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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.

Parasitism is an energetically costly event for host species. Dynamic energy budget (DEB) theory describes the metabolic dynamics of an individual organism through its lifetime. Models derived from DEB theory specify how an organism converts food to reserves (maintenance-free energy available for metabolism) and allocates mobilized reserves to maintenance, growth (increase of structural body mass) and maturation or reproduction. DEB models thus provide a useful approach to describe the consequences of parasitism for host species. We developed a DEB model for siscowet lake trout and modeled the impact of sea lamprey parasitism on growth and reproduction using data collected from studies documenting the long-term effects following a non-lethal sea lamprey attack. The model was parameterized to reflect the changes in allocation of energy towards growth and reproduction observed in lake trout following sea lamprey parasitism and includes an estradiol module that describes the conversion of reproductive reserves to ovarian mass based on estradiol concentration. In our DEB model, parasitism increased somatic and maturity maintenance costs, reduced estradiol and decreased the estradiol-mediated conversion efficiency of reproductive reserves to ovarian mass. Muscle lipid composition of lake trout influenced energy mobilization from the reserve (efficiency of converting reserves allocated to reproduction into eggs) and reproductive efficiency. These model changes accurately reflect observed empirical changes to ovarian mass and growth. This model provides a plausible explanation of the energetic mechanisms that lead to skipped spawning following sea lamprey parasitism and could be used in population models to explore sublethal impacts of sea lamprey parasitism and other stressors on population dynamics.

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.

European sea bass is a species of great commercial value for fisheries and aquaculture. Rising temperatures may jeopardize the performance and survival of the species across its distribution and farming range, making the investigation of its thermal responses highly relevant. In this article, the metabolic scope, performance, and tolerance of juvenile E. sea bass reared under three high water temperatures (24, 28, 33°C), for a period of three months was evaluated via analysis of selected growth performance and physiological indicators. Effects on molecular, hormonal, and biochemical variables were analyzed along with effects of acclimation temperature on the metabolic rate and Critical Thermal maximum (CTmax). Despite signs of thermal stress at 28°C indicated by high plasma cortisol and lactate levels as well as the upregulation of genes coding for Heat Shock Proteins (HSP), E. sea bass can maintain high performance at that temperature which is encouraging for the species culture in the context of a warming ocean. Critical survivability thresholds appear sharply close to 33°C, where the aerobic capacity declines and the overall performance diminishes. European sea bass demonstrates appreciable capacity to cope with acute thermal stress exhibiting CTmax as high as 40°C for fish acclimated at high temperatures, which may indicate resilience to future heatwaves events.

To address challenges in management and conservation of fishes and fisheries it is essential to understand their life histories and energetics. The Add-my-Pet (AmP) collection of data on energetics and Dynamic Energy Budget (DEB) parameters currently contains 1150 of the 40000 extant species of fish. It gives 250–280 traits per species, depending on the model type that was applied, such as maximum reserve capacity, lifespan, specific respiration and precociality index, based on which the ray-finned fish (Actinopterygii) was compared with the four other fish classes (Cyclostomata, Chondrichthyes, Actinistia, Dipnoi) and the Tetrapoda. The Actinopterygii are the only vertebrate class that shows metabolic acceleration, and clearly so in only three sub-clades. Different from chondrichthyans, quite a few species follow the waste-to-hurry strategy, especially small bodied freshwater fish such as tropical annual killifish, but also in small minnows and darters in continental climates. We briefly discuss links between waste-to-hurry, which is associated with a large specific somatic maintenance, and sensitivity for pesticides. We discuss why this interferes with the physical co-variation between maximum reserve capacity and ultimate structural length or weight and explains why maximum reserve capacity increases with body length in chondrichthyans, but not in actinopterygians. Reserve capacity has relevance, e.g. mass-specific maintenance, starvation and the kinetics of lipophyllic compounds (such as pesticides), since reserve is relatively rich in lipids in fish. Also, unlike chondrichthyans, the size at birth is very small and not linked to ultimate size; we discuss the implications. Actinopterygians allocate more to soma, compared with chondrichthyans; the latter allocate more to maturity or reproduction. Actinopterygians, Actinistia and Dipnoi are near the supply-end of the supply–demand spectrum, while chondrichthyans clearly show demand properties.

