Relative information contributions of model vs. data to short- and long-term forecasts of forest carbon dynamics

Using neural ordinary differential equations to predict complex ecological dynamics from population density data

Simple models have been used to describe ecological processes for over a century. However, the complexity of ecological systems makes simple models subject to modelling bias due to simplifying assumptions or unaccounted factors, limiting their predictive power. Neural ordinary differential equations (NODEs) have surged as a machine-learning algorithm that preserves the dynamic nature of the data (Chen et al. 2018 Adv. Neural Inf. Process. Syst.). Although preserving the dynamics in the data is an advantage, the question of how NODEs perform as a forecasting tool of ecological communities is unanswered. Here, we explore this question using simulated time series of competing species in a time-varying environment. We find that NODEs provide more precise forecasts than autoregressive integrated moving average (ARIMA) models. We also find that untuned NODEs have a similar forecasting accuracy to untuned long-short term memory neural networks and both are outperformed in accuracy and precision by empirical dynamical modelling . However, we also find NODEs generally outperform all other methods when evaluating with the interval score, which evaluates precision and accuracy in terms of prediction intervals rather than pointwise accuracy. We also discuss ways to improve the forecasting performance of NODEs. The power of a forecasting tool such as NODEs is that it can provide insights into population dynamics and should thus broaden the approaches to studying time series of ecological communities.

Differential effects of nitrogen vs. phosphorus limitation on terrestrial carbon storage in two subtropical forests: A Bayesian approach

Nitrogen (N) and phosphorus (P) have been demonstrated to limit terrestrial carbon (C) storage in terrestrial ecosystems. However, the reliable indicator to infer N and P limitation are still lacking, especially in subtropical forests. Here we used a terrestrial ecosystem (TECO) model framework in combination with a Bayesian approach to evaluate effects of nutrient limitation from added N/P processes and data sets on C storage capacities in two subtropical forests (Tiantong and Qianyanzhou [QYZ]). Three of the six simulation experiments were developed with assimilating data (TECO C model with C data [C-C], TECO C-N coupling model with C and N data [CN-CN], and TECO C-N-P model with C, N, and P data [CNP-CNP]), and the other three ones were simulated without assimilating data (C-only, CN-only, and CNP-only). We found that P dominantly constrained C storage capacities in Tiantong (42%) whereas N limitation decreased C storage projections in QYZ (44%). Our analysis indicated that the stoichiometry of wood biomass and soil microbe (e.g., N:P ratio) were more sensitive indicators of N or P limitation than that of other pools. Furthermore, effects of P-induced limitation were mainly on root biomass by additional P data and on both metabolic litter and soil organic carbon (SOC) by added P processes. N-induced effects were mainly from added N data that limited plant non-photosynthetic tissues (e.g., woody biomass and litter). The different effects of N and P modules on C storage projections reflected the diverse nutrient acquisition strategies associated with stand ages and plant species under nutrient stressed environment. These findings suggest that the interaction between plants and microorganisms regulate effects of nutrient availability on ecosystem C storage, and stoichiometric flexibility of N and P in plant and soil C pools could improve the representation of N and P limitation in terrestrial ecosystem models.

Stimulation of soil respiration by elevated CO2 is enhanced under nitrogen limitation in a decade-long grassland study

Whether and how CO₂ and nitrogen (N) availability interact to influence carbon (C) cycling processes such as soil respiration remains a question of considerable uncertainty in projecting future C-climate feedbacks, which are strongly influenced by multiple global change drivers, including elevated atmospheric CO₂ concentrations (eCO₂) and increased N deposition. However, because decades of research on the responses of ecosystems to eCO₂ and N enrichment have been done largely independently, their interactive effects on soil respiratory CO₂ efflux remain unresolved. Here, we show that in a multifactor free-air CO₂ enrichment experiment, BioCON (Biodiversity, CO₂, and N deposition) in Minnesota, the positive response of soil respiration to eCO₂ gradually strengthened at ambient (low) N supply but not enriched (high) N supply for the 12-y experimental period from 1998 to 2009. In contrast to earlier years, eCO₂ stimulated soil respiration twice as much at low than at high N supply from 2006 to 2009. In parallel, microbial C degradation genes were significantly boosted by eCO₂ at low but not high N supply. Incorporating those functional genes into a coupled C-N ecosystem model reduced model parameter uncertainty and improved the projections of the effects of different CO₂ and N levels on soil respiration. If our observed results generalize to other ecosystems, they imply widely positive effects of eCO₂ on soil respiration even in infertile systems.

