Revealing ecological networks using Bayesian network inference algorithms

Bayesian networks for network inference in biology

Bayesian networks (BNs) have been used for reconstructing interactions from biological data, in disciplines ranging from molecular biology to ecology and neuroscience. BNs learn conditional dependencies between variables, which best 'explain' the data, represented as a directed graph which approximates the relationships between variables. In the 2000s, BNs were a popular method that promised an approach capable of inferring biological networks from data. Here, we review the use of BNs applied to biological data over the past two decades and evaluate their efficacy. We find that BNs are successful in inferring biological networks, frequently identifying novel interactions or network components missed by previous analyses. We suggest that as false positive results are underreported, it is difficult to assess the accuracy of BNs in inferring biological networks. BN learning appears most successful for small numbers of variables with high-quality datasets that either discretize the data into few states or include perturbative data. We suggest that BNs have failed to live up to the promise of the 2000s but that this is most likely due to experimental constraints on datasets, and the success of BNs at inferring networks in a variety of biological contexts suggests they are a powerful tool for biologists.

A framework for identifying factors controlling cyanobacterium Microcystis flos-aquae blooms by coupled CCM-ECCM Bayesian networks

Cyanobacterial blooms in freshwater sources are a global concern, and gaining insight into their causes is crucial for effective resource management and control. In this study, we present a novel computational framework for the causal analysis of cyanobacterial harmful algal blooms (cyanoHABs) in Lake Kinneret. Our framework integrates Convergent Cross Mapping (CCM) and Extended CCM (ECCM) causal networks with Bayesian Network (BN) models. The constructed CCM-ECCM causal networks and BN models unveil significant interactions among factors influencing cyanoHAB formation. These interactions have been validated by domain experts and supported by evidence from peer-reviewed publications. Our findings suggest that Microcystis flos-aquae levels are influenced not only by community structure but also by ammonium, phosphate, oxygen, and temperature levels in the weeks preceding bloom occurrences. We demonstrated a non-parametric computational framework for causal analysis of a multivariate ecosystem. Our framework offers a more comprehensive understanding of the underlying mechanisms driving M. flos-aquae blooms in Lake Kinneret. It captures complex interactions and provides an explainable prediction model. By considering causal relationships, temporal dynamics, and joint probabilities of environmental factors, the proposed framework enhances our understanding of cyanoHABs in Lake Kinneret.

Videla Rodriguez E, Smith VA, van den Brand H, Rodenburg TB, Visser B. A two-step Bayesian network approach to identify key SNPs associated to multiple phenotypic traits in four purebred laying hen lines

When purebred laying hen chicks hatch, they remain at a rearing farm until approximately 17 weeks of age, after which they are transferred to a laying farm. Chicks or pullets are removed from the flocks during these 17 weeks if they display any rearing abnormality. The aim of this study was to investigate associations between single nucleotide polymorphisms (SNPs) and rearing success of 4 purebred White Leghorns layer lines by implementing a Bayesian network approach. Phenotypic traits and SNPs of four purebred genetic White Leghorn layer lines were available for 23,000 rearing batches obtained between 2010 and 2020. Associations between incubation traits (clutch size, embryo mortality), rearing traits (genetic line, first week mortality, rearing abnormalities, natural death, rearing success, pullet flock age, and season) and SNPs were analyzed, using a two-step Bayesian Network (BN) approach. Furthermore, the SNPs were connected to their corresponding genes, which were further explored in bioinformatics databases. BN analysis revealed a total of 28 SNPs associated with some of the traits: ten SNPs were associated with clutch size, another 10 with rearing abnormalities, a single SNP with natural death, and seven SNPs with first week mortality. Exploration via bioinformatics databases showed that one of the SNPs (ENAH) had a protein predicted network composed of 11 other proteins. The major hub of this SNP was CDC42 protein, which has a role in egg production and reproduction. The results highlight the power of BNs in knowledge discovery and how their application in complex biological systems can help getting a deeper understanding of functionality underlying genetic variation of rearing success in laying hens. Improved welfare and production might result from the identified SNPs. Selecting for these SNPs through breeding could reduce stress and increase livability during rearing.