Birds build up their reproductive system and undergo major tissue remodeling for each reproductive season. Energetic specifics of this process are still not completely clear, despite the increasing interest. We focused on the bobwhite quail — one of the most intensely studied species due to commercial and conservation interest — to elucidate the energy fluxes associated with reproduction, including the fate of the extra assimilates ingested prior to and during reproduction. We used the standard Dynamic Energy Budget model, which is a mechanistic process-based model capable of fully specifying and predicting the life cycle of the bobwhite quail: its growth, maturation and reproduction. We expanded the standard model with an explicit egg-laying module and formulated and tested two hypotheses for energy allocation of extra assimilates associated with reproduction: Hypothesis 1, that the energy and nutrients are used directly for egg production; and Hypothesis 2, that the energy is mostly spent fueling the increased metabolic costs incurred by building up and maintaining the reproductive system and, subsequently, by egg-laying itself. Our results suggest that Hypothesis 2 is the more likely energy pathway. Model predictions capture well the whole ontogeny of a generalized northern bobwhite quail and are able to reproduce most of the data variability via variability in (i) egg size, (ii) egg-laying rate and (iii) inter-individual physiological variability modeled via the zoom factor, i.e. assimilation potential. Reliable models with a capacity to predict physiological responses of individuals are relevant not only for experimental setups studying effects of various natural and anthropogenic pressures on the quail as a bird model organism, but also for wild quail management and conservation. The model is, with minor modifications, applicable to other species of interest, making it a most valuable tool in the emerging field of conservation physiology.

The abundance and grazing effect of small ( Synechococcus ) were assessed during April 2016 at four stations along a longitudinal transect in the ultra-oligotrophic Eastern Mediterranean Sea and at two selected depths with varying nutrient and light conditions; the 5 m depth representing surface water and the 75 m depth representing the deeper euphotic layer, targeting the Deep Chlorophyll Maximum (DCM) zone at the sampling stations. Cells of size Synechococcus consumption, respectively. On the other hand, PNF were the dominant grazers of prokaryotic picoplankton at 75 m accounting for 72–80% of the HB consumption and 60–74% of the Synechococcus consumption. HNF and PNF together consumed 4.4 ± 3.2% d −1 (mean ± sd) of the HB standing stock and 19.7 ± 16% d −1 (mean ± sd) of the Synechococcus standing stock. Moreover, a negative relationship between phosphate concentration and ingestion rates of PNF on prokaryotic picoplankton was observed. Pigment analysis showed that the major PNF groups were Prymnesiophytes followed by Pelagophytes/Chrysophytes. Prymnesiophytes was the group mostly associated with mixotrophy. Overall, our results pinpoint the role of small nanoflagellates as prokaryotic picoplankton consumers and the importance of mixotrophy as a trophic mode for PNF in the ultra-oligotrophic E. Mediterranean Sea.

Finfish aquaculture in the Mediterranean Sea faces increasing challenges due to climate change while potential adaptation requires a robust assessment of the arising threats and opportunities. This paper presents an approach developed to investigate effects of climate drivers on Greek aquaculture, a representative Mediterranean country with a leading role in the sector. Using a farm level approach, Dynamic Energy Budget models for European seabass and meagre were developed and environmental forcing was used to simulate changes in production and farm profitability under IPCC scenarios RCP45 and RCP85. The effects of temperature and extreme weather events at the individual and farm level were considered along with that of husbandry parameters such as stocking timing, market size, and farm location (inshore, offshore) for nine regions. The simulations suggest that at the individual level fish may benefit from warmer temperatures in the future in terms of growth, thus reaching commercial sizes faster, while the husbandry parameters may have as large an effect on growth as the projected shifts in climatic cues. However, this benefit will be largely offset by the adverse effects of extreme weather events at the population level. Such events will be more frequent in the future and, depending on the intensity one assigns to them, they could cause losses in biomass and farm profits that range from mild to detrimental for the industry. Overall, these results provide quantification of some of the potential threats for an important aquaculture sector while suggesting possibilities to benefit from emerging opportunities. Therefore, they could contribute to improving the sector’s readiness for tackling important challenges in the future.

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.

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 water temperature (15, 20 and 25 °C) on the stress response of European sea bass, Dicentrarchus labrax, were studied. Blood and water samples were collected prior and at 0.5, 1, 2, 4 and 8 h post-stress for hormonal and biochemical analysis. Water temperature affected the resting concentrations of all stress indicators examined, as well as their response after stress, apart from lactate which response was unaffected by temperature. Cortisol showed the response with the highest outcome at 15 °C, and the fastest at 25 °C. Cortisol release rate in the water was also faster and of higher magnitude at higher temperatures. Glucose had both the fastest and higher in magnitude response at 25 °C, while lactate responded similarly in all temperatures tested. Finally, osmolality changed only at the highest temperature. These results suggest that temperature should be taken into consideration when evaluating the resting levels of stress indicators of European sea bass in laboratory, rearing and field conditions. Additionally, the present results show that temperature affects the stress response, suggesting that fish can differ in their susceptibility to stress depending on the acclimatization temperature. Moreover, it was shown that cortisol release rate in the water, a non-invasive stress indicator, can depict the effects of temperature on cortisol stress response.