Aboveground Wood Production Is Sustained in the First Growing Season after Phloem-Disrupting Disturbance

Carbon (C) cycling processes are particularly dynamic following disturbance, with initial responses often indicative of longer-term change. In northern Michigan, USA, we initiated the Forest Resilience Threshold Experiment (FoRTE) to identify the processes that sustain or lead to the decline of C cycling rates across multiple levels (0, 45, 65 and 85% targeted gross leaf area index loss) of disturbance severity and, in response, to separate disturbance types preferentially targeting large or small diameter trees. Simulating the effects of boring insects, we stem girdled > 3600 trees below diameter at breast height (DBH), immediately and permanently disrupting the phloem. Weekly DBH measurements of girdled and otherwise healthy trees (n > 700) revealed small but significant increases in daily aboveground wood net primary production (ANPPw) in the 65 and 85% disturbance severity treatments that emerged six weeks after girdling. However, we observed minimal change in end-of-season leaf area index and no significant differences in annual ANPPw among disturbance severities or between disturbance types, suggesting continued C fixation by girdled trees sustained stand-scale wood production in the first growing season after disturbance. We hypothesized higher disturbance severities would favor the growth of early successional species but observed no significant difference between early and middle to late successional species’ contributions to ANPPw across the disturbance severity gradient. We conclude that ANPPw stability immediately following phloem disruption is dependent on the continued, but inevitably temporary, growth of phloem-disrupted trees. Our findings provide insight into the tree-to-ecosystem mechanisms supporting stand-scale wood production stability in the first growing season following a phloem-disrupting disturbance.

Gene-informed decomposition model predicts lower soil carbon loss due to persistent microbial adaptation to warming

Soil microbial respiration is an important source of uncertainty in projecting future climate and carbon (C) cycle feedbacks. However, its feedbacks to climate warming and underlying microbial mechanisms are still poorly understood. Here we show that the temperature sensitivity of soil microbial respiration (Q₁₀) in a temperate grassland ecosystem persistently decreases by 12.0 ± 3.7% across 7 years of warming. Also, the shifts of microbial communities play critical roles in regulating thermal adaptation of soil respiration. Incorporating microbial functional gene abundance data into a microbially-enabled ecosystem model significantly improves the modeling performance of soil microbial respiration by 5–19%, and reduces model parametric uncertainty by 55–71%. In addition, modeling analyses show that the microbial thermal adaptation can lead to considerably less heterotrophic respiration (11.6 ± 7.5%), and hence less soil C loss. If such microbially mediated dampening effects occur generally across different spatial and temporal scales, the potential positive feedback of soil microbial respiration in response to climate warming may be less than previously predicted.

Mechanisms and consequences of the acclimation of soil respiration to warming are unclear. Here, the authors combine soil respiration, metagenomics, and functional gene results from a 7-year grassland warming experiment to a microbial-enzyme decomposition model, showing functional gene information to lower uncertainty and improve fit.

Predicting lymphatic filariasis elimination in data-limited settings: A reconstructive computational framework for combining data generation and model discovery

Although there is increasing importance placed on the use of mathematical models for the effective design and management of long-term parasite elimination, it is becoming clear that transmission models are most useful when they reflect the processes pertaining to local infection dynamics as opposed to generalized dynamics. Such localized models must also be developed even when the data required for characterizing local transmission processes are limited or incomplete, as is often the case for neglected tropical diseases, including the disease system studied in this work, viz. lymphatic filariasis (LF). Here, we draw on progress made in the field of computational knowledge discovery to present a reconstructive simulation framework that addresses these challenges by facilitating the discovery of both data and models concurrently in areas where we have insufficient observational data. Using available data from eight sites from Nigeria and elsewhere, we demonstrate that our data-model discovery system is able to estimate local transmission models and missing pre-control infection information using generalized knowledge of filarial transmission dynamics, monitoring survey data, and details of historical interventions. Forecasts of the impacts of interventions carried out in each site made by the models estimated using the reconstructed baseline data matched temporal infection observations and provided useful information regarding when transmission interruption is likely to have occurred. Assessments of elimination and resurgence probabilities based on the models also suggest a protective effect of vector control against the reemergence of LF transmission after stopping drug treatments. The reconstructive computational framework for model and data discovery developed here highlights how coupling models with available data can generate new knowledge about complex, data-limited systems, and support the effective management of disease programs in the face of critical data gaps.

