A comparison of numerical approaches for statistical inference with stochastic models.

Due to our limited knowledge about complex environmental systems, our predictions of their behavior under different scenarios or decision alternatives are subject to considerable uncertainty. As this uncertainty can often be relevant for societal decisions, the consideration, quantification and communication of it is very important. Due to internal stochasticity, often poorly known influence factors, and only partly known mechanisms, in many cases, a stochastic model is needed to get an adequate description of uncertainty. As this implies the need to infer constant parameters, as well as the time-course of stochastic model states, a very high-dimensional inference problem for model calibration has to be solved. This is very challenging from a methodological and a numerical perspective. To illustrate aspects of this problem and show options to successfully tackle it, we compare three numerical approaches: Hamiltonian Monte Carlo, Particle Markov Chain Monte Carlo, and Conditional Ornstein-Uhlenbeck Sampling. As a case study, we select the analysis of hydrological data with a stochastic hydrological model. We conclude that the performance of the investigated techniques is comparable for the analyzed system, and that also generality and practical considerations may be taken into account to guide the choice of which technique is more appropriate for a particular application. Supplementary Information: The online version contains supplementary material available at 10.1007/s00477-023-02434-z.

Longevity interventions temporally scale healthspan in Caenorhabditis elegans.

Human centenarians and longevity mutants of model organisms show lower incidence rates of late-life morbidities than the average population. However, whether longevity is caused by a compression of the portion of life spent in a state of morbidity, i.e., "sickspan," is highly debated even in isogenic Caenorhabditis elegans. Here, we developed a microfluidic device that employs acoustophoretic force fields to quantify the maximum muscle strength and dynamic power in aging C. elegans. Together with different biomarkers for healthspan, we found a stochastic onset of morbidity, starting with a decline in dynamic muscle power and structural integrity, culminating in frailty. Surprisingly, we did not observe a compression of sickspan in longevity mutants but instead observed a temporal scaling of healthspan. Given the conservation of these longevity interventions, this raises the question of whether the healthspan of mammalian longevity interventions is also temporally scaled.

Towards a comprehensive uncertainty assessment in environmental research and decision support.

Uncertainty quantification is very important in environmental management to allow decision makers to consider the reliability of predictions of the consequences of decision alternatives and relate them to their risk attitudes and the uncertainty about their preferences. Nevertheless, uncertainty quantification in environmental decision support is often incomplete and the robustness of the results regarding assumptions made for uncertainty quantification is often not investigated. In this article, an attempt is made to demonstrate how uncertainty can be considered more comprehensively in environmental research and decision support by combining well-established with rarely applied statistical techniques. In particular, the following elements of uncertainty quantification are discussed: (i) using stochastic, mechanistic models that consider and propagate uncertainties from their origin to the output; (ii) profiting from the support of modern techniques of data science to increase the diversity of the exploration process, to benchmark mechanistic models, and to find new relationships; (iii) analysing structural alternatives by multi-model and non-parametric approaches; (iv) quantitatively formulating and using societal preferences in decision support; (v) explicitly considering the uncertainty of elicited preferences in addition to the uncertainty of predictions in decision support; and (vi) explicitly considering the ambiguity about prior distributions for predictions and preferences by using imprecise probabilities. In particular, (v) and (vi) have mostly been ignored in the past and a guideline is provided on how these uncertainties can be considered without significantly increasing the computational burden. The methodological approach to (v) and (vi) is based on expected expected utility theory, which extends expected utility theory to the consideration of uncertain preferences, and on imprecise, intersubjective Bayesian probabilities.

Integrating uncertainty of preferences and predictions in decision models: An application to regional wastewater planning.

