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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.

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.

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.

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.

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.

Smoking is perceived as a major epidemic with regard to mortality. Modelling is a major tool used to obtain insight in the dynamics and possible solutions to decrease or even eradicate this epidemic. Most models on smoking consider the epidemiological context explicitly, in which smoking is regarded as an 'infectious disease', in which individuals 'infect' each other. However, the population dynamics are often ignored, while these occur at roughly the same timescale as smoking, and hence should explicitly be considered in the modelling of smoking. We present a simple but dynamical eco-epidemiological model. The model formulation consists of a resource-population dynamic part coupled to an epidemiological part resembling a SIR type model for the three compartments: non-smokers, smokers and ex-smokers. The coupling is via birth of non-smokers and death of the three classes with different death rates. The final four-dimensional system of ordinary differential equations are studied using brute force simulations for the short term dynamics and bifurcation analysis for the long-term dynamics. Due to a feed-back mechanism of the two coupling terms there is a codim-two tangent-transcritical bifurcation. This leads to bi-stability of one smoker endemic interior equilibrium and a smoker free boundary equilibrium. Changing parameters beyond the emerging tangent bifurcation leads on the short term to eradicating smoking. We consider the Netherlands in this paper for parametrization, but the modelling approach may be generally applicable. © 2013 Elsevier B.V.

To determine the response of Pacific salmon (Oncorhynchus spp.) populations to environmental change, we need to understand impacts on all life stages. However, an integrative and mechanistic approach is particularly challenging for Pacific salmon as they use multiple habitats (river, estuarine and marine) during their life cycle. Here we develop a bioenergetic model that predicts development, growth and reproduction of a Pacific salmon in a dynamic environment, from an egg to a reproducing female, and that links female state to egg traits. This model uses Dynamic Energy Budget (DEB) theory to predict how life history traits vary among five species of Pacific salmon: Pink, Sockeye, Coho, Chum and Chinook. Supplemented with a limited number of assumptions on anadromy and semelparity and external signals for migrations, the model reproduces the qualitative patterns in egg size, fry size and fecundity both at the inter- and intra-species levels. Our results highlight how modeling all life stages within a single framework enables us to better understand complex life-history patterns. Additionally we show that body size scaling relationships implied by DEB theory provide a simple way to transfer model parameters among Pacific salmon species, thus providing a generic approach to study the impact of environmental conditions on the life cycle of Pacific salmon. © 2011 Elsevier B.V.

In many countries in Asia and South-America dengue fever (DF) and dengue hemorrhagic fever (DHF) has become a substantial public health concern leading to serious social-economic costs. Mathematical models describing the transmission of dengue viruses have focussed on the so-called antibody-dependent enhancement (ADE) effect and temporary cross-immunity trying to explain the irregular behavior of dengue epidemics by analyzing available data. However, no systematic investigation of the possible dynamical structures has been performed so far. Our study focuses on a seasonally forced (non-autonomous) model with temporary cross-immunity and possible secondary infection, motivated by dengue fever epidemiology. The notion of at least two different strains is needed in a minimalistic model to describe differences between primary infections, often asymptomatic, and secondary infection, associated with the severe form of the disease. We extend the previously studied non-seasonal (autonomous) model by adding seasonal forcing, mimicking the vectorial dynamics, and a low import of infected individuals, which is realistic in the dynamics of dengue fever epidemics. A comparative study between three different scenarios (non-seasonal, low seasonal and high seasonal with a low import of infected individuals) is performed. The extended models show complex dynamics and qualitatively a good agreement between empirical DHF monitoring data and the obtained model simulation. We discuss the role of seasonal forcing and the import of infected individuals in such systems, the biological relevance and its implications for the analysis of the available dengue data. At the moment only such minimalistic models have a chance to be qualitatively understood well and eventually tested against existing data. The simplicity of the model (low number of parameters and state variables) offer a promising perspective on parameter values inference from the DHF case notifications. © 2011 Elsevier Ltd.

Food chain models of ordinary differential equations (ode's) are often used in ecology to gain insight in the dynamics of populations of species, and the interactions of these species with each other and their environment. One powerful analysis technique is bifurcation analysis, focusing on the changes in long-term (asymptotic) behaviour under parameter variation. For the detection of local bifurcations there exists standardised software, but until quite recently most software did not include any capabilities for the detection and continuation of global bifurcations. We focus here on the occurrence of global bifurcations in four food chain models, and discuss the implications of their occurrence. In two stoichiometric models (one piecewise continuous, one smooth) there exists a homoclinic bifurcation, that results in the disappearance of a limit cycle attractor. Instead, a stable positive equilibrium becomes the global attractor. The models are also capable of bistability. In two three-dimensional models a Shil'nikov homoclinic bifurcation functions as the organising centre of chaos, while tangencies of homoclinic cycle-to-cycle connections 'cut' the chaotic attractors, which is associated with boundary crises. In one model this leads to extinction of the top predator, while in the other model hysteresis occurs. The types of ecological events occurring because of a global bifurcation will be categorized. Global bifurcations are always catastrophic, leading to the disappearance or merging of attractors. However, there is no 1-on-1 coupling between global bifurcation type and the possible ecological consequences. This only emphasizes the importance of including global bifurcations in the analysis of food chain models. © 2010 Elsevier Inc.

