An approximate Bayesian algorithm for training fuzzy cognitive map models of forest responses to deer control in a New Zealand adaptive management experiment

Abstract

Forest management decisions are characterised by a high level of uncertainty because responses reflect a range of interacting ecological processes. Faced with this situation, modelling can be a useful tool for characterising that uncertainty and for predicting its impacts on management decisions. In the adaptive management paradigm, different model structures are essentially hypotheses of system behaviour that are formulated to encapsulate structural uncertainty about the system. Here we report upon the initial stages of a management-scale experiment designed to increase our understanding of the effects of deer control on forest ecosystems in New Zealand. Using a modelling approach based on fuzzy cognitive maps (FCM) we were able to formalise expert knowledge and explore how growth rates of tree seedlings would respond to lower deer densities, with or without responses by other plants in the forest understorey. Alternative models predicted that the response of seedling growth and biomass in small (16m2) plots used in the experiment were dependent on hypotheses about the strength of plant competition for soil nutrients and moisture which, in turn, were conditional on light availability in the plot. To learn about which model best may describe the system, we used recently proposed methods in Approximate Bayesian Computation (ABC) to perform model selection and inference using a simulated data set generated from one of our candidate models. Using a novel Markov chain Monte Carlo algorithm together with ABC model selection on our simulated data we show that these procedures provide reliable model selection and parameter inference and hence, should be suitable for confronting our candidate FCM models with data collected at the end of the experiment.