flows of carbon (C) and P through the EMS microbial food web that takes into account the mixotrophic behavior of PNF. In the present modelling study, we explore qualitatively the pathways of C- and P-flow through the HB-mixotrophic PNF-HNF link under varying availability of inorganic P. At low P availability, given the assumption that PNF can fulfill most of their P requirements through HB consumption when P-limited, model simulations show that PNF support bacterial production and P uptake by supplying HB with dissolved organic carbon (DOC), leading to a win-win stable scenario, with PNF holding a key role in P-transfer through the microbial food web. Conversely, increased P availability results in lower PNF grazing upon HB, amplifying the relative contribution of HNF to bacterial grazing. Based on our modelling study we propose a novel conceptual framework for bacteria-nanoflagellate interactions in the EMS, where PNF have the functional role of DOC primary producers and also share with HNF the functional role of bacterial consumers via mixotrophy. This alternative microbial loop operates in a Pdependent way. Our modelling study pinpoints the significance of the adaptive physiology of PNF for the functioning of the oligotrophic ecosystem of the EMS.

Traditionally, the terms altricial and precocial are used to described the state at birth of birds and mammals. We suggest an explanation for why birds evolved from precocial to altricial and mammals from altricial to precocial. However, the concept is not confined to these groups alone and is an important pattern underlying all animal metabolism. Being able to quantify it, helps position species in multi-dimensional diversity trait space. We here argue that a quantification of the state of development of an individual at birth, in the context of its life cycle, can best be done by comparison with the state at puberty. Two natural quantifiers for the altricial-precocial spectrum exist in the context of the Dynamic Energy Budget (DEB) theory that are applicable to the whole animal kingdom: maturity and maturity density at birth divided by that at puberty. These quantities have been estimated, in combination with other parameters, for some 875 species belonging to all large phyla. We study how taxa are ranked according to both the maturity and maturity density ratios. We conclude that only the maturity ratio qualifies as quantifier for the altricial-precocial spectrum. We were able to retrieve known patterns in altriciality for birds and mammals, while the concept is now applicable to all animal taxa. This new quantifier for animal altriciality can be linked quantitatively to other properties. These linkages are studied by examining how maturity parameters interact with other DEB parameters and implied properties. With the exception of mammals, cartilaginous fish and insects, bigger-bodied species show a clear tendency for to be more frequently altricial. We discuss possible explanations. Age at birth as fraction of age at puberty was found to be proportional to the maturity ratio to the power 1/3; this is consistent with DEB's co-variation rules, but does not follow from them. Maturity at puberty follows a Weibull distribution with great accuracy while that at birth does not, which is consistent with the idea that Weibull distributions can be expected when many factors contribute. We found that species from all taxa with a very high allocation fraction to soma, tend to have low maturities at birth and puberty. We discuss the possible implications of these patterns.

The Add-my-Pet (AmP) collection of data on energetics and Dynamic Energy Budget (DEB) parameters currently contains 200 out of over 1100 extant species of chondrichthyans. This milestone in the compilation of data for this group led us to investigate: (1) do the characteristics that we reported in 2014 for 20 chondrichthyan species, relative to other fish, still hold (2) are novel patterns in properties revealed given the additional data and (3) do the four chondrichthyan subgroups (galean, squaleans, rays and chimaeras) differ in properties? We argue that a better understanding of these properties is key to sustainable management of the rapidly dwindling populations worldwide. Most of the inter-specific scatter in ultimate reproduction rate as function of ultimate body weight stems from differences in the mass of neonates as fraction of that of the mother, which is very high in chondrichthyans. The ultimate neonate mass production is found to be proportional to the ultimate respiration rate, with proportionality factor of 10 g/mol. The lifespan is found to be inversely proportional to weight-specific respiration, with a proportionality factor of 0.1 mol/g. The ultimate weight equals the life-time cumulated neonate mass production. These relationships also apply, with more scatter, to all 3000 animal species in the AmP collection. Sharks and rays were found to be more demand-species, contrary to ray-finned fish and chimaeras, which are supply species. Chimaeras also have that smallest weight at birth and precociality coefficient, compared to sharks and rays. Galeans grow much slower than squaleans and rays, but the chimaeras grow even slower. The lifespan equals 25 times the incubation time for chondrichthyans, but they are rather unique in this respect. Last but not least, we discuss the odd implications of recently published data on the energetics of the Greenland shark.

