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.
The role of biodiversity in ecosystem structure and functioning is central for conservation and environmental quality management, as well as biospherics and earth system studies. Biodiversity is not only about the number of species present, but also the number and nature of the different characteristics and functions which make up a community or an ecosystem, often referred to as traits. Scientists and managers are turning towards such trait-based approaches to measure the health and vitality of ecosystems. In this context of apprehending biodiversity on the basis of diversity of characteristics and functionalities we have been developing the AmP (Add-my-Pet) project. AmP is a database of referenced data on animal energetics, parameter values of models based on Dynamic Energy Budget (DEB) theory [1–4], and properties derived from these parameters. Some 125 authors contributed to the database at 2018/03/12. The AmP project aims: (i) to find the simplest organization principles for metabolism upon which all life is based and (ii) to understand taxon-specific patterns as variations on this common organization. The development of DEB theory started in 1979 and meanwhile over 700 papers have been published on DEB theory, see www. zotero. org/groups/500643/deb_library/. Partly based on the fact that a large number of popular empirical models turned out to be special cases of DEB models [4], we claim that DEB theory is presently the best tested quantitative theory in biology. The comparison of species on the basis of parameter values is an important aspect of the AmP project. Species-comparisons based on measured quantities suffer from the problem that these quantities typically have contributions from many underlying interacting processes, and were not measured for all species of interest. Parameters of mechanistic models, however, have much simpler links with such processes, which makes it easier to find explanations for differences between species. Moreover, the complete parameter set is available for each entry, allowing to predict, e. g. respiration, without any measured data on respiration. Comparison of species is, however, not the only important application of the AmP website. Prediction of effects of global change [5], understanding the geographic distribution of species [6–8], the effects of (toxic) chemical compounds [9–12], the optimization of bio-production (e. g. aquaculture and agriculture [13–15]), stock management, the best re-introduction of endangered species or the control of invading species [16], are just examples of applications where detailed knowledge of energetics of species in a DEB context is very useful. Like many ecologists, we see energetics as the key to understand the ecological behavior of species [17], and as the root of population [18] and ecosystem dynamics [19,20], with consequences at the planetary level [21]. This is the context that motivated the development of DEB theory, of which the AmP project is an application. In view of the rapid build-up of ecological stress all over the world, we think that the field is in urgent need of an online database like AmP. AmP started in 2009 as an educational initiative, to teach researchers how to estimate DEB parameters from their data and animals have the simplest metabolisms (if we compare with say plants, bacteria or microalgae). The database grew and in 2013, (at about 300 entries) we teamed up, formed the first AmP curator board, and together developed the code and web-platform underlying AmP. We wanted to get an overview on: (i) how well the standard DEB model worked for describing animal metabolism, (ii) standardize and improve the parameter estimation procedure and (iii) improve our capacity to judge the realism of parameter values. We start with a brief introduction of DEB theory. All applications of models, including testing of the model against data, start with knowledge of parameter values. The parameters of a DEB model must be estimated from a collection of data sets on the various aspects of energy budgets and life history, using all this information in combination. This involves new features in the methodology of parameter estimation. The next section of this paper describes improvements we implemented, based on the co-variation method [22,23], which was used in an early phase of the database project. Moreover we needed more administrative rigor and improved methods for detecting patterns in parameter values. Development of new routines and re-organization of the previous estimation procedure allowed us to include these new extensions. So the following section describes the new web-interface and structure of the database. Finally we present and discuss the results obtained after implementing the new method and reaching 1035 species in the collection at 2018/03/12. Given that these entries employ together 270 different types of data, in 585 combinations, the estimation of 14 parameters of each species not only illustrates the scope of the data reduction, but also the step-up in comparison potential.
