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

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 linear response of ecosystems to environmental perturbations in generalized consumer-resource models. 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.