WOS:000453497600006; Dynamic Energy Budget (DEB) theory constitutes a coherent set of universal biological processes that have been used as building blocks for modeling biological systems over the last 40 years in many applied disciplines. In the context of extracting parameters for DEB models from data, we discuss the methodology of fitting multiple models, which share parameters, to multiple data sets in a single parameter estimation. This problem is not specific to DEB models, and is (or should be) really general in biology. We discovered that a lot of estimation problems that we suffered from in the past originated from the use of a loss function that was not symmetric in the role of data and predictions. We here propose two much better symmetric candidates, that proved to work well in practice. We illustrate estimation problems and their solutions with a Monte-Carlo case study for increasing amount of scatter, which decreased the amount of information in the data about one or more parameter values. We here validate the method using a set of models with known parameters and different scatter structures. We compare the loss functions on the basis of convergence, point and interval estimates. We also discuss the use of pseudo-data, i.e. realistic values for parameters that we treat as data from which predictions can differ. These pseudo-data are used to avoid that a good fit results in parameter values that make no biological sense. We discuss our new method for estimating confidence intervals and present a list of concrete recommendations for parameter estimation. We conclude that the proposed method performs very well in recovering parameter values of a set of models, applied to a set of data. This is consistent with our large-scale applications in practice.

Body size is not an independent variable, but an emergent property: the result of a number of inter-linked eco-physiological processes, like most other quantities that we can measure on organisms. Organisms do not have a particular body size. They are born small and grow to larger sizes during their life trajectory, while changing properties during the growth process in interaction with the environment. The use of maximum body mass of a species as an independent variable when analyzing some other trait, bypasses the important question: What factors control maximum body mass and how do these factors affect the trait of interest? We argue that the old, famous question of why weight-specific respiration decreases for increasing maximum body mass of species was difficult to explain because ecological literature typically treats body size as an independent variable. We demonstrate that Dynamic Energy Budget (DEB) theory could explain this phenomenon by treating body size as an emergent property. The question of why specific respiration decreases with increasing body size then translates to the question of why specific assimilation and/or specific maintenance would vary among species. We discuss the four parameters that control maximum body weight in the DEB theory and study how they co-vary. One of these parameters, the allocation fraction to soma, turned out to follow a beta distribution in the Add-my-Pet collection, with perplexing accuracy. We found the explanation after discovering that the supply stress, i.e. maturity maintenance times squared somatic maintenance divided by cubed assimilation, also followed a (scaled) beta distribution. The allocation fraction can be written as the ratio of somatic maintenance and assimilation for fully-grown individuals and we found that these rates turn out to follow Weibull distributions. Beta-distributions are known to result from appropriate ratios of gamma-distributed variables and we demonstrate that this also applies, to a very good approximation, for ratios of Weibull-distributed variables. We noticed similarities between Weibull distributions and allometric functions and suggest that they fit data well because many factors contribute to the underlying processes. This explains why the allocation fraction, the supply stress and some other ratios of fluxes follow beta distributions. We support our findings with empirical data.