Decision-making in environmental management requires eliciting preferences of stakeholders and predicting outcomes of decision alternatives. Usually, preferences and predictions are both uncertain. Uncertainty of predictions can be tackled by multi-attribute utility theory, but the uncertainty of preferences remains a challenge. We demonstrate an approach for including both uncertainties in a multi-criteria decision analysis (MCDA), using utility theory and the concept of expected expected utility. For a decision regarding a regional merger of wastewater infrastructure in Switzerland, we constructed preference models for four stakeholders. These models also allowed for non-additive interactions between objectives. We evaluated the performance of eleven decision alternatives for which we predicted potential outcomes. Even though uncertainties were high, we could draw conclusions based on the expected expected utility of alternatives. Building a pipeline to discharge treated wastewater to a larger river emerged as a potential consensus alternative to mitigate the problem of micropollutants in a small stream. We investigated the robustness of the findings with sensitivity analysis regarding the preference parameters and the included objectives. In their actual decision, the stakeholders partly preferred other alternatives than those proposed by the model. Their choices could be explained by reduced decision models in which only few objectives were included. This may indicate the use of simplified choice heuristics by the stakeholders. The presented approach is feasible for supporting other difficult environmental or engineering decisions in practice, for which we give a number of recommendations.

Ecological assessment of river networks: From reach to catchment scale.

Freshwater ecosystems are increasingly under threat as they are confronted with multiple anthropogenic impairments. This calls for comprehensive management strategies to counteract, or even prevent, long-term impacts on habitats and their biodiversity, as well as on their ecological functions and services. The basis for the efficient management and effective conservation of any ecosystem is sufficient knowledge on the state of the system and its response to external influence factors. In freshwater ecosystems, state information is currently drawn from ecological assessments at the reach or site scale. While these assessments are essential, they are not sufficient to assess the expected outcome of different river restoration strategies, because they do not account for important characteristics of the whole river network, such as habitat connectivity or headwater reachability. This is of particular importance for the spatial prioritization of restoration measures. River restoration could be supported best by integrative catchment-scale ecological assessments that are sensitive to the spatial arrangement of river reaches and barriers. Assessments at this scale are of increasing interest to environmental managers and conservation practitioners to prioritize restoration measures or to locate areas worth protecting. We present an approach based on decision support methods that integrates abiotic and biotic ecological assessments at the reach-scale and aggregates them spatially to describe the ecological state of entire catchments. This aggregation is based on spatial criteria that represent important ecological catchment properties, such as fish migration potential, resilience, fragmentation and habitat diversity in a spatially explicit way. We identify the most promising assessment criteria from different alternatives based on theoretical considerations and a comparison with biological indicators. Potential applications are discussed, particularly for supporting the strategic, long-term planning and spatial prioritization of restoration measures.

Acoustic Compressibility of Caenorhabditis elegans.

The acoustic compressibility of Caenorhabditis elegans is a necessary parameter for further understanding the underlying physics of acoustic manipulation techniques of this widely used model organism in biological sciences. In this work, numerical simulations were combined with experimental trajectory velocimetry of L1 C. elegans larvae to estimate the acoustic compressibility of C. elegans. A method based on bulk acoustic wave acoustophoresis was used for trajectory velocimetry experiments in a microfluidic channel. The model-based data analysis took into account the different sizes and shapes of L1 C. elegans larvae (255 ± 26 µm in length and 15 ± 2 µm in diameter). Moreover, the top and bottom walls of the microfluidic channel were considered in the hydrodynamic drag coefficient calculations, for both the C. elegans and the calibration particles. The hydrodynamic interaction between the specimen and the channel walls was further minimized by acoustically levitating the C. elegans and the particles to the middle of the measurement channel. Our data suggest an acoustic compressibility κCe of 430 TPa-1 with an uncertainty range of ±20 TPa-1 for C. elegans, a much lower value than what was previously reported for adult C. elegans using static methods. Our estimated compressibility is consistent with the relative volume fraction of lipids and proteins that would mainly make up for the body of C. elegans. This work is a departing point for practical engineering and design criteria for integrated acoustofluidic devices for biological applications.

Thin film piezoelectrics for bulk acoustic wave (BAW) acoustophoresis.

