The practice of prediction: What can ecologists learn from applied, ecology-related fields?

Designing More Informative Multiple-Driver Experiments

For decades, multiple-driver/stressor research has examined interactions among drivers that will undergo large changes in the future: temperature, pH, nutrients, oxygen, pathogens, and more. However, the most commonly used experimental designs-present-versus-future and ANOVA-fail to contribute to general understanding or predictive power. Linking experimental design to process-based mathematical models would help us predict how ecosystems will behave in novel environmental conditions. We review a range of experimental designs and assess the best experimental path toward a predictive ecology. Full factorial response surface, fractional factorial, quadratic response surface, custom, space-filling, and especially optimal and sequential/adaptive designs can help us achieve more valuable scientific goals. Experiments using these designs are challenging to perform with long-lived organisms or at the community and ecosystem levels. But they remain our most promising path toward linking experiments and theory in multiple-driver research and making accurate, useful predictions.

Making spatial-temporal marine ecosystem modelling better - A perspective

Marine Ecosystem Models (MEMs) provide a deeper understanding of marine ecosystem dynamics. The United Nations Decade of Ocean Science for Sustainable Development has highlighted the need to deploy these complex mechanistic spatial-temporal models to engage policy makers and society into dialogues towards sustainably managed oceans. From our shared perspective, MEMs remain underutilized because they still lack formal validation, calibration, and uncertainty quantifications that undermines their credibility and uptake in policy arenas. We explore why these shortcomings exist and how to enable the global modelling community to increase MEMs' usefulness. We identify a clear gap between proposed solutions to assess model skills, uncertainty, and confidence and their actual systematic deployment. We attribute this gap to an underlying factor that the ecosystem modelling literature largely ignores: technical issues. We conclude by proposing a conceptual solution that is cost-effective, scalable and simple, because complex spatial-temporal marine ecosystem modelling is already complicated enough.

Evaluating probabilistic ecological forecasts

Probabilistic near-term forecasting facilitates evaluation of model predictions against observations and is of pressing need in ecology to inform environmental decision-making and effect societal change. Despite this imperative, many ecologists are unfamiliar with the widely used tools for evaluating probabilistic forecasts developed in other fields. We address this gap by reviewing the literature on probabilistic forecast evaluation from diverse fields including climatology, economics, and epidemiology. We present established practices for selecting evaluation data (end-sample hold out), graphical forecast evaluation (times-series plots with uncertainty, probability integral transform plots), quantitative evaluation using scoring rules (log, quadratic, spherical, and ranked probability scores), and comparing scores across models (skill score, Diebold-Mariano test). We cover common approaches, highlight mathematical concepts to follow, and note decision points to allow application of general principles to specific forecasting endeavors. We illustrate these approaches with an application to a long-term rodent population time series currently used for ecological forecasting and discuss how ecology can continue to learn from and drive the cross-disciplinary field of forecasting science.

Ecological forecasts reveal limitations of common model selection methods: predicting changes in beaver colony densities

Over the past two decades, there have been numerous calls to make ecology a more predictive science through direct empirical assessments of ecological models and predictions. While the widespread use of model selection using information criteria has pushed ecology toward placing a higher emphasis on prediction, few attempts have been made to validate the ability of information criteria to correctly identify the most parsimonious model with the greatest predictive accuracy. Here, we used an ecological forecasting framework to test the ability of information criteria to accurately predict the relative contribution of density dependence and density-independent factors (forage availability, harvest, weather, wolf [Canis lupus] density) on inter-annual fluctuations in beaver (Castor canadensis) colony densities. We modeled changes in colony densities using a discrete-time Gompertz model, and assessed the performance of four models using information criteria values: density-independent models with (1) and without (2) environmental covariates; and density-dependent models with (3) and without (4) environmental covariates. We then evaluated the forecasting accuracy of each model by withholding the final one-third of observations from each population and compared observed vs. predicted densities. Information criteria and our forecasting accuracy metrics both provided strong evidence of compensatory density dependence in the annual dynamics of beaver colony densities. However, despite strong within-sample performance by the most complex model (density-dependent with covariates) as determined using information criteria, hindcasts of colony densities revealed that the much simpler density-dependent model without covariates performed nearly as well predicting out-of-sample colony densities. The hindcast results indicated that the complex model over-fit our data, suggesting that parameters identified by information criteria as important predictor variables are only marginally valuable for predicting landscape-scale beaver colony dynamics. Our study demonstrates the importance of evaluating ecological models and predictions with long-term data and revealed how a known limitation of information criteria (over-fitting of complex models) can affect our interpretation of ecological dynamics. While incorporating knowledge of the factors that influence animal population dynamics can improve population forecasts, we suggest that comparing forecast performance metrics can likewise improve our knowledge of the factors driving population dynamics.

An epidemiological model for SARS-CoV-2

•

Four transmission pathways are considered in an epidemic model for SARS-CoV-2.

•

The endemic steady-state and conditions for eradication are analytically derived.

•

The model gives realistic values for R0 and the proportion of asymptomatic carriers.

•

Simulations show that the disease can persist after an oscillatory transient.