Bayesian network highlights the contributing factors for efficient arsenic phytoextraction by Pteris vittata in a contaminated field

Phytoextraction is a low-cost and eco-friendly method for removing pollutants, such as arsenic (As), from contaminated soil. One of the most studied As hyperaccumulators for soil remediation include Pteris vittata. Although phytoextraction using plant-assisted microbes has been considered a promising soil remediation method, microbial harnessing has not been achieved due to the complex and difficult to understand interactions between microbes and plants. This problem can possibly be addressed with a multi-omics approach using a Bayesian network. However, limited studies have used Bayesian networks to analyze plant-microbe interactions. Therefore, to understand this complex interaction and to facilitate efficient As phytoextraction using microbial inoculants, we conducted field cultivation experiments at two sites with different total As contents (62 and 8.9 mg/kg). Metabolome and microbiome data were obtained from rhizosphere soil samples using nuclear magnetic resonance and high-throughput sequencing, respectively, and a Bayesian network was applied to the obtained multi-omics data. In a highly As-contaminated site, inoculation with Pseudomonas sp. strain m307, which is an arsenite-oxidizing microbe having multiple copies of the arsenite oxidase gene, increased As concentration in the shoots of P. vittata to 157.5 mg/kg under this treatment; this was 1.5-fold higher than that of the other treatments. Bayesian network demonstrated that strain m307 contributed to As accumulation in P. vittata. Furthermore, the network showed that microbes belonging to the MND1 order positively contributed to As accumulation in P. vittata. Based on the ecological characteristics of MND1, it was suggested that the rhizosphere of P. vittata inoculated with strain m307 was under low-nitrogen conditions. Strain m307 may have induced low-nitrogen conditions via arsenite oxidation accompanied by nitrate reduction, potentially resulting in microbial iron reduction or the prevention of microbial iron oxidation. These conditions may have enhanced the bioavailability of arsenate, leading to increased As accumulation in P. vittata.

New insight into blue carbon stocks and natural-human drivers under reclamation history districts for sustainable coastal development: A case study from Liaohe River Delta, China

Blue carbon is a vital aspect of climate change mitigation, which necessitates the identification of stocks and drivers for implementing mitigation strategies. However, reclamation may be among the most invasive forms, and the question of its influence has not been addressed well in blue carbon research. Therefore, the effects of reclamation on carbon stocks and the interaction of crucial drivers from reclamation time areas (1930s, 1960s, 1990s) were evaluated in the Liaohe River Delta (LRD) and compared with natural reserves (core, buffer, experimental areas). Carbon stocks based on InVEST model were lower than preexisting conditions (1.930 × 10⁶ Mg-1.893 × 10⁶ Mg). One-way Analysis of Variance showed that average carbon stocks accumulated 55 years after reclamation and reached the lowest value (13.19 Mg·ha^-1) in 85 years. The interaction analysis of dominant drivers affecting carbon showed the difference between reclaimed areas and reserves regarding potential effect pathways. In the 1930s and 1960s reclamation time areas, crop yield and industrial output determined blue carbon by changing NO₃^--N and AP. In the 1990s reclamation time area, population density played an important role. In defining the impact of vegetation cover on carbon within the reserves, the distance to the coast and residence were significant factors. This study demonstrated that coastal management practices, such as the size of industry and population control and the balanced fertilization techniques in reclamation areas, maintaining adequate vegetation cover in reserve, played a crucial role in the improvement of blue carbon sinks.

Treatment of missing data in Bayesian network structure learning: an application to linked biomedical and social survey data

BACKGROUND

Availability of linked biomedical and social science data has risen dramatically in past decades, facilitating holistic and systems-based analyses. Among these, Bayesian networks have great potential to tackle complex interdisciplinary problems, because they can easily model inter-relations between variables. They work by encoding conditional independence relationships discovered via advanced inference algorithms. One challenge is dealing with missing data, ubiquitous in survey or biomedical datasets. Missing data is rarely addressed in an advanced way in Bayesian networks; the most common approach is to discard all samples containing missing measurements. This can lead to biased estimates. Here, we examine how Bayesian network structure learning can incorporate missing data.

METHODS

We use a simulation approach to compare a commonly used method in frequentist statistics, multiple imputation by chained equations (MICE), with one specific for Bayesian network learning, structural expectation-maximization (SEM). We simulate multiple incomplete categorical (discrete) data sets with different missingness mechanisms, variable numbers, data amount, and missingness proportions. We evaluate performance of MICE and SEM in capturing network structure. We then apply SEM combined with community analysis to a real-world dataset of linked biomedical and social data to investigate associations between socio-demographic factors and multiple chronic conditions in the US elderly population.

RESULTS

We find that applying either method (MICE or SEM) provides better structure recovery than doing nothing, and SEM in general outperforms MICE. This finding is robust across missingness mechanisms, variable numbers, data amount and missingness proportions. We also find that imputed data from SEM is more accurate than from MICE. Our real-world application recovers known inter-relationships among socio-demographic factors and common multimorbidities. This network analysis also highlights potential areas of investigation, such as links between cancer and cognitive impairment and disconnect between self-assessed memory decline and standard cognitive impairment measurement.

