Uncertainty propagation in vegetation distribution models based on ensemble classifiers

Ensemble learning techniques are increasingly applied for species and vegetation distribution modelling, often resulting in more accurate predictions. At the same time, uncertainty assessment of distribution models is gaining attention. In this study, Random Forests, an ensemble learning technique, is selected for vegetation distribution modelling based on environmental variables. The impact of two important sources of uncertainty, that is the uncertainty on spatial interpolation of environmental variables and the uncertainty on species clustering into vegetation types, is quantified based on sequential Gaussian simulation and pseudo-randomization tests, respectively. An empirical assessment of the uncertainty propagation to the distribution modelling results indicated a gradual decrease in performance with increasing input uncertainty. The test set error ranged from 30.83% to 52.63% and from 30.83% to 83.62%, when the uncertainty ranges on spatial interpolation and on vegetation clustering, respectively, were fully covered. Shannon’s entropy, which is proposed as a measure for uncertainty of ensemble predictions, revealed a similar increasing trend in prediction uncertainty. The implications of these results in an empirical distribution modelling framework are further discussed with respect to monitoring setup, spatial interpolation and species clustering.     

Predicting tree distributions in an East African biodiversity hotspot: model selection, data bias and envelope uncertainty

The Eastern Arc Mountains (EAMs) of Tanzania and Kenya support some of the most ancient tropical rainforest on Earth. The forests are a global priority for biodiversity conservation and provide vital resources to the Tanzanian population. Here, we make a first attempt to predict the spatial distribution of 40 EAM tree species, using generalised additive models, plot data and environmental predictor maps at sub 1 km resolution. The results of three modelling experiments are presented, investigating predictions obtained by (1) two different procedures for the stepwise selection of predictors, (2) down-weighting absence data, and (3) incorporating an autocovariate term to describe fine-scale spatial aggregation. In response to recent concerns regarding the extrapolation of model predictions beyond the restricted environmental range of training data, we also demonstrate a novel graphical tool for quantifying envelope uncertainty in restricted range niche-based models (envelope uncertainty maps). We find that even for species with very few documented occurrences useful estimates of distribution can be achieved. Initiating selection with a null model is found to be useful for explanatory purposes, while beginning with a full predictor set can over-fit the data. We show that a simple multimodel average of these two best-model predictions yields a superior compromise between generality and precision (parsimony). Down-weighting absences shifts the balance of errors in favour of higher sensitivity, reducing the number of serious mistakes (i.e., falsely predicted absences); however, response functions are more complex, exacerbating uncertainty in larger models. Spatial autocovariates help describe fine-scale patterns of occurrence and significantly improve explained deviance, though if important environmental constraints are omitted then model stability and explanatory power can be compromised. We conclude that the best modelling practice is contingent both on the intentions of the analyst (explanation or prediction) and on the quality of distribution data; generalised additive models have potential to provide valuable information for conservation in the EAMs, but methods must be carefully considered, particularly if occurrence data are scarce. Full results and details of all species models are supplied in an online Appendix.     

Transport and dynamics of toxic pollutants in the natural environment and their effect on human health: research gaps and challenge

The source–pathway–receptor (SPR) approach to human exposure and risk assessment contains considerable uncertainty when using the refined modelling approaches to pollutant transport and dispersal, not least in how compounds of concern might be prioritised, proxy or indicator substances identified and the basic environmental and toxicological data collected. The impact of external environmental variables, urban systems and lifestyle is still poorly understood. This determines exposure of individuals and there are a number of methods being developed to provide more reliable spatial assessments. Within the human body, the dynamics of pollutants and effects on target organs from diffuse, transient sources of exposure sets ambitious challenges for traditional risk assessment approaches. Considerable potential exists in the application of, e.g. physiologically based pharmacokinetic (PBPK) models. The reduction in uncertainties associated with the effects of contaminants on humans, transport and dynamics influencing exposure, implications of adult versus child exposure and lifestyle and the development of realistic toxicological and exposure data are all highlighted as urgent research needs. The potential to integrate environmental with toxicological models provides the next phase of research opportunity and should be used to drive empirical and model assessments.     