Reserve capacity quantifies the ability of an animal to smooth out fluctuations in food availability. It is defined as the maximum reserve density, and can be quantified through the application of the Dynamic Energy Budget (DEB) theory. In this study, we analyze inter-specific patterns in DEB parameters of 1041 animal species, focusing on those that control reserve capacity (maximum specific assimilation and energy conductance) and maintenance. The co-variation rules of DEB theory expect that specific somatic maintenance and energy conductance are independent of maximum structural length, with the implication that reserve capacity is proportional to maximum structural length among species and independent of somatic maintenance. We found however that the reserve density increases with somatic maintenance among all large animal taxa in the collection: invertebrates, fish and amphibians, sauropsids and mammals. The waste-to-hurry phenomenon implies that small-bodied species frequently have both a higher specific maintenance and higher specific assimilation (with respect to larger species) allowing them to boost growth and reproduction. If waste-to-hurry strategists would increase both parameters in proportion, maximum structural length would not be affected, reserve capacity would become proportional to somatic maintenance and its relationship with maximum structural length would depend on quantitative details. We did find a positive relationship between reserve capacity and specific somatic maintenance, but the increase (as an average over all taxa) is less than proportional. The reason is that specific assimilation is less than proportional to specific somatic maintenance, the scaling parameter roughly being 0.8, while energy conductance hardly depends on somatic maintenance. The implication is that maximum assimilation is proportional to structural length to the power − 0.7, which explains why the waste-to-hurry strategy is not a viable route for big-bodied species: they would need more assimilates than small-bodied ones, not less. We discuss applications of these findings in the context of parameter estimation. As a side-result we also found that birds have a higher specific somatic maintenance and also a higher (mean) energy conductance, compared to other sauropsids at the same body temperature. The first is to be expected because they are demand species, the latter might be an adaptation to flight: reserve density increases for decreasing energy conductance, while it contributes to weight.

The effects of rearing volume on on-growing European sea bass performance and stress parameters were investigated for the first time in a pilot aquaculture farm. Fish were held under the same initial stocking densities in triplicate net-pen cages of different sizes (1.4, 45 and 252 m3) for a period of 8 months. Results showed significant differences among the experimental groups in most parameters tested, with better performance in the two larger rearing volumes. In particular, growth rate showed a linear association with rearing volume, being 0.68 g day−1 for the large cage group, 0.56 g day−1 and 0.32 g day−1 for the medium and the small groups respectively. The feed conversion ratio and per cent survival (%) were also better in the large cage group. Fish reared in the small and medium-sized cages showed higher plasma cortisol concentrations than those reared in large cages, which showed low basal cortisol concentrations. Additionally, after an acute chasing stress challenge, fish in the large and small groups, but not the medium group, showed increased cortisol concentrations. Differences also occurred in the ratio of the expression of cortisol receptors, namely the mineralocorticoid (mr) and glucocorticoid receptors (gr). In specific, the ratio of mr to grmRNA expression in the liver was higher in fish reared in the small cages. These findings verify that experimental scale significantly affects experimental results and is a critical factor for the interpretation of results.

The accurate representation of species distribution derived from sampled data is essential for management purposes and to underpin population modelling. Additionally, the prediction of species distribution for an expanded area, beyond the sampling area can reduce sampling costs. Here, several well-established and recently developed habitat modelling techniques are investigated in order to identify the most suitable approach to use with presence–absence acoustic data. The fitting efficiency of the modelling techniques are initially tested on the training dataset while their predictive capacity is evaluated using a verification set. For the comparison among models, Receiver Operating Characteristics (ROC), Kappa statistics, correlation and confusion matrices are used. Boosted Regression Trees (BRT) and Associative Neural Networks (ASNN), which are both within the machine learning category, outperformed the other modelling approaches tested.

An organism's feeding rate is governed by constraints imposed by processes associated with consumption. We present a general feeding model that incorporates encounter, successful pursuit, handling, and digestion in one functional representation where we treat digestion as a parallel process. The model produces type II functional response curves. However, the asymptotic maximum feeding rate is determined by the sum of the time spent for handling and digesting a prey minus the gain in time, since the digestion process is parallel to the handling process. We use our model in combination with existing models of encounter, successful pursuit, and digestion to evaluate the feeding rate of fish larvae. We test the model against experimental data for sea bream (Sparus aurata) larvae and find a very close quantitative correspondence between predictions and experiments. Sensitivity analysis shows that for the early developmental stages, the model is sensitive to parameters related to the visual and locomotion abilities of larvae to detect and capture the prey. Later, when they establish these abilities, the choice of accepting or not the prey becomes more important.

