# Reordered hierarchical complexity in ecosystems with delayed interactions

## TL;DR

This paper shows that time delays in ecosystems can change the usual hierarchy of complexity, especially in predator-prey systems.

## Contribution

The study reveals that time delays can reorder ecosystem complexity, challenging previous assumptions.

## Key findings

- Predator-prey communities' complexity is significantly affected by time delays.
- Time delays can reorder the hierarchy of ecosystem complexity at a critical threshold.
- Nonmonotonic behavior is observed with continuous time delays in realistic ecosystems.

## Abstract

It was once believed that large ecosystems with random interactions are unstable, limiting their complexity. Thus, large community size or numerous interactions are rare in nature. Later, a strict hierarchical complexity was revealed: competitive and mutualistic communities have the least complexity, followed by random ones, and then predator–prey communities. Recently, a hierarchy of recovery times for ecosystems with identical complexity was found, influenced by discrete time delays. A key question is whether this hierarchical complexity holds under noninstantaneous interactions. We surprisingly show that it does not. Specifically, the complexity of predator–prey communities is significantly affected by time delays, reordering the hierarchy at a critical threshold. These changes exhibit nonmonotonic behavior with continuous time delays, another realistic interaction type. We validated our findings in various realistic ecosystems. Our results indicate that incorporating factors like time delays and their appropriate forms can lead to correct and even deeper understanding about complexity of large ecosystems and other biophysical systems.