Dynamic Energy Budget (DEB) theory, aims to specify commonalities underlying metabolic organization for all life. It does this by delimiting a small set of assumptions from which mathematical formulae for metabolism are derived, covering the start of embryo development to death by aging through a range of life stages [24–27]. DEB models are meant to apply to all life on earth and allow species comparisons on the basis of (functions of) parameters of that model. The standard DEB model (’std’) is the simplest non-degenerated DEB model implied by the theory and it applies to heterotrophic animals (see Fig 1 for the summary). We refer the reader to [28] for an accessible summary of the principles of DEB theory and a description of the standard DEB model. A detailed derivation of the model on the basis of underlying assumptions is presented in [4], chap. 2. Each DEB parameter of the std-DEB model (see Table 1) has a clear link with one underlying physiological process (specified on the arrows of Fig 1). The combination of parameters covers all aspects of energetics throughout the full life cycle of organisms, include feeding, digestion, storage, maintenance, growth, development, reproduction, aging. Parameter values are individual-specific in the context of DEB theory, but the difference between individuals are typically small enough to average for a species in a meaningful way. Parameter values determine how state variables of an individual (reserve, structure, maturity and reproduction buffer) change in time through all life stages (embryo, juvenile, adult). Life stages have specific definitions: Embryos do not assimilate; Juveniles assimilate and allocate to maturity but not to reproduction; Adults feed, no longer allocate to maturity but store energy/ mass allocated to reproduction into a reproduction buffer which is converted to offspring. To complete the background information needed for this study, we must point to the co-variation rules [29]. If there was no selection pressure of parameter values then particular parameters would co-vary in a simple way with the dimensionless zoom factor z (Table 1), purely based on parameters being either intensive or extensive. The estimation of parameters for each species allows comparing parameters between species and seeing to what extent each parameter is in fact either dependent or independent of body size for different taxonomic groups, thus revealing important patterns in how environmental pressures exert selection pressure on parameter values. Prior to this work, DEB parameters for the AmP entries were obtained with the covariation-method for parameter estimation [22,23]. All the code for parameter estimation is developed in the DEBtool_M package, which is frequently updated and freely available at https: //github. com/add-my-pet/DEBtool_M/. In this section we describe improvements to the method which are implemented in DEBtool. The improvements comprise: The overview of the parameter estimation procedure is presented in Fig 2. In the next section we describe the important new components. One way to judge how good the parameter estimates are is to compute a goodness of fit measure which assesses how close the model predictions are to all of the data. Goodness of fit is not enough, one also needs to check for biological realism. The previous system used goodness of fit measures defined in section 2 of [23]. The new system uses the Mean Relative Error (MRE) and the Symmetric Mean Squared Error (SMSE) to quantify the goodness of fit. MRE = 1 n ′ ∑ i = 1 n RE i, where RE i = ∑ j = 1 n i w i j w i | p i j - d i j | | d i | (w i = ∑ j = 1 n i w i j > 0), that simplifies to R E i = | p i 1 d i 1 - 1 | for zero-variate data. n′ is the number of data sets with wi greater than 0. SMSE = 1 n ′ ∑ i = 1 n SSE i where SSE i = ∑ j = 1 n i w i j w i (p i j - d i j) 2 d i 2 + p i 2, that simplifies to SSE i = (p i 1 / d i 1 - 1) 2 1 + (p i 1 / d i 1) 2 for zero-variate data. See section on loss functions for the definition of the other symbols. MRE can have values in the interval [0, ∞], while SMSE has values in the interval [0,1]. In both cases, 0 means predictions match data exactly. MRE assesses the differences between data and predictions additively, judging equally an overestimation and underestimation of the same relative size (e. g, +20% or −20% have the same contribution), while SMSE assesses the difference multiplicatively, judging overestimation and underestimation by the same factor equally (e. g. × 2 or ×1/2 have the same contribution). Notice that the result of the minimization of loss functions does not, generally, correspond with the minimum of MRE or SMSE (unless the fit is perfect). AmPtool is a software package that is designed to analyse patterns in (functions of) parameter values in selected entries. It is available via github. com/add-my-pet/AmPtool/, and changes frequently since the AmP collection is rapidly expanding. Meta-data, parameters and implied properties (biologically relevant quantities which are functions of parameters as well as food and temperature) are collected in a single Matlab structure (allStat. mat). Advanced plot-routines were developed to plot (functions of) parameters against other (functions of) parameters, for selected species. These selections make use of the taxonomic tree. The tree actually consists of lists-of-lists, based on the newest insights in taxonomy, as presented in the Catalog of Life, the Encyclopedia of Life and Wikipedia. Legends can be created where different taxomonic groups in the tree are attributed user-defined markers. This legend functionality allows selecting taxa at a large number of taxonomic levels. We mentioned in the previous section that goodness of fit is not enough to judge a set of DEB parameters and that one must also check for biological realism. AmPtool is one way to do this. The user can visualize how parameters of closely and less closely related taxonomic groups relate to each other and see if the new parameter estimates are extreme outliers or not. Careful examination of the coherence of the implied properties within an entry is the other way. AmPtool can also be used to find entries on the basis of data types that have been used, or print values of parameters and statistics of selected species.
