Bayesian networks as a novel tool to enhance interpretability and predictive power of ecological models

In today's world, it is becoming increasingly important to have the tools to understand, and ultimately to predict, the response of ecosystems to disturbance. However, understanding such dynamics is not simple. Ecosystems are a complex network of species interactions, and therefore any change to a population of one species will have some degree of community level effect. In recent years, the use of Bayesian networks (BNs) has seen successful applications in molecular biology and ecology, where they were able to recover plausible links in the respective systems they were applied to. The recovered network also comes with a quantifiable metric of interaction strength between variables. While the latter is an invaluable piece of information in ecology, an unexplored application of BNs would be using them as a novel variable selection tool in the training of predictive models. To this end, we evaluate the potential usefulness of BNs in two aspects: (1) we apply BN inference on species abundance data from a rocky shore ecosystem, a system with well documented links, to test the ecological validity of the revealed network; and (2) we evaluate BNs as a novel variable selection method to guide the training of an artificial neural network (ANN). Here, we demonstrate that not only was this approach able to recover meaningful species interactions networks from ecological data, but it also served as a meaningful tool to inform the training of predictive models, where there was an improvement in predictive performance in models with BN variable selection. Combining these results, we demonstrate the potential of this novel application of BNs in enhancing the interpretability and predictive power of ecological models; this has general applicability beyond the studied system, to ecosystems where existing relationships between species and other functional components are unknown.     

Bioclimatic Modeling of Southern African Bioregions and Biomes Using Bayesian Networks

This study uses Bayesian networks (BNs) to simulate the spatial distribution of southern African biomes and bioregions using bioclimatic variables. Two Tree-Augmented Naïve (TAN) BN models were parameterized from 23 bioclimatic variables using the expectation-maximization (EM) algorithm. Using sensitivity analyses, the relative influence of each variable was determined using the mutual information from which six bioclimatic variables were selected for the final models. Precipitation of the warmest quarter and extra-terrestrial solar radiation was found to be the most influential variables on both bioregion and biome distributions. Isothermality was the least influential bioclimatic variable at both bioregion and biome levels. Overall correspondence was very high at 93.8 and 87.1% for biomes and bioregions, respectively, whereas classification errors were obtained in transition areas indicating the uncertainties associated with vegetation mapping around margins. The findings indicate that southern African bioregions and biomes can be classified and mapped according to key bioclimatic variables. Spatio-temporal, in particular, monthly and quarterly variations in both precipitation and temperature are found to be ecologically significant in determining the spatial distribution of biomes and bioregions. The findings also reflect the hierarchical relationship of biomes and bioregions as a function of local bioclimatic gradients and interactions. The results indicate the ecological significance of bioclimatic conditions in ecosystem science and offer the opportunity to utilize the models for predicting future responses and sensitivities to climatic changes.     

Evolving sensitivity balances Boolean Networks

We investigate the sensitivity of Boolean Networks (BNs) to mutations. We are interested in Boolean Networks as a model of Gene Regulatory Networks (GRNs). We adopt Ribeiro and Kauffman's Ergodic Set and use it to study the long term dynamics of a BN. We define the sensitivity of a BN to be the mean change in its Ergodic Set structure under all possible loss of interaction mutations. In silico experiments were used to selectively evolve BNs for sensitivity to losing interactions. We find that maximum sensitivity was often achievable and resulted in the BNs becoming topologically balanced, i.e. they evolve towards network structures in which they have a similar number of inhibitory and excitatory interactions. In terms of the dynamics, the dominant sensitivity strategy that evolved was to build BNs with Ergodic Sets dominated by a single long limit cycle which is easily destabilised by mutations. We discuss the relevance of our findings in the context of Stem Cell Differentiation and propose a relationship between pluripotent stem cells and our evolved sensitive networks.     

Statistical methods in finite element analysis

Finite element analysis (FEA) is a commonly used tool within many areas of engineering and can provide useful information in structural analysis of mechanical systems. However, most analyses within the field of biomechanics usually take no account either of the wide variation in material properties and geometry that may occur in natural tissues or manufacturing imperfections in synthetic materials. This paper discusses two different methods of incorporating uncertainty in FE models. The first, Taguchi's robust parameter design, uses orthogonal matrices to determine how to vary the parameters in a series of FE models, and provides information on the sensitivity of a model to input parameters. The second, probabilistic analysis, enables the distribution of a response variable to be determined from the distributions of the input variables. The methods are demonstrated using a simple example of an FE model of a beam that is assigned material properties and geometry over a range similar to an orthopaedic fixation plate. In addition to showing how each method may be used on its own, we also show how computational effort may be minimised by first identifying the most important input variables before determining the effects of imprecision.     