As modelling becomes commonly used in the design and evaluation of parasite elimination programs, the need for well-defined models and datasets describing the nature of transmission processes in local settings is becoming pronounced. For many neglected tropical diseases, however, data for site-specific model identification are typically sparse or incomplete. In this study, we present a new data-model computational discovery system that couples data-assimilation methods based on existing monitoring survey data with model-generated data about baseline conditions to discover the local transmission models required for simulating the impacts of interventions in typical endemic locations for the macroparasitic disease, lymphatic filariasis (LF). Using data from eight study sites in Nigeria and elsewhere, we show that our reconstructive computational framework is able to combine information contained within partially-available site-specific monitoring data with knowledge of parasite transmission dynamics embedded in process-based models to generate the missing data required for inducing reliable locally applicable LF models. We also show that the models so discovered are able to generate the intervention forecasts required for supporting management-relevant decisions in parasite elimination.

Model parameterization to represent processes at unresolved scales and changing properties of evolving systems

Modeling has become an indispensable tool for scientific research. However, models generate great uncertainty when they are used to predict or forecast ecosystem responses to global change. This uncertainty is partly due to parameterization, which is an essential procedure for model specification via defining parameter values for a model. The classic doctrine of parameterization is that a parameter is constant. However, it is commonly known from modeling practice that a model that is well calibrated for its parameters at one site may not simulate well at another site unless its parameters are tuned again. This common practice implies that parameter values have to vary with sites. Indeed, parameter values that are estimated using a statistically rigorous approach, that is, data assimilation, vary with time, space, and treatments in global change experiments. This paper illustrates that varying parameters is to account for both processes at unresolved scales and changing properties of evolving systems. A model, no matter how complex it is, could not represent all the processes of one system at resolved scales. Interactions of processes at unresolved scales with those at resolved scales should be reflected in model parameters. Meanwhile, it is pervasively observed that properties of ecosystems change over time, space, and environmental conditions. Parameters, which represent properties of a system under study, should change as well. Tuning has been practiced for many decades to change parameter values. Yet this activity, unfortunately, did not contribute to our knowledge on model parameterization at all. Data assimilation makes it possible to rigorously estimate parameter values and, consequently, offers an approach to understand which, how, how much, and why parameters vary. To fully understand those issues, extensive research is required. Nonetheless, it is clear that changes in parameter values lead to different model predictions even if the model structure is the same.

Quantifying the value of surveillance data for improving model predictions of lymphatic filariasis elimination

Background

Mathematical models are increasingly being used to evaluate strategies aiming to achieve the control or elimination of parasitic diseases. Recently, owing to growing realization that process-oriented models are useful for ecological forecasts only if the biological processes are well defined, attention has focused on data assimilation as a means to improve the predictive performance of these models.

Methodology and principal findings

We report on the development of an analytical framework to quantify the relative values of various longitudinal infection surveillance data collected in field sites undergoing mass drug administrations (MDAs) for calibrating three lymphatic filariasis (LF) models (EPIFIL, LYMFASIM, and TRANSFIL), and for improving their predictions of the required durations of drug interventions to achieve parasite elimination in endemic populations. The relative information contribution of site-specific data collected at the time points proposed by the WHO monitoring framework was evaluated using model-data updating procedures, and via calculations of the Shannon information index and weighted variances from the probability distributions of the estimated timelines to parasite extinction made by each model. Results show that data-informed models provided more precise forecasts of elimination timelines in each site compared to model-only simulations. Data streams that included year 5 post-MDA microfilariae (mf) survey data, however, reduced each model’s uncertainty most compared to data streams containing only baseline and/or post-MDA 3 or longer-term mf survey data irrespective of MDA coverage, suggesting that data up to this monitoring point may be optimal for informing the present LF models. We show that the improvements observed in the predictive performance of the best data-informed models may be a function of temporal changes in inter-parameter interactions. Such best data-informed models may also produce more accurate predictions of the durations of drug interventions required to achieve parasite elimination.

Significance

Knowledge of relative information contributions of model only versus data-informed models is valuable for improving the usefulness of LF model predictions in management decision making, learning system dynamics, and for supporting the design of parasite monitoring programmes. The present results further pinpoint the crucial need for longitudinal infection surveillance data for enhancing the precision and accuracy of model predictions of the intervention durations required to achieve parasite elimination in an endemic location.