CONCLUSION

Our simulation results suggest taking advantage of the additional information provided by network structure during SEM improves the performance of Bayesian networks; this might be especially useful for social science and other interdisciplinary analyses. Our case study show that comorbidities of different diseases interact with each other and are closely associated with socio-demographic factors.

Practical application of a Bayesian network approach to poultry epigenetics and stress

Background

Relationships among genetic or epigenetic features can be explored by learning probabilistic networks and unravelling the dependencies among a set of given genetic/epigenetic features. Bayesian networks (BNs) consist of nodes that represent the variables and arcs that represent the probabilistic relationships between the variables. However, practical guidance on how to make choices among the wide array of possibilities in Bayesian network analysis is limited. Our study aimed to apply a BN approach, while clearly laying out our analysis choices as an example for future researchers, in order to provide further insights into the relationships among epigenetic features and a stressful condition in chickens (Gallus gallus).

Results

Chickens raised under control conditions (n = 22) and chickens exposed to a social isolation protocol (n = 24) were used to identify differentially methylated regions (DMRs). A total of 60 DMRs were selected by a threshold, after bioinformatic pre-processing and analysis. The treatment was included as a binary variable (control = 0; stress = 1). Thereafter, a BN approach was applied: initially, a pre-filtering test was used for identifying pairs of features that must not be included in the process of learning the structure of the network; then, the average probability values for each arc of being part of the network were calculated; and finally, the arcs that were part of the consensus network were selected. The structure of the BN consisted of 47 out of 61 features (60 DMRs and the stressful condition), displaying 43 functional relationships. The stress condition was connected to two DMRs, one of them playing a role in tight and adhesive intracellular junctions in organs such as ovary, intestine, and brain.

Conclusions

We clearly explain our steps in making each analysis choice, from discrete BN models to final generation of a consensus network from multiple model averaging searches. The epigenetic BN unravelled functional relationships among the DMRs, as well as epigenetic features in close association with the stressful condition the chickens were exposed to. The DMRs interacting with the stress condition could be further explored in future studies as possible biomarkers of stress in poultry species.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12859-022-04800-0.

A Bayesian network structure learning approach to identify genes associated with stress in spleens of chickens

Differences in the expression patterns of genes have been used to measure the effects of non-stress or stress conditions in poultry species. However, the list of genes identified can be extensive and they might be related to several biological systems. Therefore, the aim of this study was to identify a small set of genes closely associated with stress in a poultry animal model, the chicken (Gallus gallus), by reusing and combining data previously published together with bioinformatic analysis and Bayesian networks in a multi-step approach. Two datasets were collected from publicly available repositories and pre-processed. Bioinformatics analyses were performed to identify genes common to both datasets that showed differential expression patterns between non-stress and stress conditions. Bayesian networks were learnt using a Simulated Annealing algorithm implemented in the software Banjo. The structure of the Bayesian network consisted of 16 out of 19 genes together with the stress condition. Network structure showed CARD19 directly connected to the stress condition plus highlighted CYGB, BRAT1, and EPN3 as relevant, suggesting these genes could play a role in stress. The biological functionality of these genes is related to damage, apoptosis, and oxygen provision, and they could potentially be further explored as biomarkers of stress.

Use of spatio-temporal habitat suitability modelling to prioritise areas for common carp biocontrol in Australia using the virus CyHV-3

Common carp (Cyprinus carpio) are an invasive species of the rivers and waterways of south-eastern Australia, implicated in the serious decline of many native fish species. Over the past 50 years a variety of control options have been explored, all of which to date have proved either ineffective or cost prohibitive. Most recently the use of cyprinid herpesvirus 3 (CyHV-3) has been proposed as a biocontrol agent, but to assess the risks and benefits of this, as well as to develop a strategy for the release of the virus, a knowledge of the fundamental processes driving carp distribution and abundance is required. To this end, we developed a novel process-based modelling framework that integrates expert opinion with spatio-temporal datasets via the construction of a Bayesian Network. The resulting weekly networks thus enabled an estimate of the habitat suitability for carp across a range of hydrological habitats in south-eastern Australia, covering five diverse catchment areas encompassing in total a drainage area of 132,129 km² over a period of 17-27 years. This showed that while suitability for adult and subadult carp was medium-high across most habitats throughout the period, nevertheless the majority of habitats were poorly suited for the recruitment of larvae and young-of-year (YOY). Instead, high population abundance was confirmed to depend on a small number of recruitment hotspots which occur in years of favourable inundation. Quantification of the underlying ecological drivers of carp abundance thus makes possible detailed planning by focusing on critical weaknesses in the population biology of carp. More specifically, it permits the rational planning for population reduction using the biocontrol agent, CyHV-3, targeting areas where the total population density is above a "damage threshold" of approximately 100 kg/ha.

