Extending a combined dynamic energy budget matrix population model with a bayesian approach to assess variation in the intrinsic rate of population increase. An example in the earthworm Dendrobaena octaedra

Earthworm distributions are not driven by measurable soil properties. Do they really indicate soil quality?

Abundance and distribution of earthworms in agricultural fields is frequently proposed as a measure of soil quality assuming that observed patterns of abundance are in response to improved or degraded environmental conditions. However, it is not clear that earthworm abundances can be directly related to their edaphic environment, as noted in Darwin’s final publication, perhaps limiting or restricting their value as indicators of ecological quality in any given field. We present results from a spatially explicit intensive survey of pastures within United Kingdom farms, looking for the main drivers of earthworm density at a range of scales. When describing spatial variability of both total and ecotype-specific earthworm abundance within any given field, the best predictor was earthworm abundance itself within 20–30 m of the sampling point; there were no consistent environmental correlates with earthworm numbers, suggesting that biological factors (e.g. colonisation rate, competition, predation, parasitism) drive or at least significantly modify earthworm distributions at this spatial level. However, at the national scale, earthworm abundance is well predicted by soil nitrate levels, density, temperature and moisture content, albeit not in a simple linear fashion. This suggests that although land can be managed at the farm scale to promote earthworm abundance and the resulting soil processes that deliver ecosystem services, within a field, earthworm distributions will remain patchy. The use of earthworms as soil quality indicators must therefore be carried out with care, ensuring that sufficient samples are taken within field to take account of variability in earthworm populations that is unrelated to soil chemical and physical properties.

When significance becomes insignificant: Effect sizes and their uncertainties in Bayesian and frequentist frameworks as an alternative approach when analyzing ecotoxicological data

Bayesian methods and frequentist confidence intervals are proposed as an alternative approach in ecotoxicology, emphasizing effect sizes and associated (un)certainties to judge the biological relevance of effects instead of basing decisions on p values. These approaches show advantages over null hypothesis significance testing. In particular, Bayesian methods revealed more potential than frequentist counterparts, as the posterior distribution and its credible intervals can be directly interpreted as the probability of effect sizes. Environ Toxicol Chem 2018;37:1949-1955. © 2018 SETAC.

An energy budget agent-based model of earthworm populations and its application to study the effects of pesticides

Earthworms are important organisms in soil communities and so are used as model organisms in environmental risk assessments of chemicals. However current risk assessments of soil invertebrates are based on short-term laboratory studies, of limited ecological relevance, supplemented if necessary by site-specific field trials, which sometimes are challenging to apply across the whole agricultural landscape. Here, we investigate whether population responses to environmental stressors and pesticide exposure can be accurately predicted by combining energy budget and agent-based models (ABMs), based on knowledge of how individuals respond to their local circumstances. A simple energy budget model was implemented within each earthworm Eisenia fetida in the ABM, based on a priori parameter estimates. From broadly accepted physiological principles, simple algorithms specify how energy acquisition and expenditure drive life cycle processes. Each individual allocates energy between maintenance, growth and/or reproduction under varying conditions of food density, soil temperature and soil moisture. When simulating published experiments, good model fits were obtained to experimental data on individual growth, reproduction and starvation. Using the energy budget model as a platform we developed methods to identify which of the physiological parameters in the energy budget model (rates of ingestion, maintenance, growth or reproduction) are primarily affected by pesticide applications, producing four hypotheses about how toxicity acts. We tested these hypotheses by comparing model outputs with published toxicity data on the effects of copper oxychloride and chlorpyrifos on E. fetida. Both growth and reproduction were directly affected in experiments in which sufficient food was provided, whilst maintenance was targeted under food limitation. Although we only incorporate toxic effects at the individual level we show how ABMs can readily extrapolate to larger scales by providing good model fits to field population data. The ability of the presented model to fit the available field and laboratory data for E. fetida demonstrates the promise of the agent-based approach in ecology, by showing how biological knowledge can be used to make ecological inferences. Further work is required to extend the approach to populations of more ecologically relevant species studied at the field scale. Such a model could help extrapolate from laboratory to field conditions and from one set of field conditions to another or from species to species.

