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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 collection of data on energetics and Dynamic Energy Budget parameters currently contains 92 species of turtles and 23 species of crocodiles. We discuss patterns of eco-physiological traits of turtles and crocodiles, as functions of parameter values, and compare them with other taxa. Turtles and crocodiles accurately match the general rule that the life-time cumulated neonate mass production equals ultimate weight. The weight at birth for reptiles scales with ultimate weight to the power 0.6. The scaling exponent is between that of amphibians and birds, while that for mammals is close to 1. We explain why this points to limitations imposed by embryonic respiration, the role of water stress and the accumulation of nitrogen waste during the embryo stage. Weight at puberty is proportional to ultimate weight, and is the largest for crocodiles, followed by that of turtles. These facts explain why the precociality coefficient, (Formula presented.) —approximated by the ratio of weight at birth and weight at puberty at abundant food—decreases with ultimate weight. It is the smallest for crocodiles because of their large size and is smaller for turtles than for lizards and snakes. The sea turtles have a smaller (Formula presented.) than the rest of the turtles, linked to their large size and small offspring size. We link their small weight and age at birth to reducing risks on the beach. The maximum reserve capacity in both turtles and crocodiles clearly decreases with the precociality coefficient. This relationship has not been found that clearly in other taxa, not even in other reptiles, with the exception of the chondrichthyans. Among reptiles, crocodiles and sea turtles have a relatively large assimilation rate and a large reserve capacity.

Dynamic energy budget (DEB) theory provides a generalised way to quantify how an organism assimilates and utilizes energy throughout its life cycle. Over 800 DEB models have been created to date, typically under the assumption of constant food supply. The Critically Endangered, semi-aquatic western swamp turtle occupies an ephemeral wetland environment in which food resources fluctuate from abundant to absent with the seasonal filling and drying of swamps. Approximately six months of each year are spent in aestivation underground when the swamps are dry and conditions are warm. We estimated DEB parameters for the western swamp turtle with the explicit incorporation of these seasonal fluctuations in food and temperature. A metabolic depression factor was applied during the aestivation stage, without which turtles lost both mass and length, and reserves were insufficient to reach puberty. The swamp turtle had a very high Arrhenius temperature, being almost 2.5-fold greater than that of the other Testudine species for which there are DEB models (typical Arrhenius temperatures are around 8000 K; western swamp turtle is 19,371 K). It also had the second highest somatic maintenance costs of the reptiles in the DEB ‘Add My Pet’ collection, and the highest for Testudines. We explore these results in context of the “waste to hurry” hypothesis, which we suggest may apply for this species. We also consider how a DEB model for this species might be applied in its future conservation and management.

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 method of multidimensional scaling (MDS) has long existed, but could only recently be applied to animal traits in the context of dynamic energy budget (DEB) theory. The application became possible because of the following: (i) the Add-my-Pet (AmP) collection of DEB parameters and traits (approximately 280) recently reached 3000 animal species with 45000 data sets of measurements; (ii) we found a natural distance measure for species based on their traits as a side result of our research on parameter estimation in DEB context; and (iii) we developed plotting code for visualization that allows labelling of taxonomic relationships. Traits, here defined as DEB parameters or any function of these parameters, have different dimensions, which hamper application of many popular distance measures since they (implicitly) assume that all traits have the same dimensions. The AmP collection follows the workflow that measured data determine parameters and parameters determine trait values. In this way we could fill up the species traits table completely, which we could not do by using measured values only, as data availability varies considerably between species and is typically poor. The goodness of fit of predictions for all data sets is generally excellent. This paper discusses links between the MDS method and parameter estimation and illustrates the application of MDS for the AmP collection to five taxa, three ectothermic and two endothermic, which we consider to be ‘complete’, in the sense that we expect that it will be difficult to find more species with data in the open literature. This application of MDS shows links between traits and taxonomy that supplements our efforts to find patterns in the co-variation of parameter values. Knowledge about metabolic performance is key to conservation biology, sustainable management and environmental risk assessment, which are seen as interlinked fields.

Quantifying sublethal effects of plastics ingestion on marine wildlife is difficult, but key to understanding the ontogeny and population dynamics of affected species. We developed a method that overcomes the difficulties by modelling individual ontogeny under reduced energy intake and expenditure caused by debris ingestion. The predicted ontogeny is combined with a population dynamics model to identify ecological breakpoints: cessation of reproduction or negative population growth. Exemplifying this approach on loggerhead turtles, we find that between 3% and 25% of plastics in digestive contents causes a 2.5–20% reduction in perceived food abundance and total available energy, resulting in a 10–15% lower condition index and 10% to 88% lower total seasonal reproductive output compared to unaffected turtles. The reported plastics ingestion is insufficient to impede sexual maturation, but population declines are possible. The method is readily applicable to other species impacted by debris ingestion.

Population growth, and other population characteristics, have been computed and made available online for over 2000 animal species in the Add-my-Pet (AmP) collection, assuming constant food and temperature environments. The AmP collection – online database of Dynamic Energy Budget model parameters, implied properties and referenced underlying data – provides an unique opportunity to study how energetics of individuals relates to population growth. For the comparisons of traits, we assume that the background hazard rate is zero, but aging applies to all species and ‘thinning’ to species with high reproduction rates. The new concept ‘thinning’ is a state-dependent hazard rate such that the feeding rate of a cohort does not change in time: the increase of individual feeding rates due to growth is exactly compensated by a reduction in numbers. Thinning affects population growth rate, but the impact differs substantially between species. Some 11% of species do not survive thinning, even at abundant food. The population growth rate relates to the underlying energetics; we discuss and suggest explanations for how population growth rates fit into all known patterns in the co-variation of parameter values: body size-scaling, metabolic acceleration, waste-to-hurry, supply-demand spectrum and altricial-precocial spectrum. We show that, after reproduction, age at puberty dominates population growth. The specific population growth rate scales with maximum body weight in the same way as the weight-specific respiration scales with body weight. DEB theory, which explains both, shows, however, that no direct relationship exists between the population growth rate and respiration. We suggest that the similarity in scaling results from the equality between specific population growth and specific growth rate at maximum growth of structure, and might be an evolutionary relict from times that life consisted of dividing unicellulars; population and body growth are directly connected for unicellulars. We show that the specific growth rate at maximum growth equals 1.5 times the von Bertalanffy growth rate, in a DEB context, which is a new interpretation of the latter growth rate. We expected the population growth rate to co-vary with specific somatic maintenance rate, based on a previously discovered pattern, called the waste-to-hurry strategy, where growth and reproduction are increased by simultaneously increasing assimilation and somatic maintenance in species that live off temporarily abundant food supplies. We did find this effect in ecdysozoa and spiralia, which comprise roughly 95% of animal species, but hardly so in tetrapods. The reason might be that specific somatic maintenance also co-varies with specific maturity levels at puberty for tetrapods. The scaled functional response at which the population growth rate is zero is very close to that at which puberty can just be reached in absence of thinning, and somewhat higher in presence of thinning. The specific population growth rate at abundant food correlates negatively with the functional response for which population growth rate is zero. It also correlates negatively with the precociality index, i.e. the ratio of maturity levels at puberty and birth: the more precocial, the larger neonate size, the smaller reproduction rate, especially in restricted taxa such as mammals and cartilaginous fish. Like other traits, the population growth rate shows considerable segregation among taxa, where mammals have a relatively low rate, glires a relatively high rate among mammals, followed by marsupials; afrotherians have the lowest population growth rates.