Acoustophoresis, the movement of particles with sound, has evolved as a promising handling tool for micrometer-sized particles. Recent developments in thin film deposition technologies have enabled the reproducible fabrication of thin film piezoelectric materials for miniaturized ultrasound transducers. In this study, we combine both technologies and present the first implementation of a thin film Pb(Zr,Ti)O3 (PZT) transducer as actuation source for bulk acoustic wave (BAW) acoustophoresis. The design and fabrication process was developed for thin film BAW (TFBAW) devices. High-quality piezoelectric layers were produced using Solmates SMP-800 pulsed laser deposition (PLD) equipment which enables wafer-level batch fabrication. Results from simulations and experiments enabled the characterization of different designs and the prediction of the pressure field inside the TFBAW device. Moreover, the acoustic streaming field was analyzed to determine critical particle diameters for acoustophoresis. Operation conditions were identified for the acoustophoretic unit operations particle concentration and sorting. The TFBAW device was able to generate a high acoustic pressure amplitude of 0.55 MPa at a low peak input voltage of 0.5 V. Overall, this study demonstrates that TFBAW devices have the potential of a miniaturized, predictable and reproducible acoustic particle manipulation at a low voltage for lab-on-a-chip applications.

Molecular scale structure and dynamics at an ionic liquid/electrode interface.

After a century of research, the potential-dependent ion distribution at electrode/electrolyte interfaces is still under debate. In particular for solvent-free electrolytes such as room-temperature ionic liquids, classical theories for the electrical double layer are not applicable. Using a combination of in situ high-energy X-ray reflectivity and impedance spectroscopy measurements, we determined this distribution with sub-molecular resolution. We find oscillatory charge density profiles consisting of alternating anion- and cation-enriched layers at both cathodic and anodic potentials. This structure is shown to arise from the same ion-ion correlations dominating the liquid bulk structure. The relaxation dynamics of the interfacial structure upon charging/discharging were studied by impedance spectroscopy and time resolved X-ray reflectivity experiments with sub-millisecond resolution. The analysis revealed three relaxation processes of vastly different characteristic time scales: a 2 ms scale interface-normal ion transport, a 100 ms scale molecular reorientation, and a minute scale lateral ordering within the first layer.

Modeling Macroinvertebrate Community Dynamics in Stream Mesocosms Contaminated with a Pesticide.

Modeling community dynamics of aquatic invertebrates is an important but challenging task, in particular in ecotoxicological risk assessment. Systematic parameter estimation and rigorous assessment of model uncertainty are often lacking in such applications. We applied the mechanistic food web model Streambugs to investigate the temporal development of the macroinvertebrate community in an ecotoxicological mesocosm experiment with pulsed contaminations with the insecticide thiacloprid. We used Bayesian inference to estimate parameters and their uncertainty. Approx. 85% of all experimental observations lie within the 90% uncertainty intervals indicating reasonably good fits of the calibrated model. However, a validation with independent data was not possible due to lacking data. Investigation of vital rates and limiting factors in the model yielded insights into recovery dynamics. Inclusion of the emergence process and sub-lethal effects turned out to be potentially relevant model extensions. Measurements of food source dynamics, individual body size (classes), and additional knowledge on sub-lethal effects would support more accurate modeling. This application of a process-based, ecotoxicological community model with uncertainty assessment by Bayesian inference increased our process understanding of toxicant effects in macroinvertebrate communities and helped identifying potential improvements in model structure and experimental design.

Microfluidic droplet handling by bulk acoustic wave (BAW) acoustophoresis.

Droplet microfluidics has emerged as a prospering field for lab-on-a-chip devices, where droplets serve as liquid vessels e.g. for biochemical reagents. Key to the fluid processing in droplet format are the controlled droplet handling and movement on the microscale. Hence this paper proposes droplet handling by combining droplet microfluidics with bulk acoustic wave (BAW) acoustophoresis. BAW acoustophoresis has formerly focused on cell and particle handling, whereas here we determine the various abilities of this method for the field of droplet microfluidics. In silicon microdevices, water-in-oil droplets of 200 µm size were generated for a set of unit operations including droplet fusion, focusing, sorting and medium exchange around 0.5-1 MHz acoustic frequency. Compared to existing droplet handling methods, the shown method is simple in fabrication, robust in operation and versatile to meet the needs of various droplet processing microfluidic devices.

