Rigorous (in)validation of ecological models

The complexity of ecosystems poses a formidable challenge for confidently invalidating ecological models, as current practices struggle to distinguish model inadequacies from the confounding effects of unobserved biotic or abiotic factors. The prevailing inability to falsify models has resulted in an accumulation of models but not an accumulation of confidence. Here, we introduce a new approach rooted in queueing theory, termed the covariance criteria, that establishes a rigorous test for model validity based on covariance relationships between observable quantities. These criteria set a high bar for models to pass by specifying necessary conditions that must hold regardless of unobserved factors. We demonstrate the broad applicability and discriminatory power of the covariance criteria by applying them to three long-standing challenges in ecological theory: resolving competing models of predator-prey functional responses, disentangling ecological and evolutionary dynamics in systems with rapid evolution, and detecting the often-elusive influence of higher-order species interactions. Across these diverse case studies, the covariance criteria consistently rule out inadequate models, while building strong confidence in those that provide strategically useful approximations. The covariance criteria approach is mathematically rigorous, computationally efficient, and often non-parametric, making it immediately applicable to existing data and models.