Insights into coral reef benthic dynamics from nonlinear spatial forecasting.

Dylan E Mcnamara,Nick Cortale,Stuart A Sandin,Yoan Eynaud,Clinton Edwards

doi:10.1098/rsif.2019.0047

Abstract

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) phases. Common state-based metrics that sum community response to environmental forcing lack resolution to detect dynamics of (potential) recovery phases; incorporating signal of spatial patterning among sessile taxa holds unique promise to elucidate dynamical characters of complex ecological systems, thereby enhancing study and response efforts.

Highlights

When scientists take data from a natural system, they do so with the hope that the underlying dynamics, the determinism, will be discovered
Linear dynamics can only lead to exponential growth, exponential decay or periodic oscillations, that themselves could grow or decay; any irregular behaviours in time are attributed to random inputs
For many ecological investigations that use nonlinear time-series methods, the goal has been to characterize the extent to which a system is dominated by nonlinear dynamics versus outside forcing from random influences [2,3]

Summary

Introduction

When scientists take data from a natural system, they do so with the hope that the underlying dynamics, the determinism, will be discovered. Nonlinear time-series analysis is a data-intensive approach that can reveal evidence of a wide range of nonlinear dynamics in the search for deterministic structure [1]. For many ecological investigations that use nonlinear time-series methods, the goal has been to characterize the extent to which a system is dominated by nonlinear dynamics versus outside forcing from random influences [2,3]. In these efforts, care is taken to ensure the analysis focuses on regions of the data that step beyond auto-correlated behaviour that could result from linear decays of external perturbations. More recent work has used the forecasting capability that results

Methods

Results

Conclusion