International audience; We study a predator-prey model with different characteristic time scales for the prey and predator populations, assuming that the predator dynamics is much slower than the prey one. Geometrical Singular Perturbation theory provides the mathematical framework for analyzing the dynamical properties of the model. This model exhibits a Hopf bifurcation and we prove that when this bifurcation occurs, a canard phenomenon arises. We provide an analytic expression to get an approximation of the bifurcation parameter value for which a maximal canard solution occurs. The model is the well-known Rosenzweig-MacArthur predator-prey differential system. An invariant manifold with a stable and an unstable branches occurs and a geometrical approach is used to explicitly determine a solution at the intersection of these branches. The method used to perform this analysis is based on Blow-up techniques. The analysis of the vector field on the blown-up object at an equilibrium point where a Hopf bifurcation occurs with zero perturbation parameter representing the time scales ratio, allows to prove the result. Numerical simulations illustrate the result and allow to see the canard explosion phenomenon.

The pervasive influence of human induced global environmental change affects biodiversity across the globe, and there is great uncertainty as to how the biosphere will react on short and longer time scales. To adapt to what the future holds and to manage the impacts of global change, scientists need to predict theexpected effects with some confidence and communicate these predictions to policy makers. However, recent reviews found that we currently lack a clear understanding of how predictable ecology is, with views seeing it as mostly unpredictable to potentially predictable, at least over short time frames. However, in applied, ecology-related fields predictions are more commonly formulated and reported, as well as evaluated in hindsight, potentially allowing one to define baselines of predictive proficiency in these fields. We searched the literature for representative case studies in these fields and collectedinformation about modeling approaches, target variables of prediction, predictive proficiency achieved, as well as the availability of data to parameterize predictive models. We find that some fields such as epidemiology achieve high predictive proficiency, but even in the more predictive fields proficiency isevaluated in different ways. Both phenomenological and mechanistic approaches are used in most fields, but differences are often small, with no clear superiority of one approach over the other. Data availability is limiting in most fields, with long-term studies being rare and detailed data for parameterizing mechanistic models being in short supply. We suggest that ecologists adopt a more rigorous approach to report and assess predictive proficiency, and embrace the challenges of real world decision making to strengthen the practice of prediction in ecology.

Understanding the relationship between the environmental conditions and life-history traits (such as growth, reproduction, and size at specific life stages) is important for understanding the population dynamics of a species and for constructing adaptable, relevant, and efficient conservation measures. For the endangered loggerhead turtle, characterizing effects of environmental conditions on the life-history traits is complicated by this species’ longevity, global distribution, and migratory way of life. Two significant environmental factors – temperature and available food – often account for most of observed intra-population variability in growth and reproduction rates, suggesting that those two factors determine the biological responses of an individual. Adopting this hypothesis, we simulate a range of the two environmental factors to quantify effects of changes in temperature and food availability on an individual's physiology (energy investment into processes such as growth, maturation, and reproduction) and the resulting life-history traits. To represent an individual, we use a previously developed mechanistic dynamic energy budget (DEB) model for loggerhead turtles. DEB models rely on one of the empirically best validated general ecological theories, which captures rules of energy acquisition and utilization. We found that the ultimate size (length and mass) is primarily affected by food availability, whereas growth and maturation are primarily affected by temperature whilst also showing positive correlation with available food. Reproduction increases with both food availability and temperature because food availability determines energy investment into egg production, and temperature affects the rate of related processes (such as vitellogenesis). Length at puberty varies between simulated scenarios by only a small proportion, suggesting that inter-individual variability plays a larger role for length at puberty than the environmental factors do.

Loggerhead turtle is an endangered sea turtle species with a migratory lifestyle and worldwide distribution, experiencing markedly different habitats throughout its lifetime. Environmental conditions, especially food availability and temperature, constrain the acquisition and the use of available energy, thus affecting physiological processes such as growth, maturation, and reproduction. These physiological processes at the population level determine survival, fecundity, and ultimately the population growth rate—a key indicator of the success of conservation efforts. As a first step towards the comprehensive understanding of how environment shapes the physiology and the life cycle of a loggerhead turtle, we constructed a full life cycle model based on the principles of energy acquisition and utilization embedded in the Dynamic Energy Budget (DEB) theory. We adapted the standard DEB model using data from published and unpublished sources to obtain parameter estimates and model predictions that could be compared with data. The outcome was a successful mathematical description of ontogeny and life history traits of the loggerhead turtle. Some deviations between the model and the data existed (such as an earlier age at sexual maturity and faster growth of the post-hatchlings), yet probable causes for these deviations were found informative and discussed in great detail. Physiological traits such as the capacity to withstand starvation, trade-offs between reproduction and growth, and changes in the energy budget throughout the ontogeny were inferred from the model. The results offer new insights into physiology and ecology of loggerhead turtle with the potential to lead to novel approaches in conservation of this endangered species.

A predator-prey system is analysed where the transmissible disease can spread into the prey population. This will lead to a three-dimensional ecoepidemic model described by the temporal change of the healthy and diseased prey and the predator populations. The predator-prey interaction is modelled using the square root functional response such that the prey experience group defence: only the healthy individuals at the edge of the herd are consumed while the infected drift behind the herd. The predator feeds on both healthy and diseased prey individuals. The two prey populations are assumed substitutable so that a deficiency in one of the prey populations can be compensated by consuming the other. The resulting model for the trophic interaction is an extension of the classical Holling type II functional response for one prey population. Bifurcation analysis gives long-term dynamics of the boundary and interior equilibria, limit cycles and heteroclinic connections to saddle equilibria. The main goal is to gain insight into the effects of simultaneous predator feeding of both healthy and diseased individuals on the dynamics of the predator-prey system. With simultaneous feeding the feasibility of the system becomes smaller.

