Zigzag persistence for coral reef resilience using a stochastic spatial model

TL;DR

This paper extends a mathematical model of coral reef dynamics to include stochastic and spatial interactions, applying topological data analysis techniques to characterize reef resilience and distinguish different ecological scenarios.

Contribution

It introduces new descriptors for analyzing heterogeneous spatio-temporal data and demonstrates the utility of persistent homology and zigzag persistence in ecological data analysis.

Findings

Local competition leads to coral clustering.

Neighbourhood composition influences coral survival.

Spatial configurations affect reef resilience.

Abstract

A complex interplay between species governs the evolution of spatial patterns in ecology. An open problem in the biological sciences is characterising spatio-temporal data and understanding how changes at the local scale affect global dynamics/behaviour. Here, we extend a well-studied temporal mathematical model of coral reef dynamics to include stochastic and spatial interactions and generate data to study different ecological scenarios. We present descriptors to characterise patterns in heterogeneous spatio-temporal data surpassing spatially averaged measures. We apply these descriptors to simulated coral data and demonstrate the utility of two topological data analysis techniques--persistent homology and zigzag persistence--for characterising mechanisms of reef resilience. We show that the introduction of local competition between species leads to the appearance of coral clusters in the reef. We use our analyses to distinguish temporal dynamics stemming from different initial configurations of coral, showing that the neighbourhood composition of coral sites determines their long-term survival. Using zigzag persistence, we determine which spatial configurations protect coral from extinction in different environments. Finally, we apply this toolkit of multi-scale methods to empirical coral reef data, which distinguish spatio-temporal reef dynamics in different locations, and demonstrate the applicability to a range of datasets.