Inferring species interactions from ecological survey data: A mechanistic approach to predict quantitative food webs of seed feeding by carabid beetles

Ecological networks are valuable for ecosystem analysis but their use is often limited by a lack of data because many types of ecological interaction, for example, predation, are short-lived and difficult to observe or detect. While there are different methods for inferring the presence of interactions, they have rarely been used to predict the interaction strengths that are required to construct weighted, or quantitative, ecological networks.Here, we develop a trait-based approach suitable for inferring weighted networks, that is, with varying interaction strengths. We developed the method for seed-feeding carabid ground beetles (Coleoptera: Carabidae) although the principles can be applied to other species and types of interaction.Using existing literature data from experimental seed-feeding trials, we predicted a per-individual interaction cost index based on carabid and seed size. This was scaled up to the population level to create inferred weighted networks using the abundance of carabids and seeds from empirical samples and energetic intake rates of carabids from the literature. From these weighted networks, we also derived a novel measure of expected predation pressure per seed type per network.This method was applied to existing ecological survey data from 255 arable fields with carabid data from pitfall traps and plant seeds from seed rain traps. Analysis of these inferred networks led to testable hypotheses about how network structure and predation pressure varied among fields.Inferred networks are valuable because (a) they provide null models for the structuring of food webs to test against empirical species interaction data, for example, DNA analysis of carabid gut regurgitates and (b) they allow weighted networks to be constructed whenever we can estimate interactions between species and have ecological census data available. This permits ecological network analysis even at times and in places when interactions were not directly assessed.

Bayesian Network Analysis reveals resilience of the jellyfish Aurelia aurita to an Irish Sea regime shift

Robust time-series of direct observations of jellyfish abundance are not available for many ecosystems, leaving it difficult to determine changes in jellyfish abundance, the possible causes (e.g. climate change) or the consequences (e.g. trophic cascades). We sought an indirect ecological route to reconstruct jellyfish abundance in the Irish Sea: since zooplankton are jellyfish prey, historic variability in zooplankton communities may provide proxies for jellyfish abundance. We determined the Bayesian ecological network of jellyfish-zooplankton dependencies using jellyfish- and zooplankton-abundance data obtained using nets during a 2-week cruise to the Irish Sea in 2008. This network revealed that Aurelia aurita abundance was dependent on zooplankton groups Warm Temperate and Temperate Oceanic as defined by previous zooplankton ecology work. We then determined historic zooplankton networks across the Irish Sea from abundance data from Continuous Plankton Recorder surveys conducted between 1970 and 2000. Transposing the 2008 spatial dependencies onto the historic networks revealed that Aurelia abundance was more strongly dependent over time on sea surface temperature than on the zooplankton community. The generalist predatory abilities of Aurelia may have insulated this jellyfish over the 1985 regime shift when zooplankton composition in the Irish Sea changed abruptly, and also help explain its globally widespread distribution.

Fish ecotyping based on machine learning and inferred network analysis of chemical and physical properties

Functional diversity rather than species richness is critical for the understanding of ecological patterns and processes. This study aimed to develop novel integrated analytical strategies for the functional characterization of fish diversity based on the quantification, prediction and integration of the chemical and physical features in fish muscles. Machine learning models with an improved random forest algorithm applied on 1867 muscle nuclear magnetic resonance spectra belonging to 249 fish species successfully predicted the mobility patterns of fishes into four categories (migratory, territorial, rockfish, and demersal) with accuracies of 90.3-95.4%. Markov blanket-based feature selection method with an ecological-chemical-physical integrated network based on the Bayesian network inference algorithm highlighted the importance of nitrogen metabolism, which is critical for environmental adaptability of fishes in nutrient-rich environments, in the functional characterization of fish biodiversity. Our study provides valuable information and analytical strategies for fish home-range assessment on the basis of the chemical and physical characterization of fish muscle, which can serve as an ecological indicator for fish ecotyping and human impact monitoring.

Revealing antibiotic cross-resistance patterns in hospitalized patients through Bayesian network modelling

OBJECTIVES

Microbial resistance exhibits dependency patterns between different antibiotics, termed cross-resistance and collateral sensitivity. These patterns differ between experimental and clinical settings. It is unclear whether the differences result from biological reasons or from confounding, biasing results found in clinical settings. We set out to elucidate the underlying dependency patterns between resistance to different antibiotics from clinical data, while accounting for patient characteristics and previous antibiotic usage.

