Multidimensional scaling for animal traits in the context of dynamic energy budget theory

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

Energetic basis for bird ontogeny and egg-laying applied to the bobwhite quail

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

An individual-based model of Zebrafish population dynamics accounting for energy dynamics

International audienceDeveloping population dynamics models for zebrafish is crucial in order to extrapolate from toxicity data measured at the organism level to biological levels relevant to support and enhance ecological risk assessment. To achieve this, a dynamic energy budget for individual zebrafish (DEB model) was coupled to an individual based model of zebrafish population dynamics (IBM model). Next, we fitted the DEB model to new experimental data on zebra-fish growth and reproduction thus improving existing models. We further analysed the DEB-model and DEB-IBM using a sensitivity analysis. Finally, the predictions of the DEB-IBM were compared to existing observations on natural zebrafish populations and the predicted population dynamics are realistic. While our zebrafish DEB-IBM model can still be improved by acquiring new experimental data on the most uncertain processes (e.g. survival or feeding), it can already serve to predict the impact of compounds at the population level

The comparative energetics of the carnivorans and pangolins

Patterns in eco-physiological traits of pangolins and carnivorans are studied, which are functions of underlying Dynamic Energy Budget parameters. The data, parameter values and traits are accessible in the open access Add-my-Pet collection, which currently contains 7 out of 8 species of pangolins and 131 of the extant 276 species of carnivorans and 653 of the extant 6400 species of mammals. Paucity of data and species not included reflect the actual state of knowledge: many species are endangered and/or little measured data is readily available. Although musteloids and pinnipeds form the clade Mustelida, they appear at opposite ends of the classical multidimensional scaling diagram, using 14 traits on all mammals. Yet, in general, the energetic parameters bear a strong taxonomic signal. The weight at birth is proportional to ultimate weight: small for carnivorans and pangolins; extra small for bears; and much larger, but typical for mammals, for the pinnipeds and sea otters. How respiration scales with size is taxon-specific, and we discuss how the body-size scaling of reserve capacity interferes with the waste-to-hurry pattern. Despite their high allocation to soma, the life time cumulated mass of neonates of pangolins and carnivorans equals their own ultimate weight; pinnipeds allocate more to maturation and reproduction. Applying models to support conservation efforts entails needing realistic parameter values. This study contributes to the emerging field of assessing the realism of parameters in biological and evolutionary context

The comparative energetics of the cephalopods: they neither grow nor reproduce fast

The Add-my-Pet (AmP) collection of data on energetics and Dynamic Energy Budget (DEB) parameters currently contains 92 of the 800 extant species of cephalopods. Growth data, as reconstructed from statolith-, beak- or shell-readings, show a rather large scatter, whereas that from laboratory specimens with known age, does not. This implies that food availability varies under field conditions and/or age-determination is uncertain. We compare DEB parameter values and traits of cephalopods with those of other molluscs (Polyplacophora, Bivalvia, and Gastropoda). All cephalopods appear to start accelerating their metabolism at birth, quite few even up till puberty. As a consequence, length-at-age initially shows a clear up-curving at constant temperature and food, which is not clearly linked to morphological changes. They have a high acceleration factor, specific somatic maintenance, surface area-specific assimilation and maximum reserve density. The energy conductance, which controls reserve mobilisation, is typical for molluscs, and age at death is low. The investment into reproduction, in terms of specific offspring mass production per life span, is typical for molluscs. The negative effects that a short life span would have on reproductive output is compensated by a large allocation fraction to maturation or reproduction. Mass at birth is larger than that of gastropods, which, in turn, is much larger than that of bivalves and polyplacophorans. Cephalopod reproduction in terms of number of offspring per life time is, therefore, smaller than that of other molluscs. Although cephalopods are reputed to grow fast, gastropods grow equally fast per gram at maximum rate, while bivalves and polyplacophorans grow quite a bit slower. We conclude that 79% of the cephalopod species do not survive thinning of their populations in the long run, while this holds for some 20% of other animal species. This underscores their vulnerability for this type of harvesting

Body size as emergent property of metabolism

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

A new phase in DEB research

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

Comparing loss functions and interval estimates for survival data

We compare parameter point and interval estimates based on the symmetric bounded loss function, as used in the Add-my-Pet collection on animal energetics, with the maximum likelihood method for number of surviving individuals as function of time. The aging module of Dynamic Energy Budget theory is used to generate Monte Carlo data sets. The simulations show that estimates based on the symmetric loss function give almost the same results in terms of point as well as interval estimates, compared to maximum likelihood estimation, while this loss function avoids the need to model the stochastic component of data sets. For most data types on energetics, we don't have such stochastic models, so maximum likelihood methods cannot be used. Our findings support the view that model plasticity dominates interval estimates, rather than the detailed structure of the stochastic component