Although parasite transmission models offer powerful tools for predicting the impacts of interventions, there is growing realization that these models can be useful for this purpose only if their governing biological processes are well defined. Recently, model-data assimilation has been applied to address this problem and improve the performance of process-oriented models for ecological forecasting. Here, we developed an analytical framework that allowed the sequential coupling of the three existing lymphatic filariasis (LF) models with longitudinal infection monitoring data collected in field sites undergoing mass drug administrations (MDAs) to examine the relative value of such data for parameterizing these models and for improving their predictions of the required durations of drug interventions to break parasite transmission. We found that data-informed models provided more precise and reliable forecasts of elimination timelines in the study sites compared to model-only predictions, and that data collected up to 5 years post-MDA reduced each model’s predictive uncertainty most. We also found that this improved performance may be intriguingly related to temporal changes in system dynamics. Our results underscore the significance of sequential model-data fusion for enhancing the understanding of LF transmission dynamics, design of surveillance, and generation of reliable model predictions for management decision making.

Biotic responses buffer warming-induced soil organic carbon loss in Arctic tundra

Climate warming can result in both abiotic (e.g., permafrost thaw) and biotic (e.g., microbial functional genes) changes in Arctic tundra. Recent research has incorporated dynamic permafrost thaw in Earth system models (ESMs) and indicates that Arctic tundra could be a significant future carbon (C) source due to the enhanced decomposition of thawed deep soil C. However, warming-induced biotic changes may influence biologically related parameters and the consequent projections in ESMs. How model parameters associated with biotic responses will change under warming and to what extent these changes affect projected C budgets have not been carefully examined. In this study, we synthesized six data sets over 5 years from a soil warming experiment at the Eight Mile Lake, Alaska, into the Terrestrial ECOsystem (TECO) model with a probabilistic inversion approach. The TECO model used multiple soil layers to track dynamics of thawed soil under different treatments. Our results show that warming increased light use efficiency of vegetation photosynthesis but decreased baseline (i.e., environment-corrected) turnover rates of SOC in both the fast and slow pools in comparison with those under control. Moreover, the parameter changes generally amplified over time, suggesting processes of gradual physiological acclimation and functional gene shifts of both plants and microbes. The TECO model predicted that field warming from 2009 to 2013 resulted in cumulative C losses of 224 or 87 g/m² , respectively, without or with changes in those parameters. Thus, warming-induced parameter changes reduced predicted soil C loss by 61%. Our study suggests that it is critical to incorporate biotic changes in ESMs to improve the model performance in predicting C dynamics in permafrost regions.

Model structures amplify uncertainty in predicted soil carbon responses to climate change

Large model uncertainty in projected future soil carbon (C) dynamics has been well documented. However, our understanding of the sources of this uncertainty is limited. Here we quantify the uncertainties arising from model parameters, structures and their interactions, and how those uncertainties propagate through different models to projections of future soil carbon stocks. Both the vertically resolved model and the microbial explicit model project much greater uncertainties to climate change than the conventional soil C model, with both positive and negative C-climate feedbacks, whereas the conventional model consistently predicts positive soil C-climate feedback. Our findings suggest that diverse model structures are necessary to increase confidence in soil C projection. However, the larger uncertainty in the complex models also suggests that we need to strike a balance between model complexity and the need to include diverse model structures in order to forecast soil C dynamics with high confidence and low uncertainty.

A substantial portion of model uncertainty arises from model parameters and structures. Here, the authors show that alternative model structures with data-driven parameters project greater uncertainty in soil carbon responses to climate change than the conventional soil carbon model.

Temperature sensitivity of soil organic carbon decomposition increased with mean carbon residence time: Field incubation and data assimilation