A working group at the National Institute for Mathematical and Biological Synthesis (NIMBioS) explored the feasibility of integrating 2 complementary approaches relevant to ecological risk assessment. Adverse outcome pathway (AOP) models provide "bottom-up" mechanisms to predict specific toxicological effects that could affect an individual's ability to grow, reproduce, and/or survive from a molecular initiating event. Dynamic energy budget (DEB) models offer a "top-down" approach that reverse engineers stressor effects on growth, reproduction, and/or survival into modular characterizations related to the acquisition and processing of energy resources. Thus, AOP models quantify linkages between measurable molecular, cellular, or organ-level events, but they do not offer an explicit route to integratively characterize stressor effects at higher levels of organization. While DEB models provide the inherent basis to link effects on individuals to those at the population and ecosystem levels, their use of abstract variables obscures mechanistic connections to suborganismal biology. To take advantage of both approaches, we developed a conceptual model to link DEB and AOP models by interpreting AOP key events as measures of damage-inducing processes affecting DEB variables and rates. We report on the type and structure of data that are generated for AOP models that may also be useful for DEB models. We also report on case studies under development that merge information collected for AOPs with DEB models and highlight some of the challenges. Finally, we discuss how the linkage of these 2 approaches can improve ecological risk assessment, with possibilities for progress in predicting population responses to toxicant exposures within realistic environments. Integr Environ Assess Manag 2018;14:615-624. © 2018 SETAC.

Climate change poses increasing challenges to aquaculture, resulting in the need to develop appropriate tools to assess these challenges and support decision-making. We present ClimeGreAq, a software-based Decision Support System (DSS) co-created with stakeholders to support the adaptation of Greek aquaculture to climate change. The DSS is based on an integrated modeling approach which links a biological and an economic model in order to simulate the effects of climate drivers on Greek aquaculture in a spatially heterogeneous manner. The tool may be used by stakeholders including farmers, producer organizations, regional administrations and national authorities to support decision-making on questions ranging from selecting appropriate farming locations, to designating zones for aquaculture activities, to developing national climate adaptation plans. Along with a description of the DSS design process, its structure, and the constituent models, key results are presented relating to stakeholder involvement, the user interface, and several application examples.

This article reports on the thermal tolerance, metabolic capacity and performance of juvenile meagre (Argyrosomus regius) reared under three high water temperatures (24, 29 and 34 °C) for three months. The analysis includes the thermal effects on the growth performance, metabolism and physiology of meagre, including a range of molecular, haematological, metabolic, enzymatic and hormonal indicators, as well as the effects on the proximate composition and ingestion speed. Meagre performs best between 24 and 29 °C while the temperature of 34 °C is very close to the upper end of its temperature tolerance range. At 34 °C meagre exhibits a poor growth performance and physiological status, increased blood clotting, high mortality rates and a diminished capacity for aerobic metabolism, as indicated by its low aerobic scope (129 mg kg−1 h−1). Meagre may tolerate short exposures to high temperatures after sufficient acclimation (Critical thermal maximum of 37.5 °C after acclimation to 29 °C) but its overall performance declines under prolonged exposure, suggesting that this emerging aquaculture species may be vulnerable to global warming. Our work corroborates previous findings on the thermal preferences of the species, identifies critical biological thresholds, and provides insights into the effects of prolonged exposure to high temperature regimes.