Variability in infaunal bivalve abundance in the Wadden Sea is largely determined by recruitment variability. Post-settlement, but pre-recruitment bivalve mortality is high and related to the occurrence of their most abundant predator, the brown shrimp Crangon crangon. To investigate if the mortality patterns of newly settled bivalves can be explained by the foraging behavior of brown shrimp, we carried out experiments on shrimp functional response to three size classes of juveniles of the Baltic Tellin Macoma balthica. The functional response curves for all three prey sizes (0.62 mm, 0.73 mm, and 0.85 mm) were the hyperbolic Holling's type II. The attack rate was highest for the smallest prey size (a=0.31, medium and large prey a=0.22); the handling time was longest for the largest prey size (T

In the assessment of the quality of surface waters, the typical procedure is that the concentration of contaminants in the surface water is monitored and subsequently compared with their respective Maximum Permissible Concentrations (MPCs). If the MPCs are not exceeded the water quality is considered to be safe. But can we be certain that this is true? We compared MPCs to observed and calculated effects of measured contaminants in Dutch surface waters and showed that effects of mixtures can cause a daphnid population to go extinct within 30 h of exposure even when MPCs are not exceeded. We conclude that there are shortcomings underlying the concepts of the MPCs. And that the MPCs aim to protect 95% of all species is not met. © 2009 Elsevier Ltd. All rights reserved.

The epibenthic community of the Minho Estuary was studied during the summer of 2006. Diversity was generally low and a total of 14 fish and five crustacean taxa were identified. Multivariate analysis revealed two site clusters (A and B). Water conductivity and percentage of fine sand were the abiotic variables that most contributed to the spatial distinction between clusters. The species contributing the most to the average similarity within Cluster A were Crangon crangon and Pomatoschistus microps, while in Cluster B was Atyaephyra desmarestii. Possible factors responsible for the low diversity of the epibenthic community in Minho Estuary were the low macrozoobenthic abundance and diversity, and the high abiotic oscillations between tides (mainly salinity) acting on the ecosystem., This study was partially funded by FEDER European funds, through the project POCI CLI/61605/2004, and by a PhD grant from the Portuguese Foundation for Science and Technology – FCT – supporting. S. Costa-Dias (SFRH/BD/16922/2004)., info:eu-repo/semantics/publishedVersion

Biochemical oscillations, such as glycolytic oscillations, are often believed to be caused by a single so-called 'oscillophore'. The main characteristics of yeast glycolytic oscillations, such as frequency and amplitude, are however controlled by several enzymes. In this paper, we develop a method to quantify to which extent any enzyme determines the occurrence of oscillations. Principles extrapolated from metabolic control analysis are applied to calculate the control exerted by individual enzymes on the real and imaginary parts of the eigenvalues of the Jacobian matrix. We propose that the control exerted by an enzyme on the real part of the smallest eigenvalue, in terms of absolute value, quantifies to which extent that enzyme contributes to the emergence of instability. Likewise the control exerted by an enzyme on the imaginary part of complex eigenvalues may serve to quantify the extent to which that enzyme contributes to the tendency of the system to oscillate. The method was applied both to a core model and to a realistic model of yeast glycolytic oscillations. Both the control over stability and the control over oscillatory tendency were distributed among several enzymes, of which glucose transport, pyruvate decarboxylase and ATP utilization were the most important. The distributions of control were different for stability and oscillatory tendency, showing that control of instability does not imply control of oscillatory tendency nor vice versa. The control coefficients summed up to 1, suggesting the existence of a new summation theorem. These results constitute proof that glycolytic oscillations in yeast are not caused by a single oscillophore and provide a new, subtle, definition for the oscillophore strength of an enzyme. © 2004 Elsevier Ltd. All rights reserved.