The AmP web-interface was developed as a result of this work. The interface allows examining each entry as well as obtaining on overview on how entries relate to each other. From 2013 till 2017 the number of AmP entries (Fig 3, left) was dramatically increased from ca 300 in 2013 to 1035 at 2018/03/12 to find out whether DEB models do apply to all animals and determine how problematic it is to have limited amounts of data for estimating DEB parameters. AmP receives entries which are submitted by the international scientific community and to date some 125 authors have contributed to the collection. Every author and their associated entry (with links to the entries) are listed on the AmP web-interface. Over the course of this study, we included a bit over 700 extra species to the collection since 2013 as well as converted the previous 300 entries to this new format. We were careful to select species such that the collection had a broad taxonomic scope, as well as included species of commercial relevance and species relevant for conservation and toxicity testing. We aimed at maintaining a good balance between the different taxonomic groups (Fig 3, right) We were on the look-out for exceptional species (in terms of size or aging) that might show that the DEB model was not applicable. We did not yet find such an animal species. The increasing number of DEB applications on animal species motivated the continuing amelioration of the method, making it more robust, more efficient and easier to apply. As the collection of species grew, it became evident that the standard DEB model (Fig 1) required simple extensions for particular taxa, to accommodate larval life stages, fetal development, various forms of metabolic acceleration [36], substantial programmed shrinking (as sported by Elopocephalai), etc. DEB models are classified as s-models, a-models and h-models according to the mode of metabolic acceleration. Since we see the structured model collection that resulted from the AmP project as an important insight into animal metabolism, we come back to it in the discussion section. We here present the typified models. They must be understood as variations on the standard DEB model (std), see Methods section on DEB theory. The general idea is that the choice of typified model depends more on higher-level classifications than the species-level. Delayed stage transitions are also accounted for in the different model families. Most mammals delay the start of fetal development during gestation. Some bivalves delay the start of metabolic acceleration; this phenomenon can prove to be more common with the increase of available data. The three sets of models are detailed below.