The use of traits-based approaches and eco(toxico)logical models to advance the ecological risk assessment framework for chemicals

This article presents a framework to diagnose and predict the effects of chemicals, integrating 2 promising tools to incorporate more ecology into ecological risk assessment, namely traits-based approaches and ecological modeling. Traits-based approaches are used increasingly to derive correlations between the occurrence of species traits and chemical exposure from biological and chemical monitoring data. This assessment can also be used in a diagnostic way, i.e., to identify the chemicals probably posing the highest risks to the aquatic ecosystems. The article also describes how ecological models can be used to explore how traits govern the species-substance interactions and to predict effects at the individual, population, and community and ecosystem level, i.e., from the receptor to the landscape level. This can be done by developing models describing the toxicokinetics and toxicodynamics of the chemical in the individual, the life-history of species and the connectivity of populations, determining their recovery, and the food web relations at the community and ecosystem level that determine the indirect effects. Special attention is given on how spatial aspects can be included in the ecological risk assessments using ecological models. The components of the framework are introduced and critically discussed. We describe how the different tools and data generated through experimentation (laboratory and semifield) and biomonitoring can be integrated. The article uses examples from the aquatic compartment, but the concepts that are used, and their integration within the framework, can be generalized to other environmental compartments.

Coupled dynamics of energy budget and population growth of tilapia in response to pulsed waterborne copper

The impact of environmentally pulsed metal exposure on population dynamics of aquatic organisms remains poorly understood and highly unpredictable. The purpose of our study was to link a dynamic energy budget model to a toxicokinetic/toxicodynamic (TK/TD). We used the model to investigate tilapia population dynamics in response to pulsed waterborne copper (Cu) assessed with available empirical data. We mechanistically linked the acute and chronic bioassays of pulsed waterborne Cu at the scale of individuals to tilapia populations to capture the interaction between environment and population growth and reproduction. A three-stage matrix population model of larva-juvenile-adult was used to project offspring production through two generations. The estimated median population growth rate (λ) decreased from 1.0419 to 0.9991 under pulsed Cu activities ranging from 1.6 to 2.0 μg L(-1). Our results revealed that the influence on λ was predominately due to changes in the adult survival and larval survival and growth functions. We found that pulsed timing has potential impacts on physiological responses and population abundance. Our study indicated that increasing time intervals between first and second pulses decreased mortality and growth inhibition of tilapia populations, indicating that during long pulsed intervals tilapia may have enough time to recover. Our study concluded that the bioenergetics-based matrix population methodology could be employed in a life-cycle toxicity assessment framework to explore the effect of stage-specific mode-of-actions in population response to pulsed contaminants.

Bayesian modelling of daphnid responses to time-varying cadmium exposure in laboratory aquatic microcosms

Experiments were carried out to test the effects of cadmium on five aquatic species in 2-L indoor freshwater/sediment microcosms. Experimental data were collected over 21 days in static conditions, i.e. the microcosms evolved without water renewal. Because of speciation, the total cadmium concentration in water decreased with time. Here we present a focus on Daphnia magna responses. For the three life history traits we considered (survival, growth and reproduction), mathematical effect models were built based on threshold stress functions involving no effect concentrations (NECs). These models took the time-varying conditions of exposure into account through a time-recurrent formalism. Within a Bayesian framework, four kinds of data were fitted simultaneously (exposure, survival, growth and reproduction), using an appropriate error model for each endpoint. Hence, NECs were determined as well as their associated estimation uncertainty. Through this modelling approach, we demonstrate that thresholds for stress functions can be successfully inferred even in experimental setup more complex than standard bioassays.

Extrapolating toxic effects on individuals to the population level: the role of dynamic energy budgets

The interest of environmental management is in the long-term health of populations and ecosystems. However, toxicity is usually assessed in short-term experiments with individuals. Modelling based on dynamic energy budget (DEB) theory aids the extraction of mechanistic information from the data, which in turn supports educated extrapolation to the population level. To illustrate the use of DEB models in this extrapolation, we analyse a dataset for life cycle toxicity of copper in the earthworm Dendrobaena octaedra. We compare four approaches for the analysis of the toxicity data: no model, a simple DEB model without reserves and maturation (the Kooijman-Metz formulation), a more complex one with static reserves and simplified maturation (as used in the DEBtox software) and a full-scale DEB model (DEB3) with explicit calculation of reserves and maturation. For the population prediction, we compare two simple demographic approaches (discrete time matrix model and continuous time Euler-Lotka equation). In our case, the difference between DEB approaches and population models turned out to be small. However, differences between DEB models increased when extrapolating to more field-relevant conditions. The DEB3 model allows for a completely consistent assessment of toxic effects and therefore greater confidence in extrapolating, but poses greater demands on the available data.