Sampling and sensitivity analyses tools (SaSAT) for computational modelling

SaSAT (Sampling and Sensitivity Analysis Tools) is a user-friendly software package for applying uncertainty and sensitivity analyses to mathematical and computational models of arbitrary complexity and context. The toolbox is built in Matlab^®, a numerical mathematical software package, and utilises algorithms contained in the Matlab^® Statistics Toolbox. However, Matlab^® is not required to use SaSAT as the software package is provided as an executable file with all the necessary supplementary files. The SaSAT package is also designed to work seamlessly with Microsoft Excel but no functionality is forfeited if that software is not available. A comprehensive suite of tools is provided to enable the following tasks to be easily performed: efficient and equitable sampling of parameter space by various methodologies; calculation of correlation coefficients; regression analysis; factor prioritisation; and graphical output of results, including response surfaces, tornado plots, and scatterplots. Use of SaSAT is exemplified by application to a simple epidemic model. To our knowledge, a number of the methods available in SaSAT for performing sensitivity analyses have not previously been used in epidemiological modelling and their usefulness in this context is demonstrated.     

A hybrid life cycle assessment of water treatment chemicals: an Australian experience

Purpose

Life cycle assessment (LCA) of chemicals is usually developed using a process-based approach. In this paper, we develop a tiered hybrid LCA of water treatment chemicals combining the specificity of process data with the holistic nature of input–output analysis (IOA). We compare these results with process and input–output models for the most commonly used chemicals in the Australian water industry to identify the direct and indirect environmental impacts associated with the manufacturing of these materials.

Methods

We have improved a previous Australian hybrid LCA model by updating the environmental indicators and expanding the number of included industry sectors of the economy. We also present an alternative way to estimate the expenditure vectors to the service sectors of the economy when financial data are not available. Process-based, input–output and hybrid results were calculated for caustic soda, sodium hypochlorite, ferric chloride, aluminium sulphate, fluorosilicic acid, calcium oxide and chlorine gas. The functional unit is the same for each chemical: the production of 1 tonne in the year 2008.

Results and discussion

We have provided results for seven impact categories: global warming potential; primary energy; water use; marine, freshwater and terrestrial ecotoxicity potentials and human toxicity potential. Results are compared with previous IOA and hybrid studies. A sensitivity analysis of the results to assumed wholesale prices is included. We also present insights regarding how hybrid modelling helps to overcome the limitations of using IO- or process-based modelling individually.

Conclusions and recommendations

The advantages of using hybrid modelling have been demonstrated for water treatment chemicals by expanding the boundaries of process-based modelling and also by reducing the sensitivity of IOA to fluctuations in prices of raw materials used for the production of these industrial commodities. The development of robust hybrid life cycle inventory databases is paramount if hybrid modelling is to become a standard practice in attributional LCA.     

Data quality

A methodology is presented that enables incorporating expert judgment regarding the variability of input data for environmental life cycle assessment (LCA) modeling. The quality of input data in the life-cycle inventory (LCI) phase is evaluated by LCA practitioners using data quality indicators developed for this application. These indicators are incorporated into the traditional LCA inventory models that produce non-varying point estimate results (i.e., deterministic models) to develop LCA inventory models that produce results in the form of random variables that can be characterized by probability distributions (i.e., stochastic models). The outputs of these probabilistic LCA models are analyzed using classical statistical methods for better decision and policy making information. This methodology is applied to real-world beverage delivery system LCA inventory models. The inventory study results for five beverage delivery system alternatives are compared using statistical methods that account for the variance in the model output values for each alternative. Sensitivity analyses are also performed that indicate model output value variance increases as input data uncertainty increases (i.e., input data quality degrades). Concluding remarks point out the strengths of this approach as an alternative to providing the traditional qualitative assessment of LCA inventory study input data with no efficient means of examining the combined effects on the model results. Data quality assessments can now be captured quantitatively within the LCA inventory model structure. The approach produces inventory study results that are variables reflecting the uncertainty associated with the input data. These results can be analyzed using statistical methods that make efficient quantitative comparisons of inventory study alternatives possible. Recommendations for future research are also provided that include the screening of LCA inventory model inputs for significance and the application of selection and ranking techniques to the model outputs.     