The AmP database not only allows us to test model against data and evaluate implications, but also to identify evolutionary and ecological patterns in parameter values. The number of papers on patterns in parameter values is now increasing rapidly [10,15,30,31,33,36–41]. Apart from being of direct scientific relevance, future improvements of DEB parameter estimation methods might exploit these patterns, since lack of data is the rule rather than the exception and having some testable prediction is better than no prediction at all. Where, for instance, (measured) maximum body weight is treated as an independent variable in the eco-physiological literature, DEB theory sees this as a property resulting from underlying processes that are quantified via parameter values. So maximum body weight is a function of parameter values (and food availability). Respiration (e. g. the use of dioxygen) is another function of parameter values, which has contributions from various underlying processes, such as maintenance, development, growth and assimilation overheads, etc. While respiration has been measured for only a small part of the species in the AmP collection, it is available for all species as a prediction (i. e. a function of parameter values). This is just an illustration of the power of comparison on the basis of parameter values, rather than on the basis of measurements. The Patterns page on the AmP website illustrates some patterns in parameter values, such as (predicted) respiration as function of (predicted) maximum body weight, confirming Kleiber’s empirical law stating that (measured) respiration is about proportional to (measured) maximum weight to the power 3/4. Two other patterns illustrate the explanation provided by DEB theory: relative reserve capacity is increasing and specific somatic maintenance is decreasing with body size. Reserve does not require maintenance, so does not contribute to respiration. The increase of reserve capacity [ E m ] = { p ˙ A m } / v ˙ with maximum (structural) length follows from co-variation rules [29], where energy conductance v ˙ (which quantifies reserve mobilization) is independent of maximum length, and specific maximum assimilation rate { p ˙ A m } is proportional to it. The increase of specific somatic maintenance with decreasing maximum (structural) length is seen as an ecological adaptation to exploit short-lasting peaks in food abundance [36]. Another pattern shows that, contrary to popular believe, the maximum growth rate of dinosaurs is just in line with other taxa, given their body size. The full analysis of all patterns in parameter values is beyond the scope of this work, and is an ongoing activity [33,41]. The classification of DEB models into s–, a– and h–models has more or less clear links with the evolution of metabolism. This will be discussed here using a feature that sets a– and h–models apart from s–models: metabolic type M acceleration [36], where surface area temporarily scales with volume, while before and after this period it scales with volume to the power 2/3. The amount of type M acceleration is quantified by the ratio of body length at the end and the start of the acceleration period. The effect of this change in a DEB context is that both the specific assimilation and the energy conductance increase with length, while outside the acceleration period they stay the same. The ratio of the two, the specific reserve capacity, is not affected by this type of acceleration. The h–models differ mainly from the a–models by the fact that acceleration extends into the adult stage. Fig 7 presents evolutionary relationships among animal taxa with a color code to indicate the amount of acceleration in their species. Since the oldest animal group, the Radiata, and the oldest deuterostomes, the echinoderms, accelerate, it might well be that acceleration became suppressed in several other groups and this suppression evolved several times in evolution [36]. The Ecdysozoa (n = 99 at 2018/01/01) beautifully illustrate the link between model type and taxonomic relationship. Fig 7 shows that Chaetognatha, Tardigrada, Nematoda and Entognatha hardly accelerate metabolism, just a factor 2 or less. The basic insects, the ephemeropterans and odonata accelerate a bit more, while the crown groups, the holometabolic insects, accelerate very much. All of the h–models are found in insecta, but very interestingly, springtails Entognatha (n = 6), which are no longer classified as insects, follow the abj model. Most insects seem to skip the juvenile phase and allocate to reproduction as larvae, which classifies them as adult by definition in DEB terms, while the imago neither grows, nor eats (frequently). Holometabolic insects insert a pupal phase between the larval and imago phases that behaves like an embryo with a reproduction buffer, where most of the larval structure is first converted to reserve [42] and imago structure is build from reserve. Crustacea (n = 62) sport a mix of s– and a–models Branchiopoda (n = 18) are described by std. Copepoda (n = 6) are hardly resolved and require more research. Calanaus does not accelerate (sbp), the others do (abp). Copepods are special with respect to the other crustaceans in that the κ-rule no longer applies to the adult stage. The 1 species of ostracod is described by abj. Malacostraca are better represented in the collection (n = 36) and are described by abj. While abp now applies to most copepods, it may be that it also applies to ostracods, arachnids and scorpions. The future will teach us. The results further show that among the spiralia only some mollusk species accelerate metabolically, see Fig 8. Ray-finned fish (n = 206) sport a wide range of acceleration factors, see