METHODS

Additive Bayesian network modelling was employed to simultaneously estimate relationships between variables in a dataset of bacterial cultures derived from hospitalized patients and tested for resistance to multiple antibiotics. Data contained resistance results, patient demographics and previous antibiotic usage, for five bacterial species: Escherichia coli (n = 1054), Klebsiella pneumoniae (n = 664), Pseudomonas aeruginosa (n = 571), CoNS (n = 495) and Proteus mirabilis (n = 415).

RESULTS

All links between resistance to the various antibiotics were positive. Multiple direct links between resistance of antibiotics from different classes were observed across bacterial species. For example, resistance to gentamicin in E. coli was directly linked with resistance to ciprofloxacin (OR = 8.39, 95% credible interval 5.58-13.30) and sulfamethoxazole/trimethoprim (OR = 2.95, 95% credible interval 1.97-4.51). In addition, resistance to various antibiotics was directly linked with previous antibiotic usage.

CONCLUSIONS

Robust relationships among resistance to antibiotics belonging to different classes, as well as resistance being linked to having taken antibiotics of a different class, exist even when taking into account multiple covariate dependencies. These relationships could help inform choices of antibiotic treatment in clinical settings.

Benthic ecosystem cascade effects in Antarctica using Bayesian network inference

Antarctic sea-floor communities are unique, and more closely resemble those of the Palaeozoic than equivalent contemporary habitats. However, comparatively little is known about the processes that structure these communities or how they might respond to anthropogenic change. In order to investigate likely consequences of a decline or removal of key taxa on community dynamics we use Bayesian network inference to reconstruct ecological networks and infer changes of taxon removal. Here we show that sponges have the greatest influence on the dynamics of the Antarctic benthos. When we removed sponges from the network, the abundances of all major taxa reduced by a mean of 42%, significantly more than changes of substrate. To our knowledge, this study is the first to demonstrate the cascade effects of removing key ecosystem structuring organisms from statistical analyses of Antarctica data and demonstrates the importance of considering the community dynamics when planning ecosystem management.

System-Specific Complex Interactions Shape Soil Organic Carbon Distribution in Coastal Salt Marshes

Coastal wetlands provide many critical ecosystem services including carbon storage. Soil organic carbon (SOC) is the most important component of carbon stock in coastal salt marshes. However, there are large uncertainties when estimating SOC stock in coastal salt marshes at large spatial scales. So far, information on the spatial heterogeneity of SOC distribution and determinants remains limited. Moreover, the role of complex ecological interactions in shaping SOC distribution is poorly understood. Here, we report detailed field surveys on plant, soil and crab burrowing activities in two inter-tidal salt marsh sites with similar habitat conditions in Eastern China. Our between-site comparison revealed slight differences in SOC storage and a similar vertical SOC distribution pattern across soil depths of 0–60 cm. Between the two study sites, we found substantially different effects of biotic and abiotic factors on SOC distribution. Complex interactions involving indirect effects between soil, plants and macrobenthos (crabs) may influence SOC distribution at a landscape scale. Marked differences in the SOC determinants between the study sites indicate that the underlying driving mechanisms of SOC distribution are strongly system-specific. Future work taking into account complex interactions and spatial heterogeneity is needed for better estimating of blue carbon stock and dynamics.

Identification of conservation and restoration priority areas in the Danube River based on the multi-functionality of river-floodplain systems

Large river-floodplain systems are hotspots of biodiversity and ecosystem services but are also used for multiple human activities, making them one of the most threatened ecosystems worldwide. There is wide evidence that reconnecting river channels with their floodplains is an effective measure to increase their multi-functionality, i.e., ecological integrity, habitats for multiple species and the multiple functions and services of river-floodplain systems, although, the selection of promising sites for restoration projects can be a demanding task. In the case of the Danube River in Europe, planning and implementation of restoration projects is substantially hampered by the complexity and heterogeneity of the environmental problems, lack of data and strong differences in socio-economic conditions as well as inconsistencies in legislation related to river management. We take a quantitative approach based on best-available data to assess biodiversity using selected species and three ecosystem services (flood regulation, crop pollination, and recreation), focused on the navigable main stem of the Danube River and its floodplains. We spatially prioritize river-floodplain segments for conservation and restoration based on (1) multi-functionality related to biodiversity and ecosystem services, (2) availability of remaining semi-natural areas and (3) reversibility as it relates to multiple human activities (e.g. flood protection, hydropower and navigation). Our approach can thus serve as a strategic planning tool for the Danube and provide a method for similar analyses in other large river-floodplain systems.

