APPENDIX 1. Bayesian Belief Networks (BBN) in natural resource management.

A BBN may be defined most simply as a graphical model that incorporates probabilistic relationships among variables of interest (Heckerman 1996). The term “graphical model” is used because the BBN can be represented in the form of an influence diagram. An influence diagram can be used to provide a visual representation of the components and dependencies of a system. Different shapes (such as ellipses and rectangles) can be used to represent variables, data and parameters, which are connected by arrows to indicate causal relationships and dependencies (Burgman 2005). In the case of a BBN, the ellipses representing variables are referred to as nodes. The arrows are referred to formally as directed links
(Jensen 2001). A probability function is attached to each node, and probabilities are combined in the model using Bayes’ theorem. A BBN therefore provides both a tool for reasoning under uncertainty and a statistical model of the domain of interest (Jensen 2001).

Bayesian networks evolved in the early 1990s drawing on a deep body of theory developed for graphical models in general, due in large part to the seminal work of Pearl (1986, 1988, 1995), who established their position at the interface between statistics, applied artificial intelligence and expert system development. BBNs may be used for both predictive modelling of domain knowledge and as thought tools for structuring and analysing the results of experience in a domain. The growing interest in applying belief networks to resource management problems may be linked to the increased acceptation of Bayesian statistical approaches in general. Typically Bayesian statistics are used to find parameter values when the stochastic component of a model is represented by one or more continuous probability density functions. The directed acyclical graphs used to represent these models can follow the same formalisms as BBNs.

Bayesian analytical techniques began to be considered seriously by ecologists and resource managers largely as a result of a special addition of Ecological Applications published in 1996 (e.g. Ellison 1996). Crome et al. (1996) provided an example that showed how Bayesian methods may be particularly useful in the context of tropical forest management, for modeling the inevitably subjective uncertainties involved when forest systems are disturbed. Gertner and Zhu (1996) reached a similar conclusion in a rather narrower context. The key advantages of Bayesian methods, including BBNs, for both forestry and conservation applications concern their ability to ensure that subjectivity is explicit and transparent rather than implicit in the choices made regarding which elements in the data are presented and emphasized (Ghazoul and McAllister 2003). Lagos and Castilla (1997) also stressed this advantage when they applied Bayesian methods to the problem of managing a marine reserve.

From their inception it was clear that Bayesian networks had a great potential for building working expert systems (Lauritzen and Spiegelhalter 1988). Some successful early applications were in the field of medical diagnosis (Spiegelhalter et al. 1993). The application of such methods to resource management problems were first explored rather later (Varis 1997). One of the earliest published examples was by Haas (1991), who applied the method to a very narrow domain, the problem of predicting the density of suckers produced by rocky mountain aspen in response to a range of management options. The study stressed the flexibility of BBNs as a knowledge representation system which was contrasted with more rigid rule-based expert systems. Although the work did not reach the stage of evaluating model predictions against an independent data set, the conclusion was reached that BBNs produce results consistent with expert judgment even when precise parameter estimation is challenging.

Cain et al. (1999) have demonstrated how belief networks can be extended into the social domain of resource management. The authors stressed the importance of ensuring that rural stakeholders are involved in the identification of key variables. They also showed how BBNs can use locally derived data and experiences in a flexible and adaptive manner. This work did not however clarify methods for parameterizing BBNs in the context of participatory rural appraisal. Other recent applications of BBNs in resource management include those developed by Rieman et al. (2001) and Marcot et al. (2001) who developed BBNs for aquatic and terrestrial vertebrate species found on federal lands within the interior Columbia River basin in the United States, and Bromley et al. (2005) who explored their application to integrated water resource planning. Other references to recent research on this theme are provided by Reckhow (2003). However, we are not aware of any previous attempt to apply BBNs to the management and use of NTFPs in tropical forests. Although Ghazoul and McAllister (2003) provide a detailed account of the value of Bayesian approaches to forest research, particularly with respect to supporting adaptive management and decision-making, little explicit consideration is given to BBNs.

One of our motives for using BBNs was a desire to explicitly model belief. Under the Bayesian paradigm, evidence that is consistent with a given hypothesis (e.g. success of commercialisation) has a high likelihood. When Bayes’ theorem is used, this results in a strengthening in the belief in the hypothesis. We stress that under this interpretation "probability of success" does not refer to a prognosis of any future state. Rather it represents a strong belief based on accumulated evidence that NTFP commercialisation is successful.

The practical development of a BBN begins with construction of an influence diagram, which can be based on expert knowledge or belief about the domain of interest. The creation of an influence diagram can itself be a useful way of eliciting information from experts and structuring the information available (Burgman 2005). As in the current research, a number of different model structures may be explored, with the aim of identifying the structure that best captures the logical relationships between the variables being considered. One the structure has been defined, the main challenge is to complete the Conditional Probability Tables (CPTs) that are associated with each node. These define the probabilistic relationships between the nodes connected by directed links. Further details of how the BBN was constructed in the present study are given in App. 5.

A BBN can be explored by changing the states of the nodes (or variables) incorporated within the model. When the state of a variable is known, it is said to be instantiated (Jensen 2001). Once a node has been instantiated, then this will influence the probabilities associated with the states of other nodes to which it is linked, according to the values in the CPTs. In the current example, the BBN was instantiated by entering the factor scores obtained for each case study individually.