The effects of different tank volumes (2000, 500 and 40 l) on European sea bass Dicentrarchus labrax larval rearing, relating to growth, survival, quality and stress variables, were investigated. A dynamic energy budget (DEB) model was used to analyse the results. The hydrodynamics of the tanks exhibited differences, with the water currents in the 2000 l tanks to be almost one order of magnitude stronger than those in the 40 l ones. Important differences in fish growth were observed between small and large tank-rearing volumes, with the smallest tank resulting in the slowest growth. Based on the DEB model analysis, growth differences were related to feeding rates, with growth in the smaller tank limited by food availability. Differences in survival rates were not statistically significant among the tank-rearing volumes. The quality evaluation of the fry (in terms of swimbladder, jaw and skeletal abnormalities) showed differences, with the smallest tank having the highest percentage of deformed individuals. This could be attributed to both the feeding variances and the hydrodynamics in the tanks. No differences were observed in terms of whole-body cortisol at the two developmental stages; flexion, and when the larvae body was fully covered by melanophores; when analysis was performed. This indicates that the allostatic load exerted on fish of different groups was similar and inside the fish-coping abilities range, in terms of the cortisol response axis. The selection of the experimental scale is of importance, especially when the results are to be transferred and applied on an industrial scale.

Larval stages are considered the most critical of fish development. During a very short period of time (2 to 3 months), larvae undergo major morphoanatomical and functional changes in order to transform into juveniles while remaining functioning (developing, eating, surviving). Depending on species and environmental conditions, patterns in larval development may vary. We study the patterns of larval development for nine fish species of Perciformes reared under aquaculture conditions and compare them in terms of species-specific parameters derived from DEB theory. We extended the standard DEB model to include metabolic acceleration during the larval period, where maximum specific assimilation and energy conductance increase with length between birth and metabolic metamorphosis. Metabolic acceleration has as a consequence that larvae initially grow slower than juveniles and adults. Our results indicate that the species with higher acceleration have lower growth rates at birth and they also suggest that metabolic acceleration is related to spawning season. High metabolic acceleration of demersal species is associated with summer–autumn spawning in the Mediterranean, where temperature is high and food availability is low.

Organisms adopt different sets of physiological, behavioural and morphological trade-offs in order to cope with natural environmental fluctuations. This has consequential rebounds on ecological processes and population dynamics. Such aspects become crucial for sex-dimorphic species, where sex-specific growth variation could mirror different tactics both in energy acquisition and investment between maximum female and male body size with cascading effects on population demography. To date, different approaches have been used in order to understand the causes of individual growth rate changes in ectotherm indeterminate growers, most of which failed. Here, we propose the use of a mechanistic model based on the Dynamic Energy Budget theory (DEB; Koojiman, 2010) to investigate potential differences in energy allocation strategies adopted by individuals of different genders with the Mediterranean toothcarp Aphanius fasciatus (Valenciennes, 1821) as the model species. We collected literature and field data in order to study differences in energy allocation strategies between females and males of the same species by generating projections of possible growth performances: (1) throughout their entire life span and (2) under a context of varying functional responses. Generally, the present exercise of simulations returned different patterns of growth performance among females and males of A. fasciatus, with the former being able to better optimize energetic trade-offs under optimal environmental conditions. The present DEB parameterization exercise represents an essential step towards developing a mechanistic approach to depict metabolic strategies, which are at the base of observed sexual differences, and how such differences may impair ultimate fitness at individual and, therefore, population levels.

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.

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.