Community structure informs species geographic distributions

Understanding what determines species’ geographic distributions is crucial for assessing global change threats to biodiversity. Measuring limits on distributions is usually, and necessarily, done with data at large geographic extents and coarse spatial resolution. However, survival of individuals is determined by processes that happen at small spatial scales. The relative abundance of coexisting species (i.e. ‘community structure’) reflects assembly processes occurring at small scales, and are often available for relatively extensive areas, so could be useful for explaining species distributions. We demonstrate that Bayesian Network Inference (BNI) can overcome several challenges to including community structure into studies of species distributions, despite having been little used to date. We hypothesized that the relative abundance of coexisting species can improve predictions of species distributions. In 1570 assemblages of 68 Mediterranean woody plant species we used BNI to incorporate community structure into Species Distribution Models (SDMs), alongside environmental information. Information on species associations improved SDM predictions of community structure and species distributions moderately, though for some habitat specialists the deviance explained increased by up to 15%. We demonstrate that most species associations (95%) were positive and occurred between species with ecologically similar traits. This suggests that SDM improvement could be because species co-occurrences are a proxy for local ecological processes. Our study shows that Bayesian Networks, when interpreted carefully, can be used to include local conditions into measurements of species’ large-scale distributions, and this information can improve the predictions of species distributions.

Ecological Network Inference From Long-Term Presence-Absence Data

Ecological communities are characterized by complex networks of trophic and nontrophic interactions, which shape the dy-namics of the community. Machine learning and correlational methods are increasingly popular for inferring networks from co-occurrence and time series data, particularly in microbial systems. In this study, we test the suitability of these methods for inferring ecological interactions by constructing networks using Dynamic Bayesian Networks, Lasso regression, and Pear-son’s correlation coefficient, then comparing the model networks to empirical trophic and nontrophic webs in two ecological systems. We find that although each model significantly replicates the structure of at least one empirical network, no model significantly predicts network structure in both systems, and no model is clearly superior to the others. We also find that networks inferred for the Tatoosh intertidal match the nontrophic network much more closely than the trophic one, possibly due to the challenges of identifying trophic interactions from presence-absence data. Our findings suggest that although these methods hold some promise for ecological network inference, presence-absence data does not provide enough signal for models to consistently identify interactions, and networks inferred from these data should be interpreted with caution.

Longitudinal Prediction of the Infant Gut Microbiome with Dynamic Bayesian Networks

Sequencing of the 16S rRNA gene allows comprehensive assessment of bacterial community composition from human body sites. Previously published and publicly accessible data on 58 preterm infants in the Neonatal Intensive Care Unit who underwent frequent stool collection was used. We constructed Dynamic Bayesian Networks from the data and analyzed predictive performance and network characteristics. We constructed a DBN model of the infant gut microbial ecosystem, which explicitly captured specific relationships and general trends in the data: increasing amounts of Clostridia, residual amounts of Bacilli, and increasing amounts of Gammaproteobacteria that then give way to Clostridia. Prediction performance of DBNs with fewer edges were overall more accurate, although less so on harder-to-predict subjects (p = 0.045). DBNs provided quantitative likelihood estimates for rare abruptions events. Iterative prediction was less accurate (p < 0.001), but showed remarkable insensitivity to initial conditions and predicted convergence to a mix of Clostridia, Gammaproteobacteria, and Bacilli. DBNs were able to identify important relationships between microbiome taxa and predict future changes in microbiome composition from measured or synthetic initial conditions. DBNs also provided likelihood estimates for sudden, dramatic shifts in microbiome composition, which may be useful in guiding further analysis of those samples.

Bayesian inference-based environmental decision support systems for oil spill response strategy selection

Contingency plans are essential in guiding the response to marine oil spills. However, they are written before the pollution event occurs so must contain some degree of assumption and prediction and hence may be unsuitable for a real incident when it occurs. The use of Bayesian networks in ecology, environmental management, oil spill contingency planning and post-incident analysis is reviewed and analysed to establish their suitability for use as real-time environmental decision support systems during an oil spill response. It is demonstrated that Bayesian networks are appropriate for facilitating the re-assessment and re-validation of contingency plans following pollutant release, thus helping ensure that the optimum response strategy is adopted. This can minimise the possibility of sub-optimal response strategies causing additional environmental and socioeconomic damage beyond the original pollution event.

