Abstract
Trade-offs are commonly assumed when the statistical parameters used to define biological traits are negatively correlated. However, parameter correlations can emerge from the geometry of the model, rather than underlying biological signal. We characterize this phenomenon generally, and develop a framework to parse biological signal from statistical artifact in parameter correlations. Using the widely reported trade-off between thermal sensitivity and static upper critical thermal limit as a case study, we show that an extreme correlation between these parameters is expected even in the absence of a real trade-off. However, our method reveals that there is, in fact, a biological correlation underneath this spurious artifact. We confirm this finding, as independent genome-wide association analysis reveals genetic variation among trade-off phenotypes, but none corresponding to net thermal tolerance, suggesting that adaptive capacity to a warming climate may be severely limited. This particular trade-off is therefore biologically supported, illustrating how biological signal can be obscured by estimation artifact, thus evading correlation-based detection. We broaden our analysis, showing that artifact is present across biological systems and model types, although its manifestation may vary. Analytical results and simulations reveal how sampling design, model choice and parameterization govern the artifact, providing practical guidance for experimental planning. Our findings identify both a problem and a solution: correlations among model parameters cannot be interpreted biologically without first accounting for the structure imposed by the model and data, but genuine biological relationships can still be recovered when that structure is explicitly modeled.