Modelling spatial and temporal changes with GIS and Spatial and Dynamic Bayesian Networks

https://doi.org/10.1016/j.envsoft.2016.04.012Get rights and content

Highlights

  • We extend Dynamic Bayesian Network technology to model spatial processes.

  • A novel application of object-oriented concepts helps handle BN modelling complexity.

  • We demonstrate proof-of-concept with two environmental management case studies.

  • We include model templates and algorithms for spatio-temporal scenario simulations.

Abstract

State-and-transition models (STMs) have been successfully combined with Dynamic Bayesian Networks (DBNs) to model temporal changes in managed ecosystems. Such models are useful for exploring when and how to intervene to achieve the desired management outcomes. However, knowing where to intervene is often equally critical. We describe an approach to extend state-and-transition dynamic Bayesian networks (ST-DBNs) — incorporating spatial context via GIS data and explicitly modelling spatial processes using spatial Bayesian networks (SBNs). Our approach uses object-oriented (OO) concepts and exploits the fact that ecological systems are hierarchically structured. This allows key phenomena and ecological processes to be represented by hierarchies of components that include similar, repetitive structures. We demonstrate the generality and power of our approach using two models — one developed for adaptive management of eucalypt woodland restoration in south-eastern Australia, and another developed to manage the encroachment of invasive willows into marsh ecosystems in east-central Florida.

Introduction

Bayesian networks (Pearl, 1988) are increasingly popular for ecological and environmental modelling, decision support and adaptive management (Nyberg et al., 2006, Korb and Nicholson, 2010, Aguilera et al., 2011). Ecosystem management problems characteristically involve variable, complex and imperfectly understood biophysical, social and economic interactions. The iterative knowledge-engineering process of developing BNs is invaluable for: a) clarifying objectives; b) identifying and articulating alternatives; c) synthesising available knowledge; d) quantifying uncertainties and d) pinpointing critical assumptions to be tested by purposeful monitoring. When fully parameterised, such models help us explore and (where possible) resolve uncertainty about the consequences of management decisions. This is integral to adaptive management (sensu Holling, 1978, Walters and Hilborn, 1978) which supplies the broader framework for evaluating the performance of decision actions and updating our knowledge base to improve future management (Nichols and Williams, 2006, Duncan and Wintle, 2008).

Despite the obvious value of using BNs to support learning over time for adaptive management (see e.g., Ames et al., 2005, Chee et al., 2005), most published examples of BNs for environmental applications have focused on formalising static conceptual models of the system in question, and do not explicitly represent ongoing dynamics (e.g. multiple time steps and sequential decisions) (Barton et al., 2012). Examples that incorporate spatiality explicitly are even rarer. Yet it is critical to address these gaps because the ability to understand change over time, and to account for spatial context and interactions is often necessary for meaningful decision support.

For instance, in our eucalypt woodlands case study, restoring species composition, ecosystem structure and function is a long-term undertaking that needs to effectively manage threats like weed establishment, so that the recovery process can build upon successive gains. In our invasive willows management case study, control efforts are long-term because adult willows have become firmly established within the catchment. In both cases, spatial considerations are crucial because the encroachment of weeds (in woodlands) and willow seedlings (in marsh ecosystems) depends on seed production and dispersal from surrounding areas, and spatial characteristics also determine the applicability and effectiveness of management actions.

State-and-transition dynamic Bayesian networks (ST-DBNs) as described by Nicholson and Flores (2011) provide a viable approach for explicitly modelling change over time. Here, we extend the capabilities of ST-DBNs – first, coupling them to GIS data so we can harness spatially relevant data, and then explicitly modelling key spatial processes using spatial Bayesian networks (SBNs). Our approach makes use of object-oriented (OO) concepts and exploits the fact that ecological systems are hierarchically structured such that key phenomena and processes of interest can be represented by nesting components that include similar, repetitive structures.

First, we explain the ‘buildings blocks’ and concepts of the tools we use for modelling spatial and temporal changes with BNs. We then present and illustrate our approach using two models—one developed for adaptive management of eucalypt woodland restoration in south-eastern Australia (‘Woodlands weed’ model, Rumpff et al. (2011)), and another developed to manage willow spread into marsh ecosystems in east-central Florida, USA (‘Willows’ model, Wilkinson et al. (2013)). Of course, incorporating spatial context and processes can lead to a massive increase in the size and complexity of the networks, which in turn generates computational issues and difficulties with the probabilistic updating—we discuss our approach to handling these challenges and provide a generic system architecture, templates and algorithms for combining GIS, object-oriented spatial BNs and object-oriented state-transition DBNs.

To our knowledge, this is the first demonstration of the integration of these three tools. This novel and powerful approach allows the incorporation of spatial context where it is critical for decision-making.

Section snippets

Background: building blocks and OO concepts

State-and-transition models (STMs) are management-focused, qualitative conceptual models that synthesise knowledge about an ecological system, in the form of observed and/or hypothesised system states and transitions that are of management interest (Westoby et al., 1989, Jackson et al., 2002). STMs are a popular tool for modelling changes over time in ecological systems that have clear transitions between distinct states. They combine graphical depiction of transitions and their causal factors

Two case studies

Here we describe the problem domain and the spatial and dynamic processes that need to be modelled for each case study.

Modelling spatial processes with object-oriented spatial BNs (OOSBNs)

Scale is an inherent consideration in modelling spatial processes because the interactions of interest may vary from highly localised to spatially extensive. These contrasting situations are exemplified by each of our case studies (described below). We therefore developed a generic template with the flexibility to accommodate different scales of interest.

In this generic OOSBN (Fig. 3), the Process of Interest takes into account any salient OODBN inputs and can be represented by a single node or

System architecture and algorithm for integrating GIS data, the ST-OODBN and the OOSBN

Fig. 6 illustrates our system architecture, showing the interactions between GIS data and the input (I) and the output (O) nodes of the spatial (OOSBN) and temporal (ST-OODBN) networks. For each cell in the study area, there is conceptually one OOSBN and one ST-OODBN. In practice, we do not require multiple individual copies of OOSBNs and ST-OODBNs, but rather re-use network structures, whose input nodes are re-parameterised for each cell, at each time step.

With reference to Fig. 6 and

Example scenarios for model demonstration

To demonstrate our working implementation, we ran the woodlands weed model for an area of grassy eucalypt woodlands near Wollert, Victoria (86 by 80 cells). Weed cover in the target area was initialised using GIS data (White et al., unpublished data) and the timeframe of interest was 15 years. We investigated two scenarios — a) no management intervention at all, and b) intervention when weed cover is low.

For the willows study, we ran the model for a portion of the Blue Cypress Marsh

Discussion and conclusions

The adoption of an OO approach allowed us to design an architecture for using Bayesian networks to reason about change over both time and space. The use of abstraction and encapsulation via components with formalised input and output interfaces helped manage the complexity. We have demonstrated the generality and power of our approach through two environmental management case studies.

We note, however, that throughout the research and integration process we encountered challenges with the

Acknowledgements

This work was supported by ARC Linkage Projects LP110100304 and LP110100321, the Australian Centre of Excellence for Risk Analysis, and the ARC Centre of Excellence for Environmental Decisions. Steven R Miller, Jo Anna Emanuel, Ken Snyder, Chris Oman provided critical information about the St Johns River catchment, and knowledge about willow ecology and management. We thank Steve Sinclair for assistance with developing the woodlands weed model, and Owen Woodberry for valuable discussions about

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