Solid-liquid interfaces of ionic liquid solutions--Interfacial layering and bulk correlations.

The influence of the polar, aprotic solvent propylene carbonate on the interfacial structure of the ionic liquid (IL) 1-butyl-1-methylpyrrolidinium tris(pentafluoroethyl)trifluorophosphate on sapphire was investigated by high-energy x-ray reflectivity. Experiments at solvent concentrations between 17 mol. % and 83 mol. % bridge the gap between diluted electrolytes described by the classical Gouy-Chapman theory and pure ionic liquids. Analysis of our experimental data revealed interfacial profiles comprised of alternating anion and cation enriched regions decaying gradually into the bulk liquid. With increasing solvent concentration, we observed a decrease in correlation length of the interfacial layering structure. At high ion concentrations, solvent molecules were found to accumulate laterally within the layers. By separating like-charged ions, they reduce their Coulomb repulsion. The results are compared with the bulk structure of IL/solvent blends probed by x-ray scattering and predictions from fundamental fluid theory.

The conceptual foundation of environmental decision support.

Environmental decision support intends to use the best available scientific knowledge to help decision makers find and evaluate management alternatives. The goal of this process is to achieve the best fulfillment of societal objectives. This requires a careful analysis of (i) how scientific knowledge can be represented and quantified, (ii) how societal preferences can be described and elicited, and (iii) how these concepts can best be used to support communication with authorities, politicians, and the public in environmental management. The goal of this paper is to discuss key requirements for a conceptual framework to address these issues and to suggest how these can best be met. We argue that a combination of probability theory and scenario planning with multi-attribute utility theory fulfills these requirements, and discuss adaptations and extensions of these theories to improve their application for supporting environmental decision making. With respect to (i) we suggest the use of intersubjective probabilities, if required extended to imprecise probabilities, to describe the current state of scientific knowledge. To address (ii), we emphasize the importance of value functions, in addition to utilities, to support decisions under risk. We discuss the need for testing "non-standard" value aggregation techniques, the usefulness of flexibility of value functions regarding attribute data availability, the elicitation of value functions for sub-objectives from experts, and the consideration of uncertainty in value and utility elicitation. With respect to (iii), we outline a well-structured procedure for transparent environmental decision support that is based on a clear separation of scientific prediction and societal valuation. We illustrate aspects of the suggested methodology by its application to river management in general and with a small, didactical case study on spatial river rehabilitation prioritization.

Strategic rehabilitation planning of piped water networks using multi-criteria decision analysis.

To overcome the difficulties of strategic asset management of water distribution networks, a pipe failure and a rehabilitation model are combined to predict the long-term performance of rehabilitation strategies. Bayesian parameter estimation is performed to calibrate the failure and replacement model based on a prior distribution inferred from three large water utilities in Switzerland. Multi-criteria decision analysis (MCDA) and scenario planning build the framework for evaluating 18 strategic rehabilitation alternatives under future uncertainty. Outcomes for three fundamental objectives (low costs, high reliability, and high intergenerational equity) are assessed. Exploitation of stochastic dominance concepts helps to identify twelve non-dominated alternatives and local sensitivity analysis of stakeholder preferences is used to rank them under four scenarios. Strategies with annual replacement of 1.5-2% of the network perform reasonably well under all scenarios. In contrast, the commonly used reactive replacement is not recommendable unless cost is the only relevant objective. Exemplified for a small Swiss water utility, this approach can readily be adapted to support strategic asset management for any utility size and based on objectives and preferences that matter to the respective decision makers.

Extension of pipe failure models to consider the absence of data from replaced pipes.