Mixotrophic nanoflagellates (MNF) play a key role in the carbon flux within aquatic ecosystems. They contribute significantly to primary production while, at the same time, they are important consumers of bacteria. MNF comprise a diverse assemblage with a whole range of photosynthetic and feeding potential and with various metabolic responses to environmental drivers, such as light, nutrients and prey availability. However, in most cases MNF are modelled as a single functional group with no reference to the distinct nutritional strategies and constraints of the different types of MNF. Here we develop a mathematical framework for the distinct functional responses of four types of MNF. Our approach is based on the Dynamic Energy Budget (DEB) theory and the concept of Synthesing Unit (SU), which is used to merge phototrophic and phagotrophic nutrition into mixotrophic growth. The resulting models describe explicitly the functional diversity of the MNF group taking into account the dynamic interaction of phototrophy and phagotrophy within the four types of MNF. Our results are in agreement with theoretical expectations and a wide range of experimental observations for the different types of MNF. Our simulations suggest that the growth dynamics of the four types of MNF are affected differently by the availability of resources. Moreover, using our models to compare the rates of organic carbon production and prey consumption by the various MNF types, we show that their net ecosystem role, as producers or consumers, depends on the mixotrophic strategy and it can vary as a function of the prevailing environmental conditions. Overall, our study highlights the importance of mechanistically modelling the distinct metabolic responses of the different types of MNF to environmental drivers in order to better understand their role in the carbon cycle in anticipation of global environmental changes.

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.

A working group at the National Institute for Mathematical and Biological Synthesis (NIMBioS) explored the feasibility of integrating 2 complementary approaches relevant to ecological risk assessment. Adverse outcome pathway (AOP) models provide "bottom-up" mechanisms to predict specific toxicological effects that could affect an individual's ability to grow, reproduce, and/or survive from a molecular initiating event. Dynamic energy budget (DEB) models offer a "top-down" approach that reverse engineers stressor effects on growth, reproduction, and/or survival into modular characterizations related to the acquisition and processing of energy resources. Thus, AOP models quantify linkages between measurable molecular, cellular, or organ-level events, but they do not offer an explicit route to integratively characterize stressor effects at higher levels of organization. While DEB models provide the inherent basis to link effects on individuals to those at the population and ecosystem levels, their use of abstract variables obscures mechanistic connections to suborganismal biology. To take advantage of both approaches, we developed a conceptual model to link DEB and AOP models by interpreting AOP key events as measures of damage-inducing processes affecting DEB variables and rates. We report on the type and structure of data that are generated for AOP models that may also be useful for DEB models. We also report on case studies under development that merge information collected for AOPs with DEB models and highlight some of the challenges. Finally, we discuss how the linkage of these 2 approaches can improve ecological risk assessment, with possibilities for progress in predicting population responses to toxicant exposures within realistic environments. Integr Environ Assess Manag 2018;14:615-624. © 2018 SETAC.

Ecological risk assessment quantifies the likelihood of undesirable impacts of stressors, primarily at high levels of biological organization. Data used to inform ecological risk assessments come primarily from tests on individual organisms or from suborganismal studies, indicating a disconnect between primary data and protection goals. We know how to relate individual responses to population dynamics using individual-based models, and there are emerging ideas on how to make connections to ecosystem services. However, there is no established methodology to connect effects seen at higher levels of biological organization with suborganismal dynamics, despite progress made in identifying Adverse Outcome Pathways (AOPs) that link molecular initiating events to ecologically relevant key events. This chapter is a product of a working group at the National Center for Mathematical and Biological Synthesis (NIMBioS) that assessed the feasibility of using dynamic energy budget (DEB) models of individual organisms as a “pivot” connecting suborganismal processes to higher level ecological processes. AOP models quantify explicit molecular, cellular or organ-level processes, but do not offer a route to linking sub-organismal damage to adverse effects on individual growth, reproduction, and survival, which can be propagated to the population level through individual-based models. DEB models describe these processes, but use abstract variables with undetermined connections to suborganismal biology. We propose linking DEB and quantitative AOP models by interpreting AOP key events as measures of damage-inducing processes in a DEB model. Here, we present a conceptual model for linking AOPs to DEB models and review existing modeling tools available for both AOP and DEB.

The standard Dynamic Energy Budget (DEB) model assumes that a fraction κ of mobilised reserve is allocated to somatic maintenance plus growth, while the rest is allocated to maturity maintenance plus maturation (in embryos and juveniles) or reproduction (in adults). All DEB parameters have been estimated for 276 animal species from most large phyla and all chordate classes. The goodness of fit is generally excellent. We compared the estimated values of κ with those that would maximise reproduction in fully grown adults with abundant food. Only 13% of these species show a reproduction rate close to the maximum possible (assuming that κ can be controlled), another 4% have κ lower than the optimal value, and 83% have κ higher than the optimal value. Strong empirical support hence exists for the conclusion that reproduction is generally not maximised. We also compared the parameters of the wild chicken with those of races selected for meat and egg production and found that the latter indeed maximise reproduction in terms of κ, while surface-specific assimilation was not affected by selection. We suggest that small values of κ relate to the down-regulation of maximum body size, and large values to the down-regulation of reproduction. We briefly discuss the ecological context for these findings.