Plato’s well-known allegory of the cave describes an observerchained in a cave facing a blank wall on which shadows are projected ofobjects that are outside the cave. Only by breaking free from the chainscan the observer submerge from the cave to see what the objects reallylook like. Ecological model features compare to the objects outsidethe cave in this allegory. By performing model analysis light is shedon these features, creating projections that researchers can see. Modelanalysis methodologies like bifurcation analysis and sensitivity analysiseach focus on particular model features and thus allow researchers touncover only part of the model behaviour. By combining methodologiesfor model analysis possibilities arise for unravelling more of the model’sbehaviour, allowing researchers to ‘break free’. In this paper benefitsand issues of combining model analysis methodologies are discussedusing a case study. The case study involves three representations ofthe well-known Rosenzweig-MacArthur predator-prey model, namelythe usual one where state variables and parameters have dimensions, adimensionless representation, and a generalized representation. Basedon the results we argue that researchers should combine bifurcation andsensitivity analysis methodologies when analyzing ecological models.

The present paper describes a process oriented modelling tool that integrates physical, biogeochemical, ecological and physiological factors governing bivalve populated marine ecosystems. This modelling tool is the result of the coupling between an individual-based population model for bivalves (based on the Dynamic Energy Budgets theory, DEB) and a hydrodynamic/biogeochemical model (MOHID Water Modelling System). The model was implemented in the Balgzand area (Wadden Sea, The Netherlands) in a fine resolution domain to study mussel population dynamics and to quantify the influence of mussel communities on the pelagic system. Model results for a reference scenario (2009/2010) are in agreement with observations, and provide a consistent quantitative description of local hydrodynamics and biogeochemical cycles. The Balgzand acts as a sink of phytoplankton due to bivalves’ filtration, and a source of ammonia, exporting about 40% more than the input flux. These results suggest significant ammonia regeneration. Results show that despite the long and almost continuous spawning season, only a few cohorts are able to survive. Early stage mortality (top-down), in particular cannibalism and shrimp predation, can control the persistence of new cohorts in the first month although starvation (bottom-up) represents the main cause of biomass loss in an overall. The tendency is that new mussel beds are formed in areas adjacent to already existing mussel beds and channel edges. Bivalves’ activity intensifies the seasonal patterns of food and nutrients in areas close to the mussel beds, though not changing their overall spatial distribution. This study not only confirms but also quantifies mussels’ potential to influence ecosystem functioning due to their role in nutrient cycling. As the first integrated modelling study that focus on the mussels’ beds in the Balgzand, the main difficulties on the model design, setup and results analysis were overcome. The model can now be used further, tested and improved in the same or other systems in order to serve as an effective and reliable scientific and management tool.

An issue in mathematical modeling is that multiple models describe the same data based on different but all acceptable theoretical assumptions. To take this uncertainty in model construction into account, the classical parameter sensitivity analysis needs to be extended to consider alternative choices in model formulation. This is particularly important in population biology, where a single function often summarizes mechanisms from the physiological to the population level. Predictions based on population models were recently shown to be sometimes highly sensitive to the function that models predation. This so-called structural sensitivity extends the classical structural stability. It arises from differences between the bifurcation diagrams based on alternative model formulations. Here, we ask through an example of a predator-prey system that exhibits complex bifurcations (involving limit cycles and homoclinic orbits) how the qualitative changes in bifurcations occur during a small continuous switch between two acceptable model formulations. In this model, fixed parameter values are estimated from empirical data, free parameters allow one to explore a wide range of environmental conditions and species, and a remaining parameter makes a switch between two predation formulations. Thus, the change in model formulation becomes a parameter sensitivity problem that is studied by bifurcation analysis. A three-dimensional analysis revealed that most changes that occur with the change in formulation are related to a codimension-three degenerated Bogdanov-Takens bifurcation. Its canonical unfolding is derived, and its analysis highlights the differences in the phase portraits predicted with the two model formulations. Differences that are not related to this bifurcation are also discussed. The discussion ends with some perspectives toward the quantification of prediction uncertainty due to uncertainty in model structure in ecology, and possibly in other fields involving the modeling of complex systems.

The motivation for the research reported in this paper comes from modeling the spread of vector-borne virus diseases. To study the role of the host versus vector dynamics and their interaction we use the susceptible-infected-removed (SIR) host model and the susceptible-infected (SI) vector model. When the vector dynamical processes occur at a faster scale than those in the host-epidemics dynamics, we can use a time-scale argument to reduce the dimension of the model. This is often implemented as a quasi steady-state assumption (qssa) where the slow varying variable is set at equilibrium and an ode equation is replaced by an algebraic equation. Singular perturbation theory will appear to be a useful tool to perform this derivation. An asymptotic expansion in the small parameter that represents the ratio of the two time scales for the dynamics of the host and vector is obtained using an invariant manifold equation. In the case of a susceptible-infected-susceptible (SIS) host model this algebraic equation is a hyperbolic relationship modeling a saturated incidence rate. This is similar to the Holling type II functional response (Ecology) and the Michaelis-Menten kinetics (Biochemistry). We calculate the value for the force of infection leading to an endemic situation by performing a bifurcation analysis. The effect of seasonality is studied where the force of infection changes sinusoidally to model the annual fluctuations of the vector population. The resulting non-autonomous system is studied in the same way as the autonomous system using bifurcation analysis.

Population of loggerhead turtles nesting in the Mediterranean Sea has probably evolved from the North Atlantic (NA) population, but is geographically and genetically distinct. We aggregated previously published and new unpublished data, and took two approaches to comparing these populations: an empirical one based on statistical analyses of morphological data, and a physiological one based on a Dynamic Energy Budget (DEB) model. We then analyzed causes of faster growth and maturation, but smaller size at puberty and ultimate size of the Mediterranean (MED) loggerhead turtles relative to their NA conspecifics. The empirical analysis shows that MED eggs, hatchlings, and nesting adults are consistently smaller in terms of length and mass. The physiological approach suggests physiological adaptations of the MED population to higher salinity and scarcer food availability. In particular, these adaptations include an increase in somatic maintenance needs, and a decrease in energy investment to reach and maintain sexual maturity. Our study therefore offers a mechanistic underpinning of previously observed but unexplained life-history traits, and showcases an application of DEB theory as a tool for comparative analysis of two distinct populations of the same species.