FORUM: Ecological networks: the missing links in biomonitoring science

Monitoring anthropogenic impacts is essential for managing and conserving ecosystems, yet current biomonitoring approaches lack the tools required to deal with the effects of stressors on species and their interactions in complex natural systems.

Ecological networks (trophic or mutualistic) can offer new insights into ecosystem degradation, adding value to current taxonomically constrained schemes. We highlight some examples to show how new network approaches can be used to interpret ecological responses.

Synthesis and applications. Augmenting routine biomonitoring data with interaction data derived from the literature, complemented with ground‐truthed data from direct observations where feasible, allows us to begin to characterise large numbers of ecological networks across environmental gradients. This process can be accelerated by adopting emerging technologies and novel analytical approaches, enabling biomonitoring to move beyond simple pass/fail schemes and to address the many ecological responses that can only be understood from a network‐based perspective.

Augmenting routine biomonitoring data with interaction data derived from the literature, complemented with ground‐truthed data from direct observations where feasible, allows us to begin to characterise large numbers of ecological networks across environmental gradients. This process can be accelerated by adopting emerging technologies and novel analytical approaches, enabling biomonitoring to move beyond simple pass/fail schemes and to address the many ecological responses that can only be understood from a network‐based perspective.

Applying Bayesian network modelling to understand the links between on-farm biosecurity practice during the 2007 equine influenza outbreak and horse managers' perceptions of a subsequent outbreak

Australia experienced its first ever outbreak of equine influenza in August 2007. Horses on 9359 premises were infected over a period of 5 months before the disease was successfully eradicated through the combination of horse movement controls, on-farm biosecurity and vaccination. In a previous premises-level case-control study of the 2007 equine influenza outbreak in Australia, the protective effect of several variables representing on-farm biosecurity practices were identified. Separately, factors associated with horse managers' perceptions of the effectiveness of biosecurity measures have been identified. In this analysis we applied additive Bayesian network modelling to describe the complex web of associations linking variables representing on-farm human behaviours during the 2007 equine influenza outbreak (compliance or lack thereof with advised personal biosecurity measures) and horse managers' perceptions of the effectiveness of such measures in the event of a subsequent outbreak. Heuristic structure discovery enabled identification of a robust statistical model for 31 variables representing biosecurity practices and perceptions of the owners and managers of 148 premises. The Bayesian graphical network model we present statistically describes the associations linking horse managers' on-farm biosecurity practices during an at-risk period in the 2007 outbreak and their perceptions of whether such measures will be effective in a future outbreak. Practice of barrier infection control measures were associated with a heightened perception of preparedness, whereas horse managers that considered their on-farm biosecurity to be more stringent during the outbreak period than normal practices had a heightened perception of the effectiveness of other measures such as controlling access to the premises. Past performance in an outbreak setting may indeed be a reliable predictor of future perceptions, and should be considered when targeting infection control guidance to horse owners and managers.

Improving epidemiologic data analyses through multivariate regression modelling

: Regression modelling is one of the most widely utilized approaches in epidemiological analyses. It provides a method of identifying statistical associations, from which potential causal associations relevant to disease control may then be investigated. Multivariable regression - a single dependent variable (outcome, usually disease) with multiple independent variables (predictors) - has long been the standard model. Generalizing multivariable regression to multivariate regression - all variables potentially statistically dependent - offers a far richer modelling framework. Through a series of simple illustrative examples we compare and contrast these approaches. The technical methodology used to implement multivariate regression is well established - Bayesian network structure discovery - and while a relative newcomer to the epidemiological literature has a long history in computing science. Applications of multivariate analysis in epidemiological studies can provide a greater understanding of disease processes at the population level, leading to the design of better disease control and prevention programs.

Understanding the associations between on-farm biosecurity practice and equine influenza infection during the 2007 outbreak in Australia

In a previous premises-level case-control study of the 2007 equine influenza outbreak in Australia, the protective effect of several variables representing on-farm biosecurity practices was identified. However, using logistic regression it was not possible to definitively identify individual effects and associations between each of the personal biosecurity measures implemented by horse premises owners and managers in the face of the outbreak. In this study we apply Bayesian network modelling to identify the complex web of associations between these variables, horse premises infection status and other premises-level covariates. We focussed this analysis primarily on the inter-relationship between the nine variables representing on-farm personal biosecurity measures (of people residing on the premises and those visiting), and all other variables from the final logistic regression model of our previous analysis. Exact structure discovery was used to identify the globally optimal model from across the landscape of all directed acyclic graphs possible for our dataset. Bootstrapping was used to adjust the model for over-fitting. Our final Bayesian graphic network model included 18 variables linked by 23 arcs, each arc analogous to a single multivariable generalised linear model, combined in a probabilistically coherent way. Amongst the personal biosecurity measures, having a footbath in place, certain practices of visitors (hand-washing, changing clothes and shoes) in contact with the horses, and the regularity of horse handling were statistically associated with premises infection status. The results of this in-depth analysis provide new insight into the complex web of direct and indirect associations between risk factors and horse premises infection status during the first 7 weeks of the 2007 equine influenza outbreak in Australia. In future outbreaks, unnecessary contact and handling of horses should be avoided, especially by those coming from off the premises. Prior to any such contact, persons handling horses should use a footbath (if present), change their clothes and shoes, and wash their hands.