Potential application of population models in the European ecological risk assessment of chemicals. II. Review of models and their potential to address environmental protection aims

Whereas current chemical risk assessment (RA) schemes within the European Union (EU) focus mainly on toxicity and bioaccumulation of chemicals in individual organisms, most protection goals aim at preserving populations of nontarget organisms rather than individuals. Ecological models are tools rarely recommended in official technical documents on RA of chemicals, but are widely used by researchers to assess risks to populations, communities and ecosystems. Their great advantage is the relatively straightforward integration of the sensitivity of species to chemicals, the mode of action and fate in the environment of toxicants, life-history traits of the species of concern, and landscape features. To promote the usage of ecological models in regulatory risk assessment, this study tries to establish whether existing, published ecological modeling studies have addressed or have the potential to address the protection aims and requirements of the chemical directives of the EU. We reviewed 148 publications, and evaluated and analyzed them in a database according to defined criteria. Published models were also classified in terms of 5 areas where their application would be most useful for chemical RA. All potential application areas are well represented in the published literature. Most models were developed to estimate population-level responses on the basis of individual effects, followed by recovery process assessment, both in individuals and at the level of metapopulations. We provide case studies for each of the proposed areas of ecological model application. The lack of clarity about protection goals in legislative documents made it impossible to establish a direct link between modeling studies and protection goals. Because most of the models reviewed here were not developed for regulatory risk assessment, there is great potential and a variety of ecological models in the published literature.

Sublethal toxicant effects with dynamic energy budget theory: model formulation

We develop and test a general modeling framework to describe the sublethal effects of pollutants by adding toxicity modules to an established dynamic energy budget (DEB) model. The DEB model describes the rates of energy acquisition and expenditure by individual organisms; the toxicity modules describe how toxicants affect these rates by changing the value of one or more DEB parameters, notably the parameters quantifying the rates of feeding and maintenance. We investigate four toxicity modules that assume: (1) effects on feeding only; (2) effects on maintenance only; (3) effects on feeding and maintenance with similar values for the toxicity parameters; and (4) effects on feeding and maintenance with different values for the toxicity parameters. We test the toxicity modules by fitting each to published data on feeding, respiration, growth and reproduction. Among the pollutants tested are metals (mercury and copper) and various organic compounds (chlorophenols, toluene, polycyclic aromatic hydrocarbons, tetradifon and pyridine); organisms include mussels, oysters, earthworms, water fleas and zebrafish. In most cases, the data sets could be adequately described with any of the toxicity modules, and no single module gave superior fits to all data sets. We therefore propose that for many applications, it is reasonable to use the most general and parameter sparse module, i.e. module 3 that assumes similar effects on feeding and maintenance, as a default. For one example (water fleas), we use parameter estimates to calculate the impact of food availability and toxicant levels on the long term population growth rate.

A Bayesian approach to analyzing ecotoxicological data

Standardized chronic toxicity tests are usually analyzed using a NOEC (no observed effect concentration) or ECx (x% effect concentration) calculation. However,these methods provide very little information for the material cost they entail. It has been proposed that biology-based methods, such as the DEBtox approach, would make better use of the data available. DEBtox deals with the energy balance between physiological processes, and gives insight on how a compound disturbs it. We propose that data analysis can be further improved by estimating the DEBtox parameters using the considerable expertise available in laboratories and/or the literature. The Bayesian inference appears to be an appropriate estimation method for this purpose, as this technique takes expertise into account as prior probability distribution for each parameter, and provides the corresponding posterior distributions given the data. From these posterior distributions, point estimates can easily be deduced, but also credible intervals which are ideal for use in risk assessment. In this paper, we demonstrate this approach through the analysis of two 21-day Daphnia reproduction tests.