This editorial gives a general introduction to Dynamic Energy Budget (DEB) theory, a short description of the state of the art, an introduction to the various contributions to this 6th special issue on DEB research and a short outlook.

Simulation models are commonly used to understand and predict the developmentof ecological systems, for instance to study the occurrence of tipping points and their possibleecological effects. Sensitivity analysis is a key tool in the study of model responses to change s in conditions. The applicability of available methodologies for sensitivity analysis can be problematic if tipping points are involved. In this paper we demonstrate that not considering these tipping points may result in misleading statistics on model behaviour. In turn, this limits the applicability of simulation models in ecological research. Tipping points are bestrevealed when asymptotic model behaviour is considered, i.e. by applying bifurcation analysis. Bifurcation analysis, however, is limited to deterministic dynamic models, whereas many ecological simulation models are nondeterministic and can only be analysed using sensitivity analysis methodologies. In this paper we explore the possibilities for applying methodologies of sensitivity analysis to analyse models with tipping points. The Bazykin-Berezovskaya model, a deterministic ecological model of which the structure regarding tipping points is known a priori, is used as case study. We conclude that important clues about the occurrence of tippings points can be revealed from different sensitivity analysis methodologies, if proper statistical and graphical measures are used. The results raise awareness about how tipping points affect temporal model responses in ecological simulation models, and may also be more generally applicable for nondeterministic models that cannot be analysed using bifurcation analysis.

In this paper we analyse a predator–prey model where the prey population shows group defense and the prey individuals are affected by a transmissible disease. The resulting model is of the Rosenzweig–MacArthur predator–prey type with an SI (susceptible-infected) disease in the prey. Modeling prey group defense leads to a square root dependence in the Holling type II functional for the predator–prey interaction term. The system dynamics is investigated using simulations, classical existence and asymptotic stability analysis and numerical bifurcation analysis. A number of bifurcations, such as transcritical and Hopf bifurcations which occur commonly in predator–prey systems will be found. Because of the square root interaction term there is non-uniqueness of the solution and a singularity where the prey population goes extinct in a finite time. This results in a collapse initiated by extinction of the healthy or susceptible prey and thereafter the other population(s). When also a positive attractor exists this leads to bistability similar to what is found in predator–prey models with a strong Allee effect. For the two-dimensional disease-free (i.e. the purely demographic) system the region in the parameter space where bistability occurs is marked by a global bifurcation. At this bifurcation a heteroclinic connection exists between saddle prey-only equilibrium points where a stable limit cycle together with its basin of attraction, are destructed. In a companion paper (Gimmelli et al., 2015) the same model was formulated and analysed in which the disease was not in the prey but in the predator. There we also observed this phenomenon. Here we extend its analysis using a phase portrait analysis. For the three-dimensional ecoepidemic predator–prey system where the prey is affected by the disease, also tangent bifurcations including a cusp bifurcation and a torus bifurcation of limit cycles occur. This leads to new complex dynamics. Continuation by varying one parameter of the emerging quasi-periodic dynamics from a torus bifurcation can lead to its destruction by a collision with a saddle-cycle. Under other conditions the quasi-periodic dynamics changes gradually in a trajectory that lands on a boundary point where the prey go extinct in finite time after which a total collapse of the three-dimensional system occurs.

The conversion efficiency of prey biomass into predator biomass (or plant-biomass into herbivore-biomass) at the individual level is not constant. Measured by the yield factor, this conversion appears to depend on size, energy reserves, and a few species-specific compound parameters involving a variety of elements from the dynamic energy budget. This efficiency is studied here on the basts of a continuous time model for the energy budget of an individual organism. At the population level, the conversion of prey into predator biomass depends on harvesting processes. Included in harvesting is death by aging. In the absence of harvested individuals from a population of predators, a constant supply rate of prey results in a predator population of constant size. At equilibrium, this gives a conversion efficiency of zero. When the predator population is harvested, the conversion efficiency increases up to a maximum and then decreases to a threshold level, above which the population goes extinct. A practical implication is that it is possible that populations with substantial standing crops cannot stand sustained increased harvesting. For a well tested model for energy budgets of individuals, the conversion efficiency of prey biomass into predator biomass has been compared for two modes of prey selection by the predator: random predation and fixed age predation. Both strategies gave almost identical biomass conversion efficiencies. Propagation through eggs has been found to be a bit less efficient that propagation through binary fission. The way the efficiency depends on parameters of the individual energy budget is an important link between ecology and physiology, a fact which is highly relevant to areas of applied ecology, such as eco toxicology. The study of this relation is complicated by population oscillations induced by the harvesting process, but computer simulations show that an analysis of the conversion efficiency on the basis of stable age distributions is still valid.

We developed new methods for parameter estimation-in-context and, with the help of 125 authors, built the AmP (Add-my-Pet) database of Dynamic Energy Budget (DEB) models, parameters and referenced underlying data for animals, where each species constitutes one database entry. The combination of DEB parameters covers all aspects of energetics throughout the full organism’s life cycle, from the start of embryo development to death by aging. The species-specific parameter values capture biodiversity and can now, for the first time, be compared between animals species. An important insight brought by the AmP project is the classification of animal energetics according to a family of related DEB models that is structured on the basis of the mode of metabolic acceleration, which links up with the development of larval stages. We discuss the evolution of metabolism in this context, among animals in general, and ray-finned fish, mollusks and crustaceans in particular. New DEBtool code for estimating DEB parameters from data has been written. AmPtool code for analyzing patterns in parameter values has also been created. A new web-interface supports multiple ways to visualize data, parameters, and implied properties from the entire collection as well as on an entry by entry basis. The DEB models proved to fit data well, the median relative error is only 0.07, for the 1035 animal species at 2018/03/12, including some extinct ones, from all large phyla and all chordate orders, spanning a range of body masses of 16 orders of magnitude. This study is a first step to include evolutionary aspects into parameter estimation, allowing to infer properties of species for which very little is known., Author summary We discovered that parameters of Dynamic Energy Budget (DEB) models can be estimated from a set of simple data on animal life history aspects, growth and reproduction, if treated in combination. Apart from goodness-of-fit as an estimation criterion, relations with parameter values of other species are important, since DEB parameters have a clear physiological interpretation and a good fit for the wrong reasons is always a risk to consider. We developed and optimized methods for this type of parameter estimation-in-context and organized the results of over 1000 animal species in the open-access Add-my-Pet (AmP) database, to which 125 authors contributed so far. We also developed software package AmPtool to compare parameter values in the collection, that builds on DEBtool to assist applications of DEB theory. A family of related DEB models, structured with respect to the modes of metabolic acceleration, captures biodiversity, including various life stages. We discuss some features of the family structure of DEB models in an evolutionary context. The AmP collection has a great potential for research on the role of biodiversity in ecosystem structure and functioning, which will grow with the size of the database.