The Volatility of Data Space: Topology Oriented Sensitivity Analysis

Despite the difference among specific methods, existing Sensitivity Analysis (SA) technologies are all value-based, that is, the uncertainties in the model input and output are quantified as changes of values. This paradigm provides only limited insight into the nature of models and the modeled systems. In addition to the value of data, a potentially richer information about the model lies in the topological difference between pre-model data space and post-model data space. This paper introduces an innovative SA method called Topology Oriented Sensitivity Analysis, which defines sensitivity as the volatility of data space. It extends SA into a deeper level that lies in the topology of data.     

Combined probabilistic and principal component analysis approach for multivariate sensitivity evaluation and application to implanted patellofemoral mechanics

Many aspects of biomechanics are variable in nature, including patient geometry, joint mechanics, implant alignment and clinical outcomes. Probabilistic methods have been applied in computational models to predict distributions of performance given uncertain or variable parameters. Sensitivity analysis is commonly used in conjunction with probabilistic methods to identify the parameters that most significantly affect the performance outcome; however, it does not consider coupled relationships for multiple output measures. Principal component analysis (PCA) has been applied to characterize common modes of variation in shape and kinematics. In this study, a novel, combined probabilistic and PCA approach was developed to characterize relationships between multiple input parameters and output measures. To demonstrate the benefits of the approach, it was applied to implanted patellofemoral (PF) mechanics to characterize relationships between femoral and patellar component alignment and loading and the resulting joint mechanics. Prior studies assessing PF sensitivity have performed individual perturbation of alignment parameters. However, the probabilistic and PCA approach enabled a more holistic evaluation of sensitivity, including identification of combinations of alignment parameters that most significantly contributed to kinematic and contact mechanics outcomes throughout the flexion cycle, and the predictive capability to estimate joint mechanics based on alignment conditions without requiring additional analysis. The approach showed comparable results for Monte Carlo sampling with 500 trials and the more efficient Latin Hypercube sampling with 50 trials. The probabilistic and PCA approach has broad applicability to biomechanical analysis and can provide insight into the interdependencies between implant design, alignment and the resulting mechanics.     

Bayesian Pathway Analysis of Cancer Microarray Data

High Throughput Biological Data (HTBD) requires detailed analysis methods and from a life science perspective, these analysis results make most sense when interpreted within the context of biological pathways. Bayesian Networks (BNs) capture both linear and nonlinear interactions and handle stochastic events in a probabilistic framework accounting for noise making them viable candidates for HTBD analysis. We have recently proposed an approach, called Bayesian Pathway Analysis (BPA), for analyzing HTBD using BNs in which known biological pathways are modeled as BNs and pathways that best explain the given HTBD are found. BPA uses the fold change information to obtain an input matrix to score each pathway modeled as a BN. Scoring is achieved using the Bayesian-Dirichlet Equivalent method and significance is assessed by randomization via bootstrapping of the columns of the input matrix. In this study, we improve on the BPA system by optimizing the steps involved in “Data Preprocessing and Discretization”, “Scoring”, “Significance Assessment”, and “Software and Web Application”. We tested the improved system on synthetic data sets and achieved over 98% accuracy in identifying the active pathways. The overall approach was applied on real cancer microarray data sets in order to investigate the pathways that are commonly active in different cancer types. We compared our findings on the real data sets with a relevant approach called the Signaling Pathway Impact Analysis (SPIA).     

Analysis of macrobenthic communities in Flanders,Belgium, using a stepwise input variable selection procedure with artificial neural networks

The effect of environmental conditions on river macrobenthic communities was studied using a dataset consisting of 343 sediment samples from unnavigable watercourses in Flanders, Belgium. Artificial neural network models were used to analyse the relation among river characteristics and macrobenthic communities. The dataset included presence or absence of macroinvertebrate taxa and 12 physicochemical and hydromorphological variables for each sampling site. The abiotic variables served as input for the artificial neural networks to predict the macrobenthic community. The effects of the input variables on model performance were assessed in order to identify the most diagnostic river characteristics for macrobenthic community composition. This was done by consecutively eliminating the least important variables and, when beneficial for model performance, adding previously removed ones again. This stepwise input variable selection procedure was tested not only on a model predicting the entire macrobenthic community, but also on three models, each predicting an individual taxon. Additionally, during each step of the stepwise leave-one-out procedure, a sensitivity analysis was performed to determine the response of the predicted macroinvertebrate taxa to the input variables applied. This research illustrated that a combination of input variable selection with sensitivity analyses can contribute to the development of reliable and ecologically relevant ANN models. The river characteristics predicting presence or absence of the benthic macroinvertebrates best were the Julian day, conductivity, and dissolved oxygen content. These conditions reflect the importance of discharges of untreated wastewater that occurred during the period of investigation in nearly all Flemish rivers.     