Traditional models of chemostat systems looking at interactions between predator, prey and nutrients have used only a single currency, such as energy or nitrogen. In reality, growth of autotrophs and heterotrophs may be limited by various elements, e.g. carbon, nitrogen, phosphorous or iron. In this study we develop a dynamic energy budget model chemostat which has both carbon and nitrogen as currencies, and examine how the dual availibility of these elements affects the growth of phytoplankton, trophic transfer to zooplankton, and the resulting stability of the chemostat ecosystem. Both species have two reserve pools to obtain a larger metabolic flexibility with respect to changing external environments. Mineral nitrogen and carbon form the base of the food chain, and they are supplied at a constant rate. In addition, the biota in the chemostat recycle nutrients by means of respiration and excretion, and organic detritus is recycled at a fixed rate. We use numerical bifurcation analysis to assess the model's dynamic behavior. In the model, phytoplankton is nitrogen limited, and nitrogen enrichment can lead to oscillations and multiple stable states. Moreover, we found that recycling has a destabilizing effect on the food chain due to the increased repletion of mineral nutrients. We found that both carbon and nitrogen enrichment stimulate zooplankton growth. Therefore, we conclude that the concept of single-element limitation may not be applicable in an ecosystem context. © 2004 Elsevier Inc. All rights reserved.

Let X be a fractional Brownian motion. It is known that M t =∫m t d X, t⩾0 , where m t is a certain kernel, defines a martingale M , and also that X can be represented by X t =∫x t d M, t⩾0 , for some kernel x t . We derive these results by using the spectral representation of the covariance function of X . A formula for the covariance between X and M is also given.

The governing equations are derived for the dynamics of a population consisting of organisms which reproduce by laying one egg at the time, on the basis of a simple physiological model for the uptake and use of energy. Two life stages are assumed, the egg and the adult stage where the adults do not grow. These assumptions hold true, for instance, for rotifers. From the model for the life history of the individuals, a physiologically structured population model for a rotifer population is derived. On the basis of this discrete event reproduction population model a continuous reproduction population model is proposed. The population model together with the equation for the food result in chemostat equations which are solved numerically. We show that for the calculation of the transient population dynamic behaviour after a step-wise change of the dilution rate, an age structure suffices, despite the size and energy structure used to describe the dynamics of the individuals. Aggregation of the continuous reproduction population model yields an approximate lumped parameter model in terms of delay differential equations. In order to assess the performance of the models, experimental data from the literature are fitted. The main purpose of this paper is to discuss the consequences of discrete event versus continuous reproduction. In both population models death by starvation is taken into account. Unlike the continuous reproduction model, the discrete model captures the experimentally observed lack of egg production shortly after the step change in the dilution rate of the chemostat.

Fast exocytosis in melanotropic cells, activated by calcium entry through voltage-gated calcium channels, is very sensitive to mobile calcium buffers (complete block at 800 microM ethylene glycol bis(beta-aminoethyl ether)-N,N,N'N'-tetraacetic acid (EGTA)). This indicates that calcium diffuses a substantial distance from the channel to the vesicle. Surprisingly, 1, 2-bis(2-aminophenoxy)ethane-N,N,N',N'-tetraacetic acid (BAPTA), having a similar KD for calcium as EGTA but a approximately 100 times faster binding rate, blocked exocytosis only twice as effectively as EGTA. Using computer simulations, we demonstrate that this result cannot be explained by free diffusion and buffer binding rates. We hypothesized that local saturation of calcium buffers is involved. A diffusion barrier for both calcium and buffer molecules, located 50-300 nm from the membrane and reducing diffusion 1000 to 10,000 times, generated similar calcium concentrations for specific concentrations of EGTA and BAPTA. With such barriers, calcium rise phase kinetics upon short step depolarizations (2-20 ms) were faster for EGTA than for BAPTA, implying that short depolarizations should allow exocytosis with 50 microM EGTA but not with 25 microM BAPTA. This prediction was confirmed experimentally with capacitance measurements. Coupling exocytosis to calcium dynamics in the model, we found that a barrier with a approximately 3000 times reduced diffusion at approximately 130 nm beneath the membrane best explains the experimentally observed effects of EGTA and BAPTA on block and kinetics of release.

Microalgal growth models aim to predict growth rate as well as cellular composition, given the environmental conditions (such as temperature, nutrient availability, light, etc.). This generic purpose poses strong requirements to the structure of any model attempting to comply with it. First, cellular characteristics should be modelled, rather than taken as model input. Second, if one interprets 'cellular composition' as nutrient cell quota, rather than as nutrient ratios, models should be formulated at the level of the individual cell. Third, modelling should proceed by making assumptions about processes, rather than about states. This paper evaluates current modelling methodology in the light of these desiderata. The models examined mostly (but not exclusively) monospecific cultures in laboratory environments. Whereas the older models are inadequate in view of the generic purpose, recent models increasingly focus on cellular composition and on the processes that lead to changes in cellular composition. Models to be developed in the next few years thus have the potential to fulfil the generic purpose.