Predictions of the expected number of failures of water distribution network pipes are important to develop an optimal management strategy. A number of probabilistic pipe failure models have been proposed in the literature for this purpose. They have to be calibrated on failure records. However, common data management practices mean that replaced pipes are often absent from available data sets. This leads to a 'survival selection bias', as pipes with frequent failures are more likely to be absent from the data. To address this problem, we propose a formal statistical approach to extend the likelihood function of a pipe failure model by a replacement model. Frequentist maximum likelihood estimation or Bayesian inference can then be applied for parameter estimation. This approach is general and is not limited to a particular failure or replacement model. We implemented this approach with a Weibull-exponential failure model and a simple constant probability replacement model. Based on this distribution assumptions, we illustrated our concept with two examples. First, we used simulated data to show how replacement causes a 'survival selection bias' and how to successfully correct for it. A second example with real data illustrates how a model can be extended to consider covariables.

Bridging the gap between theoretical ecology and real ecosystems: modeling invertebrate community composition in streams.

For the first time, we combine concepts of theoretical food web modeling, the metabolic theory of ecology, and ecological stoichiometry with the use of functional trait databases to predict the coexistence of invertebrate taxa in streams. We developed a mechanistic model that describes growth, death, and respiration of different taxa dependent on various environmental influence factors to estimate survival or extinction. Parameter and input uncertainty is propagated to model results. Such a model is needed to test our current quantitative understanding of ecosystem structure and function and to predict effects of anthropogenic impacts and restoration efforts. The model was tested using macroinvertebrate monitoring data from a catchment of the Swiss Plateau. Even without fitting model parameters, the model is able to represent key patterns of the coexistence structure of invertebrates at sites varying in external conditions (litter input, shading, water quality). This confirms the suitability of the model concept. More comprehensive testing and resulting model adaptations will further increase the predictive accuracy of the model.

A Bayesian network model for integrative river rehabilitation planning and management.

As rehabilitation of previously channelized rivers becomes more common worldwide, flexible integrative modeling tools are needed to help predict the morphological, hydraulic, economic, and ecological consequences of the rehabilitation activities. Such predictions can provide the basis for planning and long-term management efforts that attempt to balance the diverse interests of river system stakeholders. We have previously reported on a variety of modeling methods and decision support concepts that can assist with various aspects of the river rehabilitation process. Here, we bring all of these tools together into a probability network model that links management actions, through morphological and hydraulic changes, to the ultimate ecological and economic consequences. Although our model uses a causal graph representation common to Bayesian networks, we do not limit ourselves to discrete-valued nodes or conditional Gaussian distributions as required by most Bayesian network implementations. This precludes us from carrying out easy probabilistic inference but gives us the advantages of functional and distributional flexibility and enhanced predictive accuracy, which we believe to be more important in most environmental management applications. We exemplify model application to a large, recently completed rehabilitation project in Switzerland.

Age-related changes in the plasticity and toughness of human cortical bone at multiple length scales.

The structure of human cortical bone evolves over multiple length scales from its basic constituents of collagen and hydroxyapatite at the nanoscale to osteonal structures at near-millimeter dimensions, which all provide the basis for its mechanical properties. To resist fracture, bone's toughness is derived intrinsically through plasticity (e.g., fibrillar sliding) at structural scales typically below a micrometer and extrinsically (i.e., during crack growth) through mechanisms (e.g., crack deflection/bridging) generated at larger structural scales. Biological factors such as aging lead to a markedly increased fracture risk, which is often associated with an age-related loss in bone mass (bone quantity). However, we find that age-related structural changes can significantly degrade the fracture resistance (bone quality) over multiple length scales. Using in situ small-angle X-ray scattering and wide-angle X-ray diffraction to characterize submicrometer structural changes and synchrotron X-ray computed tomography and in situ fracture-toughness measurements in the scanning electron microscope to characterize effects at micrometer scales, we show how these age-related structural changes at differing size scales degrade both the intrinsic and extrinsic toughness of bone. Specifically, we attribute the loss in toughness to increased nonenzymatic collagen cross-linking, which suppresses plasticity at nanoscale dimensions, and to an increased osteonal density, which limits the potency of crack-bridging mechanisms at micrometer scales. The link between these processes is that the increased stiffness of the cross-linked collagen requires energy to be absorbed by "plastic" deformation at higher structural levels, which occurs by the process of microcracking.