Maximum Number of Fixed Points in Regulatory Boolean Networks

Boolean networks (BNs) have been extensively used as mathematical models of genetic regulatory networks. The number of fixed points of a BN is a key feature of its dynamical behavior. Here, we study the maximum number of fixed points in a particular class of BNs called regulatory Boolean networks, where each interaction between the elements of the network is either an activation or an inhibition. We find relationships between the positive and negative cycles of the interaction graph and the number of fixed points of the network. As our main result, we exhibit an upper bound for the number of fixed points in terms of minimum cardinality of a set of vertices meeting all positive cycles of the network, which can be applied in the design of genetic regulatory networks.     

生态模型的灵敏度分析

灵敏度分析用于定性或定量地评价模型参数误差对模型结果产生的影响,是模型参数化过程和模型校正过程中的有用工具,具有重要的生态学意义．灵敏度分析包括局部灵敏度分析和全局灵敏度分析．局部灵敏度分析只检验单个参数的变化对模型结果的影响程度;全局灵敏度分析则检验多个参数的变化对模型运行结果总的影响,并分析每一个参数及其参数之间相互作用对模型结果的影响．目前,在对生态模型的灵敏度分析中,越来越倾向于使用全局灵敏度分析的方法．但国内仍多采用局部灵敏度分析方法,很少采用全局灵敏度分析方法．文中详细论述了局部灵敏分析和全局灵敏度分析的主要方法(一次变换法、多元回归法、Morris法、Sobol’法、傅里叶幅度灵敏度检验法和傅里叶幅度灵敏度检验扩展法),希望能为国内生态模型的发展提供一个比较完善的灵敏度分析方法库．结合国内外的灵敏度分析发展现状,指出联合灵敏度研究、灵敏度共性研究及空间直观景观模型的灵敏度分析将为生态模型灵敏度分析研究中的热点和难点．     

Cardiac Health Risk Stratification System (CHRiSS): A Bayesian-Based Decision Support System for Left Ventricular Assist Device (LVAD) Therapy

This study investigated the use of Bayesian Networks (BNs) for left ventricular assist device (LVAD) therapy; a treatment for end-stage heart failure that has been steadily growing in popularity over the past decade. Despite this growth, the number of LVAD implants performed annually remains a small fraction of the estimated population of patients who might benefit from this treatment. We believe that this demonstrates a need for an accurate stratification tool that can help identify LVAD candidates at the most appropriate point in the course of their disease. We derived BNs to predict mortality at five endpoints utilizing the Interagency Registry for Mechanically Assisted Circulatory Support (INTERMACS) database: containing over 12,000 total enrolled patients from 153 hospital sites, collected since 2006 to the present day, and consisting of approximately 230 pre-implant clinical variables. Synthetic minority oversampling technique (SMOTE) was employed to address the uneven proportion of patients with negative outcomes and to improve the performance of the models. The resulting accuracy and area under the ROC curve (%) for predicted mortality were 30 day: 94.9 and 92.5; 90 day: 84.2 and 73.9; 6 month: 78.2 and 70.6; 1 year: 73.1 and 70.6; and 2 years: 71.4 and 70.8. To foster the translation of these models to clinical practice, they have been incorporated into a web-based application, the Cardiac Health Risk Stratification System (CHRiSS). As clinical experience with LVAD therapy continues to grow, and additional data is collected, we aim to continually update these BN models to improve their accuracy and maintain their relevance. Ongoing work also aims to extend the BN models to predict the risk of adverse events post-LVAD implant as additional factors for consideration in decision making.     

Growing Bayesian network models of gene networks from seed genes

MOTIVATION: For the last few years, Bayesian networks (BNs) have received increasing attention from the computational biology community as models of gene networks, though learning them from gene-expression data is problematic. Most gene-expression databases contain measurements for thousands of genes, but the existing algorithms for learning BNs from data do not scale to such high-dimensional databases. This means that the user has to decide in advance which genes are included in the learning process, typically no more than a few hundreds, and which genes are excluded from it. This is not a trivial decision. We propose an alternative approach to overcome this problem. RESULTS: We propose a new algorithm for learning BN models of gene networks from gene-expression data. Our algorithm receives a seed gene S and a positive integer R from the user, and returns a BN for the genes that depend on S such that less than R other genes mediate the dependency. Our algorithm grows the BN, which initially only contains S, by repeating the following step R + 1 times and, then, pruning some genes; find the parents and children of all the genes in the BN and add them to it. Intuitively, our algorithm provides the user with a window of radius R around S to look at the BN model of a gene network without having to exclude any gene in advance. We prove that our algorithm is correct under the faithfulness assumption. We evaluate our algorithm on simulated and biological data (Rosetta compendium) with satisfactory results.     