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.

Summary 1. Dynamic energy budget (DEB) models describe how individuals acquire and utilize energy, and can serve as a link between diAerent levels of biological organization. 2. We describe the formulation and testing of DEB models, and show how the dynamics of individual organisms link to molecular processes, to population dynamics, and (more tenuously) to ecosystem dynamics. 3. DEB models oAer mechanistic explanations of body-size scaling relationships. 4. DEB models constitute powerful tools for applications in toxicology and bio

Aim To propose a new approach to the small island effect (SIE) and a simple mathematical procedure for the estimation of its upper limit. The main feature of the SIE is that below an upper size threshold an increase of species number with increase of area in small islands is not observed. Location Species richness patterns from different taxa and insular systems are analysed. Methods Sixteen different data sets from 12 studies are analysed. Path analysis was used for the estimation of the upper limit of the SIE. We studied each data set in order to detect whether there was a certain island size under which the direct effects of area were eliminated. This detection was carried out through the sequential exclusion of islands from the largest to the smallest. For the cases where an SIE was detected, a log-log plot of species number against area is presented. The relationships between habitat diversity, species number and area are studied within the limits of the SIE. In previous studies only area was used for the detection of the SIE, whereas we also encompass habitat diversity, a parameter with well documented influence on species richness, especially at small scales. Results An SIE was detected in six out of the 16 studied cases. The upper limit of the SIE varies, depending on the characteristics of the taxon and the archipelago under study. In general, the values of the upper limit of the SIE calculated according to the approach undertaken in our study differ from the values calculated in previous studies. Main conclusions Although the classical species–area models have been used to estimate the upper limit of the SIE, we propose that the detection of this phenomenon should be undertaken independently from the species–area relationship, so that the net effects of area are calculated excluding the surrogate action of area on other variables, such as environmental heterogeneity. The SIE appears when and where area ceases to influence species richness directly. There are two distinct SIE patterns: (1) the classical SIE where both the direct and indirect effects of area are eliminated and (2) the cryptic SIE where area affects species richness indirectly. Our approach offers the opportunity of studying the different factors influencing biodiversity on small scales more accurately. The SIE cannot be considered a general pattern with fixed behaviour that can be described by the same model for different island groups and taxa. The SIE should be recognized as a genuine but idiosyncratic phenomenon.

Aim To test the performance of the choros model in an archipelago using two measures of environmental heterogeneity. The choros model is a simple, easy-to-use mathematical relationship which approaches species richness as a combined function of area and environmental heterogeneity. Location The archipelago of Skyros in the central Aegean Sea (Greece). Methods We surveyed land snails on 12 islands of the archipelago. We informed the choros model with habitat data based on natural history information from the land snail species assemblage. We contrast this with habitat information taken from traditional vegetation classification to study the behaviour of choros with different measures of environmental heterogeneity. R2 values and Akaike's information criterion (AIC) were used to compare the choros model and the Arrhenius species–area model. Path analysis was used to evaluate the variance in species richness explained by area and habitat diversity. Results Forty-two land snail species were recorded, living in 33 different habitat types. The choros model with habitat types had more explanatory power than the classic species–area model and the choros model using vegetation types. This was true for all islands of the archipelago, as well as for the small islands alone. Combined effects of area and habitat diversity primarily explain species richness in the archipelago, but there is a decline when only small islands are considered. The effects of area are very low both for all the islands of the archipelago, and for the small islands alone. The variance explained by habitat diversity is low for the island group as a whole, but significantly increases for the small islands. Main conclusions The choros model is effective in describing species-richness patterns of land snails in the Skyros Archipelago, incorporating ecologically relevant information on habitat occupancy and area. The choros model is more effective in explaining richness patterns on small islands. When using traditional vegetation types, the choros model performs worse than the classic species–area relationship, indicating that use of proxies for habitat diversity may be problematic. The slopes for choros and Arrhenius models both assert that, for land snails, the Skyros Archipelago is a portion of a larger biogeographical province. The choros model, informed by ecologically relevant habitat measures, in conjunction with path analysis points to the importance of habitat diversity in island species richness.

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.

