Insights into coral reef benthic dynamics from nonlinear spatial forecasting

Nonlinear time-series forecasting, or empirical dynamic modelling, has been used extensively in the past two decades as a tool for distinguishing between random temporal behaviour and nonlinear deterministic dynamics. Previous authors have extended nonlinear time-series forecasting to continuous spatial data. Here, we adjust spatial forecasting to handle discrete data and apply the technique to explore the ubiquity of nonlinear determinism in irregular spatial configurations of coral and algal taxa from Palmyra Atoll, a relatively pristine reef in the central Pacific Ocean. We find that the spatial distributions of coral and algal taxa show signs of nonlinear determinism in some locations and that these signals can change through time. We introduce the hypothesis that nonlinear spatial determinism may be a signal of systems in intermediate developmental (i.e. successional) stages, with spatial randomness characterizing early (i.e. recruitment dominated) and late-successional (i.e. ‘climax’ or attractor) p...