Dealing with high uncertainty in qualitative network models using Boolean analysis

Models for predicting ecological behaviour typically require large volumes of data for parameterisation, which is a problem because data are scarce. Qualitative modelling (QM) provides an alternative by exploring the entire range of possible parameter values. When a parameter value is completely unknown, QM typically invokes the Principle of Indifference (PoI), for example by sampling the parameter from a uniform prior distribution. However, if PoI is invoked in this probabilistic way, there may be multiple possible methods for defining a parameter space and sampling values from it, and, worryingly, two different but equally defensible methods can lead to different predictions about ecosystem responses. We investigated how probabilistic PoI can give rise to problems in QM, and developed an alternative method based on Boolean PoI that does not suffer the same limitations. We used a case study that involved predicting the responses of multiple species to the suppression of a pest. The unknown model parameters were interaction strengths between species. For the standard probabilistic method, we drew the parameters randomly from uniform (PoI) and other distributions. For our new Boolean PoI method, we instead simply specified the ranges of "possible" parameter values, and developed a Boolean analysis technique to summarise model predictions. As expected, invoking probabilistic QM yielded different predictions (species-response probabilities) for different but equally defensible parameterisation and sampling schemes. Sometimes differences were large enough to impact decision-making. In contrast, our new Boolean PoI approach simply classifies outcomes (species responses) as certain, possible, or impossible. Encouragingly, some species responses that were not consistently resolved under probabilistic PoI were shown by our method to be in fact governed by simple rules. Our method can also identify key species whose responses determine whole-system outcomes. Our non-probabilistic representation of uncertainty circumvents the philosophical problems in standard implementations of PoI for QM. Our Boolean analysis method summarises results in a way that is interpretable and potentially useful to conservation decision makers. A priority for future research is to increase the efficiency of our Boolean approach to allow it to deal with problems of higher complexity (more interactions).