International audience; Many current issues in ecology require predictions made by mathematical models, which are built on somewhat arbitrary choices. Their consequences are quantified by sensitivity analysis to quantify how changes in model parameters propagate into an uncertainty in model predictions. An extension called structural sensitivity analysis deals with changes in the mathematical description of complex processes like predation. Such processes are described at the population scale by a specific mathematical function taken among similar ones, a choice that can strongly drive model predictions. However, it has only been studied in simple theoretical models. Here, we ask whether structural sensitivity is a problem of oversimplified models. We found in predator-prey models describing chemostat experiments that these models are less structurally sensitive to the choice of a specific functional response if they include mass balance resource dynamics and individual maintenance. Neglecting these processes in an ecological model (for instance by using the well-known logistic growth equation) is not only an inappropriate description of the ecological system, but also a source of more uncertain predictions.

International audience; Two predator-prey model formulations are studied: for the classical Rosenzweig-MacArthur (RM) model and the Mass Balance (MB) chemostat model. When the growth and loss rate of the predator is much smaller than that of the prey these models are slow-fast systems leading mathematically to singular perturbation problem. In contradiction to the RM-model, the resource for the prey are modelled explicitly in the MB-model but this comes with additional parameters. These parameter values are chosen such that the two models become easy to compare. In both models a transcritical bifurcation, a threshold above which invasion of predator into prey-only system occurs, and the Hopf bifurcation where the interior equilibrium becomes unstable leading to a stable limit cycle. The fast-slow limit cycles are called relaxation oscillations which for increasing differences in time scales leads to the well known degenerated trajectories being concatenations of slow parts of the trajectory and fast parts of the trajectory. In the fast-slow version of the RM-model a canard explosion of the stable limit cycles occurs in the oscillatory region of the parameter space. To our knowledge this type of dynamics has not been observed for the RM-model and not even for more complex ecosystem models. When a bifurcation parameter crosses the Hopf bifurcation point the amplitude of the emerging stable limit cycles increases. However, depending of the perturbation parameter the shape of this limit cycle changes abruptly from one consisting of two concatenated slow and fast episodes with small amplitude of the limit cycle, to a shape with large amplitude of which the shape is similar to the relaxation oscillation, the well known degenerated phase trajectories consisting of four episodes (concatenation of two slow and two fast). The canard explosion point is accurately predicted by using an extended asymptotic expansion technique in the perturbation and bifurcation parameter simultaneously where the small amplitude stable limit cycles exist. The predicted dynamics of the MB-model is in a large part of the parameter space similar to that of the RM-model. However, the fast-slow version of MB-model does not predict a canard explosion phenomenon.

At the Mid-Pleistocene Transition about 1 Ma, the dominant periodicity of the glacial-interglacial cycles shifted from ~40 to ~100 kyr. Here, we use a previously developed mathematical model to investigate the possible dynamical origin of these different periodicities. The model has two variables, one of which exhibits sawtooth oscillations, resembling the glacial-interglacial cycles, whereas the other variable exhibits spikes at the rapid transitions. When applying a sinusoidal forcing with a fixed period, there emerges a rich variety of cycles with different periodicities, each being a multiple of the forcing period. Furthermore, the dominant periodicity of the system can change, while the forcing periodicity remains fixed, due to either random variations or different frequency components of the orbital forcing. Two key relationships stand out as predictions to be tested against observations: (1) the amplitude and the periodicity of the cycles are approximately linearly proportional to each other, a relationship that is also found in the δ[superscript 18]O temperature proxy. (2) The magnitude of the spikes increases with increasing periodicity and amplitude of the sawtooth. This prediction could be used to identify one or more currently hidden spiking variables driving the glacial-interglacial transitions. Essentially, the quest would be for any proxy record, concurrent with a dynamical model prediction, that exhibits deglacial spikes which increase at times when the amplitude/periodicity of the glacial cycles increases. In the specific context of our calcifier-alkalinity mechanism, the records of interest would be calcifier productivity and calcite accumulation. We believe that such a falsifiable hypothesis should provide a strong motivation for the collection of further records., National Science Foundation (U.S.) (NSF Grant OCE-1155295), European Research Council (ERC) (Grant SP2-GA-2008-200915), National Science Foundation (U.S.) (NSF Grant OCE-1259388), Netherlands. Ministry of Economic Affairs (Knowledge Base IV (KBIV) ‘sustainable spatial development of ecosystems, landscapes, seas and regions’)

Quantitative knowledge about copepod life histories is of crucial importance to interpret and predict the impacts of natural and anthropogenic stressors in this taxonomic group. Dynamic Energy Budget (DEB) models are a useful tool in this context, as they quantitatively link the energy taken up by feeding to energy-demanding traits such as growth, development and reproduction. The copepod life cycle, however, has several features that require closer investigation. Firstly, they sport larval development through six naupliar stages (of which the initial stages do not feed), followed by six copepodite stages (which have a different shape from the nauplii). Furthermore, growth stops rather abruptly after the final moult to the adult stage, and many species build up a large lipid storage to survive, and initiate reproduction, in absence of food. After a few modifications, the simple and generic DEBkiss model could be calibrated for Calanus sinicus using data on body composition and size at age for different temperatures. Embryo and naupliar development were well explained by the model, after correcting for their deviating shape from the copepodites. Ceasing of growth after the final moult was implemented as a size-dependent switch in allocation. With these assumptions, predictions could be made for the rates of ingestion, respiration and reproduction in adults. The predictions were consistent with observed rates, which indicates the realism of the model structure and its parameterisation. Several issues remain to be addressed, specifically, the dynamics of lipid storage and its use. However, the present study provides a starting point for applications of DEB theory to copepods.