Exposure of the Irish population to PBDEs in food: consideration of parameter uncertainty and variability for risk assessment.

Polybrominated diphenyl ethers (PBDEs) are brominated flame retardants used to retard the ignition and/or spread of fire. PBDEs are used in various consumer products, such as textiles, mattresses and TV screens. This study presents a chemical risk assessment for the Irish population based on exposure to PBDEs from food. Special regard is given to the influence of parameter uncertainty and variability on the margins of safety. To quantitatively model uncertainty and variability in concentration data and variability in consumer behavior, a hierarchical probabilistic model was constructed. This model was evaluated using a two-dimensional Monte Carlo simulation (2D-MCS) approach. By considering uncertainty and variability in concentration data, margins of safety (MOS) were derived that are lower by a factor of ∼2 compared to MOS based on dose estimates that only consider variability. The lowest MOS is 7.5 × 10(4) for BDE-99, with impaired spermatogenesis as toxic endpoint. Assuming an MOS of 10(4) as acceptable, we conclude that there is no significant risk for human health through intake of contaminated food. To investigate whether additional measurements could improve the quality of dose estimates, the statistic "uncertainty-to-variability (UVR)" was developed. By applying the UVR to our dose estimates, we show that, in our case, the datasets contain little uncertainty and additional measurements would not significantly improve the quality of dose estimates.

Modeling potential herbicide loss to surface waters on the Swiss plateau.

Lack of sufficiently detailed data often limits the applicability of complex transport-reaction models for estimating potential herbicide loss to surface waters. Therefore, there is also a need for simple models that are easy to apply but still capture the main features of the underlying processes. In this study, a simple regression model was developed to assess the vulnerability of catchments in the Swiss Plateau to diffuse herbicide loss to surface waters. The model is designed as a screening tool to rank the catchments in a relative sense and not to calculate Predicted Environmental Concentrations (PEC) of pesticides. The main goal is to capture two dominating factors controlling diffuse herbicide transport into streams and rivers. These factors are herbicide application and fast flow processes that are mainly responsible for herbicide transport. In a first step vulnerability of sites to herbicide loss is estimated based on site-specific conditions irrespective of actual herbicide application. In the second step, this vulnerability assessment is combined with actual herbicide application data to estimate the potential herbicide loss. The fast flow index (FFI), derived from discharge data using a base flow separation method, was applied as a proxy for the amount of fast flow occurring. The influence of catchment attributes (including topographic, climatic and soil data) on the FFI was analyzed using a multiple regression approach based on data from 57 catchments of the Swiss Plateau. By combining regression analysis with mechanistic knowledge, a two factor non-linear model based on river density and soil permeability as dominant input factors was selected as the best model for FFI prediction given the available data. Higher dimensional models had to be excluded because the strong correlation between the potential input factors led to unrealistic dependences while only minimally improving the quality of the fit. The spatial pattern of the predicted FFI as a measure for the vulnerability to diffuse herbicide losses shows a clearly increasing trend from the western to the eastern part of the Swiss Plateau and towards the pre-alpine/alpine regions in the south. In general the pattern of herbicide use corresponds to site conditions typical of a low FFI. However, the spatial analysis revealed exceptions, namely areas in which high actual herbicide use coincides with a high FFI. Despite the uncertainties in the model, this simple approach seems to be useful for supporting site-adapted agricultural practice whenever the higher accuracy of more detailed models is not required or too expensive to achieve. In addition, in combination with data on actual herbicide application, it can support the design of monitoring strategies by identifying critical areas of actual herbicide loss.