Artificial intelligence-based approaches for modeling the effects of spirulina growth mediums on total phenolic compounds

Spirulina is a microalga and its phenolic compound is affected by growth mediums. In this study, Artificial intelligence (AI) based models, namely the Adaptive-Neuro Fuzzy Inference System (ANFIS) and Multilayer perceptron (MLP) models, and Step-Wise-Linear Regression (SWLR) were used to predict total phenolic compounds (TPC) of the spirulina algae. Spirulina productivity (P), extraction yield (EY), total flavonoids (TF), percent of flavonoid (%F) and percent of phenols (%P) are considered as input variables with the corresponding TPC as an output variable. From the result, TPC has a high positive correlation with the input variables with R = 0.99999. Also, the models showed that the ANFIS and SWLR gives superior result in the testing phase and increased its accuracy by 2% compared to MLP model in the prediction of TPC.     

Artificial neural network modelling of macrophyte indices based on physico-chemical characteristics of water

The study focused on modelling of macropyte indices against physico-chemical parameters of waters by artificial neural networks. Several macrophyte diversity indices were analysed (species richness—N, the Shannon index—H′, the Simpson index—D, and the Pielou index—J) as well as the ecological status index (the Macrophyte Index for Rivers—MIR). The aim of the study was to verify knowledge about potential application of macrophytes in the environmental monitoring. A Multi-Layer Perceptron type of network was used in the analyses. The study included 260 river sites located throughout Poland. Alkalinity, conductivity, pH, nitrate and ammonium nitrogen, reactive and total phosphorus, and biochemical oxygen demand were used as the explanatory variables. The quality of the constructed models was assessed using calculated errors (RMSE and NRMSE) and r Pearson’s linear correlation coefficient. The neural network for the MIR index was characterised by the highest quality. Neural networks for other diversity indices (N, H′, D, and J) did not provide adequate results for modelling, which shows their ineffectiveness biological monitoring. Sensitivity analysis revealed the influence of each variable to the models. It indicated that modelled values of MIR are most strongly influenced by total phosphorus and alkalinity.     

Choice of predictor variables as a source of uncertainty in continental‐scale species distribution modelling under climate change

Aim Species distribution modelling is commonly used to guide future conservation policies in the light of potential climate change. However, arbitrary decisions during the model‐building process can affect predictions and contribute to uncertainty about where suitable climate space will exist. For many species, the key climatic factors limiting distributions are unknown. This paper assesses the uncertainty generated by using different climate predictor variable sets for modelling the impacts of climate change. Location Europe, 10° W to 50° E and 30° N to 60° N. Methods Using 1453 presence pixels at 30 arcsec resolution for the great bustard (Otis tarda), predictions of future distribution were made based on two emissions scenarios, three general climate models and 26 sets of predictor variables. Twenty‐six current models were created, and 156 for both 2050 and 2080. Map comparison techniques were used to compare predictions in terms of the quantity and the location of presences (map comparison kappa, MCK) and using a range change index (RCI). Generalized linear models (GLMs) were used to partition explained deviance in MCK and RCI among sources of uncertainty. Results The 26 different variable sets achieved high values of AUC (area under the receiver operating characteristic curve) and yet introduced substantial variation into maps of current distribution. Differences between maps were even greater when distributions were projected into the future. Some 64–78% of the variation between future maps was attributable to choice of predictor variable set alone. Choice of general climate model and emissions scenario contributed a maximum of 15% variation and their order of importance differed for MCK and RCI. Main conclusions Generalized variable sets produce an unmanageable level of uncertainty in species distribution models which cannot be ignored. The use of sound ecological theory and statistical methods to check predictor variables can reduce this uncertainty, but our knowledge of species may be too limited to make more than arbitrary choices. When all sources of modelling uncertainty are considered together, it is doubtful whether ensemble methods offer an adequate solution. Future studies should explicitly acknowledge uncertainty due to arbitrary choices in the model‐building process and develop ways to convey the results to decision‐makers.