Rigorous validation of ecological models against empirical time series.

The complexity of ecosystems poses a formidable challenge for validating ecological models. The prevailing inability to falsify models has resulted in an accumulation of models but not an accumulation of confidence. Here we introduce an 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 test our approach using observed time series data on 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 confidence in those that provide strategically useful approximations. The covariance criteria approach is mathematically rigorous and computationally efficient, making it applicable to existing data and models.