Temperature sensitivity of soil organic carbon (SOC) decomposition is one of the major uncertainties in predicting climate-carbon (C) cycle feedback. Results from previous studies are highly contradictory with old soil C decomposition being more, similarly, or less sensitive to temperature than decomposition of young fractions. The contradictory results are partly from difficulties in distinguishing old from young SOC and their changes over time in the experiments with or without isotopic techniques. In this study, we have conducted a long-term field incubation experiment with deep soil collars (0-70 cm in depth, 10 cm in diameter of PVC tubes) for excluding root C input to examine apparent temperature sensitivity of SOC decomposition under ambient and warming treatments from 2002 to 2008. The data from the experiment were infused into a multi-pool soil C model to estimate intrinsic temperature sensitivity of SOC decomposition and C residence times of three SOC fractions (i.e., active, slow, and passive) using a data assimilation (DA) technique. As active SOC with the short C residence time was progressively depleted in the deep soil collars under both ambient and warming treatments, the residences times of the whole SOC became longer over time. Concomitantly, the estimated apparent and intrinsic temperature sensitivity of SOC decomposition also became gradually higher over time as more than 50% of active SOC was depleted. Thus, the temperature sensitivity of soil C decomposition in deep soil collars was positively correlated with the mean C residence times. However, the regression slope of the temperature sensitivity against the residence time was lower under the warming treatment than under ambient temperature, indicating that other processes also regulated temperature sensitivity of SOC decomposition. These results indicate that old SOC decomposition is more sensitive to temperature than young components, making the old C more vulnerable to future warmer climate.

Uncertain future soil carbon dynamics under global change predicted by models constrained by total carbon measurements

Pool-based carbon (C) models are widely applied to predict soil C dynamics under global change and infer underlying mechanisms. However, it is unclear about the credibility of model-predicted C pool size, decay rate (k), and/or microbial C use efficiency (e) as only data on bulked total C is usually available for model constraining. Using observing system simulation experiments (OSSE), we constrained a two-pool model using simulated data sets of total soil C dynamics under topical hypotheses on responses of soil C dynamics to warming and elevated CO₂ (i.e., global change scenarios). The results indicated that the model predicted great uncertainties in C pool size, k, and e under all global change scenarios, resulting in the difficulty to correctly infer the presupposed "real" values of those parameters that are used to generate the simulated total soil C for constraining the model. Furthermore, the model using the constrained parameters generated divergent future soil C dynamics. Compared with the predictions using the presupposed real parameters (i.e., the real future C dynamics), the percentage uncertainty in 100-yr predictions using the constrained parameters was up to 45% depending on global change scenarios and data availability for model-constraining. Such great uncertainty was mainly due to the high collinearity among the model parameters. Using pool-based models, we argue that soil C pool size, k, and/or e and their responses to global change have to be estimated explicitly and empirically, rather than through model-fitting, in order to accurately predict C dynamics and infer underlying mechanisms. The OSSE approach provides a powerful way to identify data requirement for the new generation of model development and test model performance.

Where does the carbon go? A model-data intercomparison of vegetation carbon allocation and turnover processes at two temperate forest free-air CO2 enrichment sites

Elevated atmospheric CO2 concentration (eCO2) has the potential to increase vegetation carbon storage if increased net primary production causes increased long-lived biomass. Model predictions of eCO2 effects on vegetation carbon storage depend on how allocation and turnover processes are represented. We used data from two temperate forest free-air CO2 enrichment (FACE) experiments to evaluate representations of allocation and turnover in 11 ecosystem models. Observed eCO2 effects on allocation were dynamic. Allocation schemes based on functional relationships among biomass fractions that vary with resource availability were best able to capture the general features of the observations. Allocation schemes based on constant fractions or resource limitations performed less well, with some models having unintended outcomes. Few models represent turnover processes mechanistically and there was wide variation in predictions of tissue lifespan. Consequently, models did not perform well at predicting eCO2 effects on vegetation carbon storage. Our recommendations to reduce uncertainty include: use of allocation schemes constrained by biomass fractions; careful testing of allocation schemes; and synthesis of allocation and turnover data in terms of model parameters. Data from intensively studied ecosystem manipulation experiments are invaluable for constraining models and we recommend that such experiments should attempt to fully quantify carbon, water and nutrient budgets.

On improving the communication between models and data

The potential for model-data synthesis is growing in importance as we enter an era of 'big data', greater connectivity and faster computation. Realizing this potential requires that the research community broaden its perspective about how and why they interact with models. Models can be viewed as scaffolds that allow data at different scales to inform each other through our understanding of underlying processes. Perceptions of relevance, accessibility and informatics are presented as the primary barriers to broader adoption of models by the community, while an inability to fully utilize the breadth of expertise and data from the community is a primary barrier to model improvement. Overall, we promote a community-based paradigm to model-data synthesis and highlight some of the tools and techniques that facilitate this approach. Scientific workflows address critical informatics issues in transparency, repeatability and automation, while intuitive, flexible web-based interfaces make running and visualizing models more accessible. Bayesian statistics provides powerful tools for assimilating a diversity of data types and for the analysis of uncertainty. Uncertainty analyses enable new measurements to target those processes most limiting our predictive ability. Moving forward, tools for information management and data assimilation need to be improved and made more accessible.

