A universal niche geometry governs the response of ecosystems to environmental perturbations

TL;DR

This paper introduces a geometric theoretical framework to predict how ecosystems respond to environmental changes, applicable to diverse models, revealing insights into niche structure shifts and the difficulty of distinguishing interaction types.

Contribution

It presents a universal geometric approach for analyzing ecosystem responses to perturbations, accommodating complex interactions and non-linear dynamics.

Findings

Framework applies to models with non-reciprocal interactions and non-linear rates

Environmental perturbations map to niche shifts via geometric transformations

Distinguishing cooperation from competition through perturbation responses is challenging

Abstract

How ecosystems respond to environmental perturbations is a fundamental question in ecology, made especially challenging due to the strong coupling between species and their environment. Here, we introduce a theoretical framework for calculating the steady-state response of ecosystems to environmental perturbations in generalized consumer-resource. Our construction is applicable to a wide class of systems, including models with non-reciprocal interactions, cross-feeding, and non-linear growth/consumption rates. Within our framework, all ecological variables are embedded into four distinct vector spaces and ecological interactions are represented by geometric transformations between these spaces. We show that near a steady state, such geometric transformations directly map environmental perturbations - in resource availability and mortality rates - to shifts in niche structure. We illustrate these ideas in a variety of settings including a minimal model for pH-induced toxicity in bacterial denitrification. We end by discussing the biological implications of our framework. In particular, we show that it is extremely difficult to distinguish cooperative and competitive interactions by measuring species' responses to external perturbations.