# Reflecting on the symmetry of ecosystem tipping points: The influence of trait dissimilarity and environmental driver dynamics in a simple ecosystem model

## TL;DR

This paper investigates how symmetry in ecosystems affects their responses to environmental changes in different directions.

## Contribution

The study introduces a simple mathematical model to explore how system and environmental symmetry influence response symmetry in ecosystems.

## Key findings

- Perfect system and environmental symmetry produce perfect response symmetry in ecosystems.
- Introducing asymmetry in biological systems or the environment increases response asymmetry proportionally.
- Symmetries in ecosystem structure can help predict similarities in degradation and restoration phases.

## Abstract

Our understanding of the similarity in trajectories of ecosystem changes during different directions of environmental change is limited. For example, do the dominant organisms exhibit the same responses to different directions of environmental change, that is, do they exhibit symmetric responses? Here, we explore whether such response symmetry is determined and controlled by the symmetry in the features of the underlying biological system (i.e., system symmetry), such as in the network and strength of biotic and abiotic processes, and in symmetry of the environmental change (i.e., environmental symmetry). For this exploration, we developed and used a simple mathematical model of a microbial ecosystem driven by mutual inhibition in which we could vary the amount of system and environmental symmetry. Our results show that perfect system and environmental symmetry indeed produce perfect response symmetry. Moreover, introducing asymmetry in biological systems or in the environment proportionally increases response asymmetry. These findings suggest using symmetries in ecosystem structure and interaction strength to better understand and predict similarities in degradation and restoration phases of environmental change.

Our understanding of the similarity in trajectories of ecosystem changes during different directions of environmental change is limited. This research article suggests using symmetries in ecosystem structures and interaction strength to better understand and predict similarities in degradation and restoration phases of environmental change.