Revealing the complexity of health determinants in resource-poor settings

An epidemiologic systems analysis of diarrhea in children in Pakistan is presented. Application of additive Bayesian network modeling to 2005-2006 data from the Pakistan Social and Living Standards Measurement Survey reveals the complexity of child diarrhea as a disease system. The key distinction between standard analytical approaches, such as multivariable regression, and Bayesian network analyses is that the latter attempt to not only identify statistically associated variables but also, additionally and empirically, separate these into those directly and indirectly dependent upon the outcome variable. Such discrimination is vastly more ambitious but has the potential to reveal far more about key features of complex disease systems. Additive Bayesian network analyses across 41 variables from the Pakistan Social and Living Standards Measurement Survey identified 182 direct dependencies but with only 3 variables: 1) access to a dry pit latrine (protective; odds ratio = 0.67); 2) access to an atypical water source (protective; odds ratio = 0.49); and 3) no formal garbage collection (unprotective; odds ratio = 1.32), supported as directly dependent with the presence of diarrhea. All but 2 of the remaining variables were also, in turn, directly or indirectly dependent upon these 3 key variables. These results are contrasted with the use of a standard approach (multivariable regression).

Microbial interactions: from networks to models

Metagenomics and 16S pyrosequencing have enabled the study of ecosystem structure and dynamics to great depth and accuracy. Co-occurrence and correlation patterns found in these data sets are increasingly used for the prediction of species interactions in environments ranging from the oceans to the human microbiome. In addition, parallelized co-culture assays and combinatorial labelling experiments allow high-throughput discovery of cooperative and competitive relationships between species. In this Review, we describe how these techniques are opening the way towards global ecosystem network prediction and the development of ecosystem-wide dynamic models.

Incorporating uncertainty in predictive species distribution modelling

Motivated by the need to solve ecological problems (climate change, habitat fragmentation and biological invasions), there has been increasing interest in species distribution models (SDMs). Predictions from these models inform conservation policy, invasive species management and disease-control measures. However, predictions are subject to uncertainty, the degree and source of which is often unrecognized. Here, we review the SDM literature in the context of uncertainty, focusing on three main classes of SDM: niche-based models, demographic models and process-based models. We identify sources of uncertainty for each class and discuss how uncertainty can be minimized or included in the modelling process to give realistic measures of confidence around predictions. Because this has typically not been performed, we conclude that uncertainty in SDMs has often been underestimated and a false precision assigned to predictions of geographical distribution. We identify areas where development of new statistical tools will improve predictions from distribution models, notably the development of hierarchical models that link different types of distribution model and their attendant uncertainties across spatial scales. Finally, we discuss the need to develop more defensible methods for assessing predictive performance, quantifying model goodness-of-fit and for assessing the significance of model covariates.

Network modeling of the transcriptional effects of copy number aberrations in glioblastoma

DNA copy number aberrations (CNAs) are a hallmark of cancer genomes. However, little is known about how such changes affect global gene expression. We develop a modeling framework, EPoC (Endogenous Perturbation analysis of Cancer), to (1) detect disease-driving CNAs and their effect on target mRNA expression, and to (2) stratify cancer patients into long- and short-term survivors. Our method constructs causal network models of gene expression by combining genome-wide DNA- and RNA-level data. Prognostic scores are obtained from a singular value decomposition of the networks. By applying EPoC to glioblastoma data from The Cancer Genome Atlas consortium, we demonstrate that the resulting network models contain known disease-relevant hub genes, reveal interesting candidate hubs, and uncover predictors of patient survival. Targeted validations in four glioblastoma cell lines support selected predictions, and implicate the p53-interacting protein Necdin in suppressing glioblastoma cell growth. We conclude that large-scale network modeling of the effects of CNAs on gene expression may provide insights into the biology of human cancer. Free software in MATLAB and R is provided.