Aim To propose a model (the choros model) for species diversity, which embodies number of species, area and habitat diversity and mathematically unifies area per se and habitat hypotheses. Location Species richness patterns from a broad scale of insular biotas, both from island and mainland ecosystems are analysed. Methods Twenty-two different data sets from seventeen studies were examined in this work. The r2 values and the Akaike's Information Criterion (AIC) were used in order to compare the quality of fit of the choros model with the Arrhenius species–area model. The classic method of log-log transformation was applied. Results In twenty of the twenty-two cases studied, the proposed model gave a better fit than the classic species–area model. The values of z parameter derived from choros model are generally lower than those derived from the classic species–area equation. Main conclusions The choros model can express the effects of area and habitat diversity on species richness, unifying area per se and the habitat hypothesis, which as many authors have noticed are not mutually exclusive but mutually supplementary. The use of habitat diversity depends on the specific determination of the ‘habitat’ term, which has to be defined based on the natural history of the taxon studied. Although the values of the z parameter are reduced, they maintain their biological significance as described by many authors in the last decades. The proposed model can also be considered as a stepping-stone in our understanding of the small island effect.

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.

We formulate a Dynamic Energy Budget (DEB) model for the growth and reproduction of individual organisms based on partitioning of net production (i.e. energy acquisition rate minus maintenance rate) between growth and energy reserves. Reproduction uses energy from reserves. The model describes both feeding and non-feeding stages, and hence is applicable to embryos (which neither feed nor reproduce), juveniles (which feed but do not reproduce), and adults (which commonly both feed and reproduce). Embryonic growth can have two forms depending on the assumptions for acquisition of energy from yolk. By default, when the energy acquisition rate exceeds the maintenance rate, a fixed proportion of the resulting net production is spent on growth (increase in structural biomass), and the remaining portion is channelled to the reserves. Feeding organisms, however, modulate their allocation of net production energy in response to their total energy content (energy in the reserves plus energy bounded to structural biomass). In variable food environment an organism alternates between periods of growth, no-growth, and balanced-growth. In the latter case the organism adopts an allocation strategy that keeps its total energy constant. Under constant environmental conditions. the growth of a juvenile is always of von Bertalanffy type. Depending on the values of model parameters there are two long-time possibilities for adults: (a) von Bertalanffy growth accompanied by reproduction at a rate that approaches zero as the organism approaches asymptotic size, or (b) abrupt cessation of growth at some finite time, following which, the rate of reproduction is constant. We illustrate the model's applicability in life history theory by studying the optimum values of the energy allocation parameters for constant environment and for each of the dynamic regimes described above.

We establish the existence of traveling wave solutions for a nonlinear partial differential equation that models a logistically growing population whose movement is governed by an advective process. Conditions are presented for which traveling wave solutions exist and for which they are stable to small semi-finite domain perturbations. The wave is of mathematical interest because its behavior is determined by a singular differential equation and those with small speed of propagation steepen into a shock-like solutions. Finally, we indicate that the smoothing presence of diffusion allows wave persistence when an advective slow moving wave may collapse.

The relationships between the dynamics of environmentally and chemically stressed populations and indicators of the effects of the stressor are explored in a model framework. The physiologically structured population, represented by a system of McKendrick–von Foerster hyperbolic partial differential equations, includes the dynamics of numerous individuals distinguished by ecotype. Chemical uptake of nonpolar narcotics is modeled by first order kinetics. Classical methodologies, frequency analysis and phase space reconstruction, are explored in a search for indicators of magnitude of stress. When these techniques proved generally unsuccessful for the objective of indicator selection in our model setting, summary statistics, as related to bifurcation diagrams, were constructed and appear more useful as indicators. It is concluded that physiological structures generally lead to more feasible measurable indicators of magnitude of stress than do specifics of population dynamics.

The standard Dynamic Energy Budget (DEB) model assumes that a fraction κ of mobilised reserve is allocated to somatic maintenance plus growth, while the rest is allocated to maturity maintenance plus maturation (in embryos and juveniles) or reproduction (in adults). All DEB parameters have been estimated for 276 animal species from most large phyla and all chordate classes. The goodness of fit is generally excellent. We compared the estimated values of κ with those that would maximise reproduction in fully grown adults with abundant food. Only 13% of these species show a reproduction rate close to the maximum possible (assuming that κ can be controlled), another 4% have κ lower than the optimal value, and 83% have κ higher than the optimal value. Strong empirical support hence exists for the conclusion that reproduction is generally not maximised. We also compared the parameters of the wild chicken with those of races selected for meat and egg production and found that the latter indeed maximise reproduction in terms of κ, while surface-specific assimilation was not affected by selection. We suggest that small values of κ relate to the down-regulation of maximum body size, and large values to the down-regulation of reproduction. We briefly discuss the ecological context for these findings.

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.

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.