Filtration capacity and feeding behaviour has been intensely studied for adult mussels (Mytilus edulis), but less information is available for juvenile mussels (1.5–25 mm

For their growth, dormant tumors, which lack angiogenesis may critically depend on gradients of nutrients and oxygen from the nearest blood vessel. Because for oxygen depletion the distance from the nearest blood vessel to depletion will generally be shorter than for glucose depletion, such tumors will contain anoxic living tumor cells. These cells are dangerous, because they are capable of inducing angiogenesis, which will "wake up" the tumor. Anoxic cells are dependent on anaerobic glucose breakdown for ATP generation. The local extracellular glucose concentration gradient is determined by the blood glucose concentration and by consumption by cells closer to the nearest blood vessel. The blood glucose concentration can be lowered by 20-40% during fasting. We calculated that glucose supply to the potentially hazardous anoxic cells can thereby be reduced significantly, resulting in cell death specifically of the anoxic tumor cells. We hypothesize that intermittent fasting will help to reduce the incidence of tumor relapse via reducing the number of anoxic tumor cells and tumor awakening.

In this paper we consider a model for the herd behavior of prey, that are subject to attacks by specialist predators. The latter are affected by a transmissible disease. With respect to other recently introduced models of the same nature, we focus here our attention to the possible feeding satiation phenomenon. The system dynamics is thoroughly investigated, to show the occurrence of several types of bifurcations. In addition to the transcritical and Hopf bifurcation that occur commonly in predator–prey system also a zero-Hopf and a global bifurcation occur. The Hopf and the global bifurcation occur only in the disease-free (so purely demographic) system. The latter is a heteroclinic connection for the between saddle equilibrium points where a stable limit cycle is disrupted and where the system disease-free collapses while in a parameter space region the endemic system exists stably.

The accumulation of carbon within the Weddell Gyre and its exchanges across the gyre boundaries are investigated with three recent full-depth oceanographic sections enclosing this climatically important region. The combination of carbon measurements with ocean circulation transport estimates from a box inverse analysis reveals that deepwater transports associated with Warm Deep Water (WDW) and Weddell Sea Deep Water dominate the gyre's carbon budget, while a dual-cell vertical overturning circulation leads to both upwelling and the delivery of large quantities of carbon to the deep ocean. Historical sea surface pCO2 observations, interpolated using a neural network technique, confirm the net summertime sink of 0.044 to 0.058?±?0.010?Pg?C?yr-1 derived from the inversion. However, a wintertime outgassing signal similar in size results in a statistically insignificant annual air-to-sea CO2 flux of 0.002?±?0.007?Pg?C?yr-1 (mean 1998–2011) to 0.012?±?0.024?Pg?C?yr-1 (mean 2008–2010) to be diagnosed for the Weddell Gyre. A surface layer carbon balance, independently derived from in situ biogeochemical measurements, reveals that freshwater inputs and biological drawdown decrease surface ocean inorganic carbon levels more than they are increased by WDW entrainment, resulting in an estimated annual carbon sink of 0.033?±?0.021?Pg?C?yr-1. Although relatively less efficient for carbon uptake than the global oceans, the summertime Weddell Gyre suppresses the winter outgassing signal, while its biological pump and deepwater formation act as key conduits for transporting natural and anthropogenic carbon to the deep ocean where they can reside for long time scales.

We study the effects of predation on the competition of prey populations for two resources in a chemostat. We investigate a variety of small food web compositions: the bi-trophic food web (two resources—two competing prey) and the three-trophic food web (two resources—two prey—generalist predator) comparing different model formulations: substitutable resources and essential resources, namely Liebig's minimum law model (perfect essential resources) and complementary resources formulations. The prediction of the outcome of competition is solely based on bifurcation analysis in which the inflow of resources into the chemostat is used as the bifurcation parameter. We show that the results for different bi-trophic food webs are very similar, as only equilibria are involved in the long-term dynamics. In the three-trophic food web, the outcome of competition is manifested largely by non-equilibrium dynamics, i.e., in oscillatory behavior. The emergence of predator–prey cycles leads to strong deviations between the predictions of the outcome of competition based on Liebig's minimum law and the complementary resources. We show that the complementary resources formulation yields a stabilization of the three-trophic food web by decreasing the existence interval of oscillations. Furthermore, we find an exchange of a region of oscillatory co-existence of all three species in Liebig's formulation by a region of bistability of two limit cycles containing only one prey and the predator in the complementary formulation.

Mathematical models (should) play a central role in quantitative research, both in the design of experiments and in the analysis of their results. This also holds for research on stress on individual organisms, where stress is defined as an environmentally induced change in their (eco-physiological) behaviour, implying the necessity to know the behaviour in absence of stress in some detail. The individual can effectively be modelled in terms of a dynamical system, where stress shows up as a change in one or more parameters that control the behaviour of the system. After a more detailed presentation of the empirical cycle and an introduction to dynamic systems, I will discuss this approach in the context of generalised ecotoxicity, where presence (e.g. toxicants) or absence (e.g. dioxygen) of particular chemical compounds in the environment might affect a variety of endpoints (feeding, growth, reproduction, maintenance, survival). To this end I will discuss chemical transformation in the environment (speciation, ionisation, degradation, absorption), transport to and from the individual (various uptake and elimination routes, popular transport models), metabolic transformation, effects of nutritional status on kinetics and effects (lethal and sublethal). (C) 2017 Elsevier B.V. All rights reserved.

The recent finding that the Greenland shark, Somniosus microcephalus, reaches a life-span of almost 4 centuries and attains sexual maturity around 1.5 centuries, made us wonder what metabolic differences were responsible for these seemingly extreme values, compared to the related and better known spurdog Squalus acanthias. We studied this in the context of the dynamic energy budget (DEB) theory for metabolic organisation, which was applied to some 700 animal species from all large phyla and all chordate orders. The referenced data, estimated parameters and implied properties for all these species are published in the online Add-my-Pet collection, which provides a frame of reference for metabolic and life history properties. Given the few known data on S. microcephalus, we were able to estimate ageing parameters and gestation time, by application of the standard DEB model. We inferred that a recently estimated life-span of 392 years is probably too short for life at 2 °C, rather than too long. The ageing acceleration is only slightly smaller than that of the spurdog, and the gestation time is very likely between 8 and 18 years with the implication of around 200–700 pups per life-time. The low body temperature and high maximum reserve density of S. microcephalus could be identified as the causes of its long life-span. We see the latter cause as an adaptation to a life in the deep sea sporadically preying on big carcasses, where it is necessary to survive long spells of starvation. This application of the standard DEB model shows that it can be applied in situations where few data are available and how implied properties (gestation) can be used to constrain parameter values. The methods used here could be further developed by fisheries biologists working with deep sea species for which very little is known.

