On the limits of detection of epistatic higher-order interactions
The function of microbial communities is often dominated by additive and pairwise interactions, raising the question of whether this reflects intrinsic biological simplicity or fundamental limits of detection. Here, we leverage the theory of fitness landscapes to bridge microbial ecology and genetics, and show that this apparent simplicity is a generic consequence of structural and statistical constraints rather than evidence for intrinsically weak higher-order interactions (HOIs). We separate the detectability of individual epistatic interactions from their contribution to functional variance, and demonstrate that local k-order interactions suffer from exponential noise amplification while their contributions to total variance are intrinsically suppressed by combinatorial geometric dilution. Applying this framework to a fully sampled 210 experimental microbial landscape, we find that only first- and second-order interactions are distinguishable from experimental noise. Furthermore, generalized Lotka-Volterra simulations reveal that experimental noise alone can generate the illusion of higher-order structure in communities where all direct mechanistic interactions are pairwise and indirect interactions are weak. Our findings identify universal, order-dependent limits on the quantification of epistasis that apply to high-dimensional landscapes across ecology and genetics, providing a principled foundation for rational community design.