Traceable components of terrestrial carbon storage capacity in biogeochemical models

Biogeochemical models have been developed to account for more and more processes, making their complex structures difficult to be understood and evaluated. Here, we introduce a framework to decompose a complex land model into traceable components based on mutually independent properties of modeled biogeochemical processes. The framework traces modeled ecosystem carbon storage capacity (Xss ) to (i) a product of net primary productivity (NPP) and ecosystem residence time (τE ). The latter τE can be further traced to (ii) baseline carbon residence times (τ'E ), which are usually preset in a model according to vegetation characteristics and soil types, (iii) environmental scalars (ξ), including temperature and water scalars, and (iv) environmental forcings. We applied the framework to the Australian Community Atmosphere Biosphere Land Exchange (CABLE) model to help understand differences in modeled carbon processes among biomes and as influenced by nitrogen processes. With the climate forcings of 1990, modeled evergreen broadleaf forest had the highest NPP among the nine biomes and moderate residence times, leading to a relatively high carbon storage capacity (31.5 kg cm(-2) ). Deciduous needle leaf forest had the longest residence time (163.3 years) and low NPP, leading to moderate carbon storage (18.3 kg cm(-2) ). The longest τE in deciduous needle leaf forest was ascribed to its longest τ'E (43.6 years) and small ξ (0.14 on litter/soil carbon decay rates). Incorporation of nitrogen processes into the CABLE model decreased Xss in all biomes via reduced NPP (e.g., -12.1% in shrub land) or decreased τE or both. The decreases in τE resulted from nitrogen-induced changes in τ'E (e.g., -26.7% in C3 grassland) through carbon allocation among plant pools and transfers from plant to litter and soil pools. Our framework can be used to facilitate data model comparisons and model intercomparisons via tracking a few traceable components for all terrestrial carbon cycle models. Nevertheless, more research is needed to develop tools to decompose NPP and transient dynamics of the modeled carbon cycle into traceable components for structural analysis of land models.

Rate my data: quantifying the value of ecological data for the development of models of the terrestrial carbon cycle

Primarily driven by concern about rising levels of atmospheric CO2, ecologists and earth system scientists are collecting vast amounts of data related to the carbon cycle. These measurements are generally time consuming and expensive to make, and, unfortunately, we live in an era where research funding is increasingly hard to come by. Thus, important questions are: "Which data streams provide the most valuable information?" and "How much data do we need?" These questions are relevant not only for model developers, who need observational data to improve, constrain, and test their models, but also for experimentalists and those designing ecological observation networks. Here we address these questions using a model-data fusion approach. We constrain a process-oriented, forest ecosystem C cycle model with 17 different data streams from the Harvard Forest (Massachusetts, USA). We iteratively rank each data source according to its contribution to reducing model uncertainty. Results show the importance of some measurements commonly unavailable to carbon-cycle modelers, such as estimates of turnover times from different carbon pools. Surprisingly, many data sources are relatively redundant in the presence of others and do not lead to a significant improvement in model performance. A few select data sources lead to the largest reduction in parameter-based model uncertainty. Projections of future carbon cycling were poorly constrained when only hourly net-ecosystem-exchange measurements were used to inform the model. They were well constrained, however, with only 5 of the 17 data streams, even though many individual parameters are not constrained. The approach taken here should stimulate further cooperation between modelers and measurement teams and may be useful in the context of setting research priorities and allocating research funds.

The model-data fusion pitfall: assuming certainty in an uncertain world

Model-data fusion is a powerful framework by which to combine models with various data streams (including observations at different spatial or temporal scales), and account for associated uncertainties. The approach can be used to constrain estimates of model states, rate constants, and driver sensitivities. The number of applications of model-data fusion in environmental biology and ecology has been rising steadily, offering insights into both model and data strengths and limitations. For reliable model-data fusion-based results, however, the approach taken must fully account for both model and data uncertainties in a statistically rigorous and transparent manner. Here we review and outline the cornerstones of a rigorous model-data fusion approach, highlighting the importance of properly accounting for uncertainty. We conclude by suggesting a code of best practices, which should serve to guide future efforts.