We studied the influence of food availability on the growth (whole body and organs) of the oyster Crassostrea gigas and on the dynamics of their d13C and d15N respective values. Juvenile oysters originating from Arcachon Bay were transplanted to two contrasting ecosystems, Baie des Veys (BDV) and Rade de Brest (RDB), for a 1-yr growth survey. In BDV, chlorophyll-a concentrations ([Chl-a]) was 3 times higher than in RDB on average, which accounts for the differences in oyster growth between BDV and RDB. Differences in trophic conditions could also explain the differences in C/N ratios and 13C values between sites; these differences widened when lipid normalised 13C values were used. Oysters clearly selected microalgae as the main food source, and especially phytoplankton. Gi (Gills), Mu (Muscle) and Re (remaining tissues) clearly exhibited different isotopic enrichment levels, with dMu > dGi > dRe regardless of C or N elements, culture sites and seasons. Isotopic discrimination between organs was rather equivalent between sites. This unexpected result would benefit from an experiment under condtions along a calibration of the lipid normalisation to correct 13C values in bivalves

One of the simplest population biological models displaying a Hopf bifurcation is the Rosenzweig–MacArthur model with Holling type II response function as essential ingredient. In seasonally forced versions the fixed point on one side of the Hopf bifurcation becomes a limit cycle and the Hopf limit cycle on the other hand becomes a torus, hence the Hopf bifurcation becomes a torus bifurcation, and via torus destruction by further increasing relevant parameters can follow deterministic chaos. We investigate this route to chaos also in view of stochastic versions, since in real world systems only such stochastic processes would be observed. However, the Holling type II response function is not directly related to a transition from one to another population class which would allow a stochastic version straight away. Instead, a time scale separation argument leads from a more complex model to the simple 2 dimensional Rosenzweig–MacArthur model, via additional classes of food handling and predators searching for prey. This extended model allows a stochastic generalization with the stochastic version of a Hopf bifurcation, and ultimately also with additional seasonality allowing a torus bifurcation under stochasticity. Our study shows that the torus destruction into chaos with positive Lyapunov exponents can occur in parameter regions where also the time scale separation and hence stochastic versions of the model are possible. The chaotic motion is observed inside Arnol’d tongues of rational ratio of the forcing frequency and the eigenfrequency of the unforced Hopf limit cycle. Such torus bifurcations and torus destruction into chaos are also observed in other population biological systems, and were for example found in extended multi-strain epidemiological models on dengue fever. To understand such dynamical scenarios better also under noise the present low dimensional system can serve as a good study case.

Most of the experimental testing in ecotoxicology takes place at the individual level, but the protection goals for environmental risk assessment are at the population level (or higher). Population modelling can fill this gap, but only models on a mechanistic basis allow for extrapolation beyond the conditions in the experimental tests. The life-history traits of individuals form the basis of population dynamics, and population modelling thus requires a proper understanding of the individual's behaviour. The dynamic energy budget (DEB) theory offers a flexible platform for the development of models at the individual level. Linking DEB models to population models can thus provide a mechanistic basis for extrapolation. Here, we provide a conceptual overview of DEB theory, with emphasis on its applications in ecotoxicology. Furthermore, we briefly review the applications in which a DEB-based individual model has been linked to structured population dynamics. Finally, we discuss some of the most important areas for further research in this context. (C) 2013 Elsevier B.V. All rights reserved.

In this paper we analyse a two-strain compartmental dengue fever model that allows us to study the behaviour of a Dengue fever epidemic. Dengue fever is the most common mosquito-borne viral disease of humans that in recent years has become a major international public health concern. The model is an extension of the classical compartmental susceptible-infected-recovered (SIR) model where the exchange between the compartments is described by ordinary differential equations (ode). Two-strains of the virus exist so that a primary infection with one strain and secondary infection by the other strain can occur. There is life-long immunity to the primary infection strain, temporary cross-immunity and after the secondary infection followed by life-long immunity, to the secondary infection strains. Newborns are assumed susceptible. Antibody Dependent Enhancement (ade) is a mechanism where the pre-existing antibodies to the previous dengue infection do not neutralize but rather enhance replication of the secondary strain. In the previously studied models the two strains are identical with respect to their epidemiological functioning: that is the epidemiological process parameters of the two strains were assumed equal. As a result the mathematical model possesses a mathematical symmetry property. In this manuscript we study a variant with epidemiological asymmetry between the strains: the force of infection rates differ while all other epidemiological parameters are equal. Comparison with the results for the epidemiologically symmetric model gives insight into its robustness. Numerical bifurcation analysis and simulation techniques including Lyapunov exponent calculation will be used to study the long-term dynamical behaviour of the model. For the single strain system stable endemic equilibria exist and for the two-strain system endemic equilibria, periodic solutions and also chaotic behaviour. © 2014 Elsevier Inc.

International audience; The standard Dynamic Energy Budget (DEB) model assumes that food is converted to reserve and a fraction kappa of mobilised reserve of an individual 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). The add\ₘy\ₚet collection of over 300 animal species from most larger phyla, and all chordate classes, shows that this model fits energy data very well. Nine parameters determine nine data points at abundant food: dry/wet weight ratio, age at birth, puberty, death, weight at birth, metamorphosis, puberty, ultimate weight and ultimate reproduction rate. We demonstrate that, given a few other parameters, these nine data points also determine the nine parameters uniquely that are independent of food availability: maturity at birth, metamorphosis and puberty, specific assimilation, somatic maintenance and costs for structure, allocation fraction of mobilised reserve to soma, energy conductance, and ageing acceleration. We provide an efficient algorithm for mapping between data and parameter space in both directions and found expressions for the boundaries of the parameter and data spaces. One of them quantifies the position of species in the supply-demand spectrum, which reflects the internalisation of energetic control. We link eco-physiological properties of species to their position in this spectrum and discuss it in the context of homeostasis. Invertebrates and ray-finned fish turn out to be close to the supply end of the spectrum, while other vertebrates, including cartilaginous fish, have stronger demand tendencies. We explain why birds and mammals up-regulate metabolism during reproduction. We study some properties of the bijection using elasticity coefficients. The properties have applications in parameter estimation and in the analysis of evolutionary constraints on parameter values; the relationship between DEB parameters and data has similarities to that between genotype and phenotype. (C) 2014 Elsevier Ltd. All rights reserved.