Testing ecological models: the meaning of validation

The ecological literature reveals considerable confusion about the meaning of validation in the context of simulation models. The confusion arises as much from semantic and philosophical considerations as from the selection of validation procedures. Validation is not a procedure for testing scientific theory or for certifying the ‘truth’ of current scientific understanding, nor is it a required activity of every modelling project. Validation means that a model is acceptable for its intended use because it meets specified performance requirements.Before validation is undertaken, (1) the purpose of the model, (2) the performance criteria, and (3) the model context must be specified. The validation process can be decomposed into several components: (1) operation, (2) theory, and (3) data. Important concepts needed to understand the model evaluation process are verification, calibration, validation, credibility, and qualification. These terms are defined in a limited technical sense applicable to the evaluation of simulation models, and not as general philosophical concepts. Different tests and standards are applied to the operational, theoretical, and data components. The operational and data components can be validated; the theoretical component cannot.The most common problem with ecological and environmental models is failure to state what the validation criteria are. Criteria must be explicitly stated because there are no universal standards for selecting what test procedures or criteria to use for validation. A test based on comparison of simulated versus observed data is generally included whenever possible. Because the objective and subjective components of validation are not mutually exclusive, disagreements over the meaning of validation can only be resolved by establishing a convention.     

Implications of ecological data constraints for integrated policy and livelihoods modelling: An example from East Kalimantan, Indonesia

Policy and human livelihoods modelling increasingly demands integrated research which requires ecological expertise. However, contributions from ecologists are often based on sparse data. Rather than discounting such data, in this paper we demonstrate how ecological modelling can effectively contribute to the development of policy recommendations in spite of data constraints. In a petrol subsidy analysis in East Kalimantan, Indonesia, we accounted for ecological data uncertainty by (a) assuming large parameter value ranges and (b) conducting a robustness test for policy recommendations. In addition to data scarcity, counter-intuitive results emerged emphasising the need for model validation. These counter-intuitive results indicated that decreasing petrol prices led to increased poverty. This informed a policy recommendation to prevent the reduction of petrol prices below IDR 5500 per litre. Using two key livelihood resources (fish and honey), we found that while a traditional sensitivity analysis suggested highly robust results, a robustness test indicated that policy recommendations would change if the incorrectness of parameter values approached 50%. The results show that ecological modelling can contribute effectively in spite of sparse data to guide policy, as well as identifying future research priorities.     

Modelling the productivity of naturalised pasture in the North Island,New Zealand: a decision tree approach

Decision tree, one of the data mining methods, has been widely used as a modelling approach and has shown better predictive ability than traditional approaches (e.g. regression). However, very little is known from the literature about how the decision tree performs in predicting pasture productivity. In this study, decision tree models were developed to investigate and predict the annual and seasonal productivity of naturalised hill-pasture in the North Island, New Zealand, and were compared with regression models with respect to model fit, validation and predictive accuracy. The results indicated that the decision tree models for annual and seasonal pasture productivity all had a smaller average squared error (ASE) and a higher percentage of correctly predicted cases than the corresponding regression models. The decision tree model for annual pasture productivity had an ASE which was only half of that of the regression model, and correctly predicted 90% of the cases in the model validation which was 10.8 percentage points higher than that of the regression model. Furthermore, the decision tree models for annual and seasonal pasture productivity also clearly revealed the relative importance of environmental and management variables in influencing pasture productivity, and the interaction among these variables. Spring rainfall was the most significant factor influencing annual pasture productivity, while hill slope was the most significant factor influencing spring and winter pasture productivity, and annual P fertiliser input and autumn rainfall were the most significant factors influencing summer and autumn pasture productivity. One limitation of using the decision tree to predict pasture productivity was that it did not generate a continuous prediction, and thus could not detect the influence of small changes in environmental and management variables on pasture productivity.     

Challenges of simulating complex environmental systems at the landscape scale: A controversial dialogue between two cups of espresso

With the advancement of computational systems and the development of model integration concepts, complexity of environmental model systems increased. In contrast to that, theory and knowledge about > environmental systems as well as the capability for environmental systems analyses remained, to a large extent, unchanged. As a consequence, model conceptualization, data gathering, and validation, have faced new challenges that hardly can be tackled by modellers alone. In this discourse-like review, we argue that modelling with reliable simulations of human-environmental interactions necessitate linking modelling and simulation research much stronger to science fields such as landscape ecology, community ecology, eco-hydrology, etc. It thus becomes more and more important to identify the adequate degree of complexity in environmental models (which is not only a technical or methodological question), to ensure data availability, and to test model performance. Even equally important, providing problem specific answers to environmental problems using simulation tools requires addressing end-user and stakeholder requirements during early stages of problem development. In doing so, we avoid modelling and simulation as an end of its own.     