Fig 9, but extreme forms of acceleration are confined to the Otomorpha, the Paracanthomorphacea and the crown groups of the Percomorphaceaei only. The coupling between the amount of acceleration in mediterranean perches with the spawning season, as reported in [39], shows that, apart from evolutionary aspects, ecological ones are involved as well and the two aspects cannot be fully separated. These examples beautifully show that the occurrence of acceleration is far from random. Energy conductance, one of the two parameters that are affected by metabolic acceleration, controls reserve mobilisation, so dominates the incubation (or gestation time), since eggs start their development as a lump of reserve. We have several cases with data for embryo development in combination with post natal development, which show that energy conductance remains constant before and after birth. We met one convincing case, the Asian freshwater leech, Barbronia weberi [43], where energy conductance makes a jump up at birth. There are quite a few cases, however, where incubation time is under-estimated. These cases do not have data on embryo development, so we cannot be sure if energy conductance also makes a jump here, or that the start embryo development is delayed. The latter might be due to a variety of reasons. Most mammalian embryos, for instance, have a period to prepare for growth during which the fetus does not increase in size. The onset of growth is typically quite clear, since consistent with DEB expectations, structural length starts to increase linearly [44,45]. Data on embryo development is relatively scarce. The colors in the taxa names of Figs 7,8 and 9 reflect the range of values of metabolic acceleration that were found in the various taxa. Although over 1000 entries is very large for a database of this type, compared to the 10 million existing animal species, it is close to nothing. Thus we cannot assume that the species in the collection are fully representative for the species in nature. Moreover, the number of species in each taxon, both in nature and in the database, varies enormously; some have just a single species. It is already an accomplishment to indicate the ranges this way, and we will not be surprised if insights on which taxa accelerate change somewhat as the collection grows. Since the database is online and freely accessible, the reader can easily check the values of metabolic acceleration for each species in each taxonomic group using the free package AmPtool (we refer the reader to the online manual for how to do this). This study represents a large scale application of a general theory for metabolic organization of living organisms: the Dynamic Energy Budget theory. Although DEB theory applies to all organisms, the AmP collection only deals with animals. The reason is that animals eat other organisms, which do not vary much in chemical composition. As a first approximation, their environment can be characterized by the variables food availability and temperature. This characterization is hard to make “complete” for other organisms, which hampers comparison. And comparison is the most useful asset of this collection. We contend that animal species can be compared on the basis of DEB parameters and that this offers a tractable means to study animal biodiversity in an ecological and evolutionary context. Moreover, by being mechanistic (= based on first principles), DEB models interpret data, rather than just describe it. They can therfore reveal inconsistencies in data and predict un-measured properties of species as functions of parameters. We present and discuss how DEB parameters can be extracted from eco-physiological data: the AmP approach. The two associated software packages, DEBtool and AmPtool, are freely available via GitHub and have online user manuals. We demonstrate the applicability of DEB theory, by showing that it is possible to extract DEB parameters for animal species even when there is little data. We evaluate goodness of fit with respect to data completeness per species and overall the models fit data well. We found that a family of related DEB models, which share the same 14 DEB parameters, are needed to capture the diversity of life-cycles in the animal kingdom. A main metabolic feature which distinguishes the life-cycles is that some groups have ‘metabolic acceleration’, which has links with larval stages. We present the latest evolutionary overview on which groups were found to have metabolic acceleration. Knowledge gaps are highlighted. The AmP project was initiated at 2009/02/12 and meanwhile 125 authors contributed with entries. It has 1035 entries at 2018/03/12, including all larger phyla and all chordate orders, and is both the smallest as well as the largest database of this kind, since it is unique. We expect that it will remain unique for a long time to come, in view of the huge amount of effort to arrive at the state we are presently in and because we think that DEB models will not have alternatives with matching generality, simplicity and realism. We hope that this study motivates the scientific community to contribute and use the AmP collection.
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.
taxonomy
invertebrates
organismal evolution
medicine and health sciences
ecology and environmental sciences
evolutionary biology
biodiversity
animals
endocrine physiology
developmental biology
data management
physiological parameters
embryos
imagos
embryology
computer and information sciences
endocrinology
life cycles
insects
arthropoda
eukaryota
ecology
physiology
animal evolution
biology and life sciences
puberty
organisms
The AmP project: Comparing species on the basis of dynamic energy budget parameters