Oscillations are widely distributed in nature and synchronization of oscillators has been described at the cellular level (e.g. heart cells) and at the population level (e.g. fireflies). Yeast glycolysis is the best known oscillatory system, although it has been studied almost exclusively at the population level (i.e. limited to observations of average behaviour in synchronized cultures). We studied individual yeast cells that were positioned with optical tweezers in a microfluidic chamber to determine the precise conditions for autonomous glycolytic oscillations. Hopf bifurcation points were determined experimentally in individual cells as a function of glucose and cyanide concentrations. The experiments were analyzed in a detailed mathematical model and could be interpreted in terms of an oscillatory manifold in a three-dimensional state-space; crossing the boundaries of the manifold coincides with the onset of oscillations and positioning along the longitudinal axis of the volume sets the period. The oscillatory manifold could be approximated by allosteric control values of phosphofructokinase for ATP and AMP.The mathematical models described here have been submitted to the JWS Online Cellular Systems Modelling Database and can be accessed at http://jjj.mib.ac.uk/webMathematica/UItester.jsp?modelName=gustavsson5. [Database section added 14 May 2014 after original online publication].

Research on the Dynamic Energy Budget (DEB) theory started 35. years ago. Initially much emphasis was put on the development of a consistent theory. During recent years attention was paid on parameterizing DEB models for a huge collection of species. This enables the search for patterns in parameter values in an ecological and evolutionary context. This special issue presents some of the results of this quest, among other things focusing on the development of metabolic acceleration, combined with various applications of DEB theory in fisheries, aquaculture, climate science and ecotoxicology.

During the last two decades, the simple view of resource limitation by a single resource has been changed due to the realization that co-limitation by multiple resources is often an important determinant of species growth. Hence, the multiple resource limitation hypothesis needs to be taken into account, when communities of species competing for resources are considered. We present a multiple species–multiple resource competition model which is based on the concept of synthesizing unit to formulate the growth rates of species competing for interactive essential resources. Using this model, we demonstrate that a more mechanistic explanation of interactive effects of co-limitation may lead to the known complex dynamics including nonequilibrium states as oscillations and chaos. We compare our findings with earlier investigations on biological mechanisms that can predict the outcome of multispecies competition. Moreover, we show that this model yields a periodic state where more species than limiting complementary resources can coexist (supersaturation) in a homogeneous environment. We identify two novel mechanisms, how such a state can emerge: a transcritical bifurcation of a limit cycle and a transition from a heteroclinic cycle. Furthermore, we demonstrate the robustness of the phenomenon of supersaturation when the environmental conditions are varied.

Toxicokinetic-toxicodynamic (TKTD) modeling offers many advantages in the analysis of ecotoxicity test data. Calibration of TKTD models, however, places different demands on test design compared with classical concentration-response approaches. In the present study, useful complementary information is provided regarding test design for TKTD modeling. A case study is presented for the pond snail Lymnaea stagnalis exposed to the narcotic compound acetone, in which the data on all endpoints were analyzed together using a relatively simple TKTD model called DEBkiss. Furthermore, the influence of the data used for calibration on accuracy and precision of model parameters is discussed. The DEBkiss model described toxic effects on survival, growth, and reproduction over time well, within a single integrated analysis. Regarding the parameter estimates (e.g., no-effect concentration), precision rather than accuracy was affected depending on which data set was used for model calibration. In addition, the present study shows that the intrinsic sensitivity of snails to acetone stays the same across different life stages, including the embryonic stage. In fact, the data on egg development allowed for selection of a unique metabolic mode of action for the toxicant. Practical and theoretical considerations for test design to accommodate TKTD modeling are discussed in the hope that this information will aid other researchers to make the best possible use of their test animals. © 2014 SETAC.

Dynamic models for toxic effects [toxicokinetic-toxicodynamic (TKTD) models] are increasingly used in the analysis of toxicity data for single-chemical exposure. However, these models also offer a natural extension to the effects of chemical mixtures. Here, we demonstrate how a simple model for the energy budget (DEBkiss) can be used to interpret the effects of cadmium and fluoranthene, in both single and mixed exposure, on the nematode Caenorhabditis elegans. The data for all time points and all end points (growth and reproduction) are combined into a single coherent framework. These modeling results are compared to a more traditional independent-action approach based on the dose-response curves for a single end point at a single time point. The analysis with DEBkiss does not lead to a radically different interpretation of the mixture effects, both indicating an antagonistic interaction in the mixture. The DEBkiss analysis does, however, provide much more insight into the relevant dynamic processes underlying the toxic effect on the organism and allows for the generation of mechanistic hypotheses that can be used to guide further research. © 2014 American Chemical Society.

Under constant environmental conditions, most animals tend to grow following the von Bertalanffy growth curve. Deviations from this curve can point to changes in the environment that the animals experience, such as food limitation when the available food is not sufficient or suitable. However, such deviations can also point to a phenomenon called metabolic acceleration, which is receiving increasing attention in the field of Dynamic Energy Budget (DEB) modeling. Reasons for such an acceleration are usually changes in shape during ontogeny, which cause changes in the surface area to volume ratio of the organism. Those changes, in turn, lead to changes in some of the model parameters that have length in their dimension. The life-history consequences of metabolic acceleration as implemented in the DEB theory are an s-shaped growth curve (when body size is expressed as a length measure) and a prolongation of the hatching time. The great pond snail . Lymnaea stagnalis was earlier found to be food limited during the juvenile phase in laboratory experiments conducted under classical ecotoxicity test protocols. The pond snail has isomorphic shell growth but yet does not exhibit the expected von Bertalanffy growth curve under food limitation. When applying the standard DEB model to data from such life-cycle experiments, we also found that the hatching time is consistently underestimated, which could be a sign of metabolic acceleration. We here present an application of the DEB model including metabolic acceleration to the great pond snail. We account for the simultaneous hermaphroditism of the snail by including a model extension that describes the relative investment into the male and female function. This model allowed us to adequately predict the life history of the snail over the entire life cycle. However, the pond snail does not change in shape substantially after birth, so the original explanation for the metabolic acceleration does not hold. Since the change in shape is not the only explanation for metabolic acceleration in animals, we discuss the possible other explanations for this pattern in . L. stagnalis.

Dynamic Energy Budget (DEB) models are used for describing the flow of energy through organisms. The most important and powerful aspect of DEB theory is that inter-specific differences can be captured in the same model by comparison of parameter values. However, estimation of these parameters is complicated and can often not be done with direct empirical measurements alone. Here, we present DEB parameter estimates obtained by combining both experimental and literature data for the filter feeder Brachidontes pharaonis, which is considered one among the 100 worst invasive marine species in the Mediterranean Basin. We utilize a statistical procedure based on the covariation method to obtain parameters that minimize the deviation between observed and predicted patterns of growth and reproduction.