The spread of SARS-CoV-2 (severe acute respiratory syndrome coronavirus 2) is here investigated from an epidemic model considering four pathways of person-to-person transmission. These pathways represent the propagation of this novel coronavirus by asymptomatic and symptomatic infected individuals. In this work, analytical expressions for the disease-free and endemic steady-states are derived. Also, the conditions for eradication of this contagious disease are determined. By taking into account realistic parameter values, the proposed model shows an oscillatory convergence to the endemic steady-state, which means the occurrence of a sequence of peaks in the number of sick individuals as time passes. These results are discussed from a public health standpoint.

Integrated Assessment of Bioconcentration, Toxicity, and Hazards of Chlorobenzenes in the Aquatic Environment

The evaluation of bioconcentration, toxicity, and hazard (BTH) of persistent lipophilic organic compounds (LOCs) are generally performed as separate rather than integrated assessments. There are adequate data sets in the literature for chlorobenzenes (CBs) consisting of (a) concentrations in aquatic biota (C_B) and water (C_w) in the natural environment, (b) laboratory-derived bioconcentration factors (K_B) and field concentration ratios (CR), the field equivalent factor of K_B, (c) measured internal lethal concentrations (ILC₅₀) and model estimated ILC₅₀ calculated from K_B and lethal concentrations (LC₅₀), and (d) calculated hazard quotients in aquatic biota (HQ_B) and in water (HQ_W). However, there have been no integrated studies of those parameter values based on the respective lipid-based parameters (C_BL, K_BL, CR_L, ILC_50L, HQ_BL) performed. This study utilized the lipid-based parameters for CBs; a group of widely occuring, bioaccumulative, and toxic LOCs, and integrated those parameters into a bioconcentration-toxicity-hazard (BTH_L) index. The values of the parameters were obtained from selected literature with known lipid contents of the aquatic biota. The results showed that the laboratory derived bioconcentration factors, K_BLs, were comparable to the corresponding field based factors, CR_Ls, and the measured internal lethal concentrations, ILC_50L, showed comparable values with the estimated ones. The integrated BTH_L index was less than an order of magnitude or moderately acceptable for the assessment of variability, uncertainty, and predictive power of the index. This integrated assessment can be used to support decision making dealing with CBs in specific and LOCs in general, both in regional and global aquatic environments.

Informing management decisions for ecological networks, using dynamic models calibrated to noisy time-series data

Well-intentioned environmental management can backfire, causing unforeseen damage. To avoid this, managers and ecologists seek accurate predictions of the ecosystem-wide impacts of interventions, given small and imprecise datasets, which is an incredibly difficult task. We generated and analysed thousands of ecosystem population time series to investigate whether fitted models can aid decision-makers to select interventions. Using these time-series data (sparse and noisy datasets drawn from deterministic Lotka-Volterra systems with two to nine species, of known network structure), dynamic model forecasts of whether a species' future population will be positively or negatively affected by rapid eradication of another species were correct > 70% of the time. Although 70% correct classifications is only slightly better than an uninformative prediction (50%), this classification accuracy can be feasibly improved by increasing monitoring accuracy and frequency. Our findings suggest that models may not need to produce well-constrained predictions before they can inform decisions that improve environmental outcomes.

Community dynamics and sensitivity to model structure: towards a probabilistic view of process-based model predictions

Statistical inference and mechanistic, process-based modelling represent two philosophically different streams of research whose primary goal is to make predictions. Here, we merge elements from both approaches to keep the theoretical power of process-based models while also considering their predictive uncertainty using Bayesian statistics. In environmental and biological sciences, the predictive uncertainty of process-based models is usually reduced to parametric uncertainty. Here, we propose a practical approach to tackle the added issue of structural sensitivity, the sensitivity of predictions to the choice between quantitatively close and biologically plausible models. In contrast to earlier studies that presented alternative predictions based on alternative models, we propose a probabilistic view of these predictions that include the uncertainty in model construction and the parametric uncertainty of each model. As a proof of concept, we apply this approach to a predator-prey system described by the classical Rosenzweig-MacArthur model, and we observe that parametric sensitivity is regularly overcome by structural sensitivity. In addition to tackling theoretical questions about model sensitivity, the proposed approach can also be extended to make probabilistic predictions based on more complex models in an operational context. Both perspectives represent important steps towards providing better model predictions in biology, and beyond.

Is structural sensitivity a problem of oversimplified biological models? Insights from nested Dynamic Energy Budget models

Many current issues in ecology require predictions made by mathematical models, which are built on somewhat arbitrary choices. Their consequences are quantified by sensitivity analysis to quantify how changes in model parameters propagate into an uncertainty in model predictions. An extension called structural sensitivity analysis deals with changes in the mathematical description of complex processes like predation. Such processes are described at the population scale by a specific mathematical function taken among similar ones, a choice that can strongly drive model predictions. However, it has only been studied in simple theoretical models. Here, we ask whether structural sensitivity is a problem of oversimplified models. We found in predator-prey models describing chemostat experiments that these models are less structurally sensitive to the choice of a specific functional response if they include mass balance resource dynamics and individual maintenance. Neglecting these processes in an ecological model (for instance by using the well-known logistic growth equation) is not only an inappropriate description of the ecological system, but also a source of more uncertain predictions.