Using global sensitivity analysis of demographic models for ecological impact assessment

Population viability analysis (PVA) is widely used to assess population‐level impacts of environmental changes on species. When combined with sensitivity analysis, PVA yields insights into the effects of parameter and model structure uncertainty. This helps researchers prioritize efforts for further data collection so that model improvements are efficient and helps managers prioritize conservation and management actions. Usually, sensitivity is analyzed by varying one input parameter at a time and observing the influence that variation has over model outcomes. This approach does not account for interactions among parameters. Global sensitivity analysis (GSA) overcomes this limitation by varying several model inputs simultaneously. Then, regression techniques allow measuring the importance of input‐parameter uncertainties. In many conservation applications, the goal of demographic modeling is to assess how different scenarios of impact or management cause changes in a population. This is challenging because the uncertainty of input‐parameter values can be confounded with the effect of impacts and management actions. We developed a GSA method that separates model outcome uncertainty resulting from parameter uncertainty from that resulting from projected ecological impacts or simulated management actions, effectively separating the 2 main questions that sensitivity analysis asks. We applied this method to assess the effects of predicted sea‐level rise on Snowy Plover (Charadrius nivosus). A relatively small number of replicate models (approximately 100) resulted in consistent measures of variable importance when not trying to separate the effects of ecological impacts from parameter uncertainty. However, many more replicate models (approximately 500) were required to separate these effects. These differences are important to consider when using demographic models to estimate ecological impacts of management actions.     

On the role of physical modelling in atmospheric and oceanic forecast

We discuss how physical modelling can be used to reproduce atmospheric or oceanic flows in the laboratory. The similarity conditions for the effects of density stratification and Earth rotation are first presented. Then examples of results obtained on the large ‘Coriolis’ platform in Grenoble are described. These include topographic wakes in a stratified fluid and gravity currents. Physical modelling is not used to get direct results of practical relevance, but rather to test numerical models on specific processes of environmental flows. Therefore it must be performed in close relationship with theory and numerical modelling, using advanced measurement and data assimilation techniques.     

Modelling with uncertainty: Introducing a probabilistic framework to predict animal population dynamics

Predictive population models designed to assist managers and policy makers require an explicit treatment of inherent uncertainty and variability. These are particular concerns when modelling non-native and reintroduced species, when data have been collected within one geographical or ecological context but predictions are required for another, or when extending models to predict the consequences of environmental change (e.g., climate or land-use). We present an aspatial, probabilistic framework of hierarchical process models for predicting population growth even when data are sparse or of poor quality. Insight into the factors affecting population dynamics in real landscapes can be provided and Kullback–Leibler distances are used to compare the relative output of models. This flexible yet robust framework gives easily interpretable results, allowing managers as well as modellers to invalidate anomalous models and apply others to real-life scenarios.We illustrate the framework’s power with a meta-analysis of European wild boar (Sus scrofa) data. We test hypotheses about the effect of geographic region, hunting and mast years on wild boar population growth, to build models of wild boar dynamics for the UK. The framework quantifies the importance of hunting pressure as a driver of population growth, and confirms that reproductive success is greatly decreased in poor mast years, suggesting that the key to predicting wild boar dynamics is to ascertain local hunting pressure and to better understand changing food availability. Geography had no significant effect, indicating that it is not a good proxy for modelling the impact of change in climate or land-use on wild boar populations at the European scale. We use the framework to predict population abundance 9 years after an isolated population of wild boar established in the UK; in a comparison with the only field data and two independent modelling exercises, our framework provides the most robust and informative results.     

The Sensitivity of Population Viability Analysis to Uncertainty about Habitat Requirements: Implications for the Management of the Endangered Southern Brown Bandicoot

Abstract:  Whenever population viability analysis (PVA) models are built to help guide decisions about the management of rare and threatened species, an important component of model building is the specification of a habitat model describing how a species is related to landscape or bioclimatic variables. Model-selection uncertainty may arise because there is often a great deal of ambiguity about which habitat model structure best approximates the true underlying biological processes. The standard approach to incorporate habitat models into PVA is to assume the best habitat model is correct, ignoring habitat-model uncertainty and alternative model structures that may lead to quantitatively different conclusions and management recommendations. Here we provide the first detailed examination of the influence of habitat-model uncertainty on the ranking of management scenarios from a PVA model. We evaluated and ranked 6 management scenarios for the endangered southern brown bandicoot ( Isoodon obesulus ) with PVA models, each derived from plausible competing habitat models developed with logistic regression. The ranking of management scenarios was sensitive to the choice of the habitat model used in PVA predictions. Our results demonstrate the need to incorporate methods into PVA that better account for model uncertainty and highlight the sensitivity of PVA to decisions made during model building. We recommend that researchers search for and consider a range of habitat models when undertaking model-based decision making and suggest that routine sensitivity analyses should be expanded to include an analysis of the impact of habitat-model uncertainty and assumptions.     

Assessment of uncertainties in expert knowledge, illustrated in fuzzy rule-based models

The coherence between different aspects in the environmental system leads to a demand for comprehensive models of this system to explore the effects of different management alternatives. Fuzzy logic has been suggested as a means to extend the application domain of environmental modelling from physical relations to expert knowledge. In such applications the expert describes the system in terms of fuzzy variables and inference rules. The result of the fuzzy reasoning process is a numerical output value. In such a model, as in any other, the model context, structure, technical aspects, parameters and inputs may contribute uncertainties to the model output. Analysis of these contributions in a simplified model for agriculture suitability shows how important information about the accuracy of the expert knowledge in relation to the other uncertainties can be provided. A method for the extensive assessment of uncertainties in compositional fuzzy rule-based models is proposed, combining the evaluation of model structure, input and parameter uncertainties. In an example model, each of these three appear to have the potential to dominate aggregated uncertainty, supporting the relevance of an ample uncertainty approach.     

Model based grouping of species across environmental gradients

We present a novel approach to the statistical analysis and prediction of multispecies data. The approach allows the simultaneous grouping and quantification of multiple species’ responses to environmental gradients. The underlying statistical model is a finite mixture model, where mixing is performed over the individual species’ responses to environmental gradients. Species with similar responses are grouped with minimal information loss. We term these groups species archetypes. Each species archetype has an associated GLM that can be used to predict distributions with appropriate measures of uncertainty. Initially, we illustrate the concept and method using artificial data and then with application to real data comprising 200 species from the Great Barrier Reef (GBR) lagoon on 13 oceanographic and geological gradients from 12°S to 24°S. The 200 species from the GBR are well represented by 15 species archetypes. The model is interpreted through maps of the probability of presence for a fine scale set of locations throughout the study area. Maps of uncertainty are also produced to provide statistical context. The presence of each species archetype was strongly influenced by oceanographic gradients, principally temperature, oxygen and salinity. The number of species in each group ranged from 4 to 34. The method has potential application to the analysis of multispecies distribution patterns and for multispecies management.     

Acknowledging the spatial heterogeneity in modelling/reconstructing carbon dioxide exchange in a northern aapa mire

Chamber method is commonly used to measure the CO₂ exchange from plant communities. Due to low time resolution, actual measurements reflect only momentary CO₂ exchange rates. Therefore, a common way to derive seasonal or annual estimates is to establish models describing the response of CO₂ exchange to environmental variables, and then to reconstruct the CO₂ exchange over the desired time period. There are several alternative ways to obtain the CO₂ balance for the entire mire: models can be parameterized by individual sample plots, plant communities or the entire site. Similarly, the CO₂ balance can be reconstructed by plots, plant communities or the entire site. We tested how the choice of the modelling and reconstruction approach influences the CO₂ exchange estimates for the entire mire and for individual sample plots and plant communities. We measured the CO₂ exchange in a spatially heterogeneous sedge-dominated northern aapa mire for two growing seasons. We observed high spatial variation in CO₂ balance between the plant communities. We noticed that when the CO₂ balances of individual sample plots or plant communities are of interest, using a model appropriate for the entire site may result in biased estimates. In worst case the different modelling approaches may turn the CO₂ balance of an individual sample plot from positive to negative. Further, while using the whole ecosystem approach in modelling, the superior ability of chamber method in acknowledging spatial variation is lost. While the modelled growing season CO₂ balance of the mire ranged from 232 to 625 g CO₂ m⁻² depending on the chosen modelling and reconstruction approach, the average estimates still remained within the uncertainty range of one another. Acknowledgement of the spatial variation in plant community level makes the areal estimate more robust to varying weather conditions. Further, the reliability of estimates is improved by explicit formulation of the choices behind the modelling and reconstruction units reflecting the study objectives.     

Uncertainty and allocation decisions involving unique environmental resources

The implications of the treatment of uncertainty in the definition of optimal investment criteria for irreversible allocations of unique environmental resources are considered herein. This analysis argues that the single-project, orientation of conventional cost-benefit analysis can lead to inconsistent decisions because it fails to take account of the potential for risk pooling across projects. In the models discussed in this paper uncertainty arises because the planner must estimate the net benefits associated with a mix of developed and preserved natural environments. The results suggest that the criteria for optimal investment plans will be affected by those factors influencing this uncertainty. Both the scale and timing of optimal investments may be altered from those prescribed with the conventional (Fisher-Krutilla-Cicchetti rule) framework when the potential for risk pooling is introduced. Thus, it is important to consider as a part of the specification of the objective function the factors which give rise to uncertainty.