Early life conditions can have profound effects on individual health, longevity, and biological fitness. Two classes of hypotheses are used to explain the evolutionary origins of these effects: developmental constraints (DC) hypotheses, which focus on the deleterious effects of low-quality early-life environments, and predictive adaptive response (PAR) models, which focus on organisms’ predictions about their adult environment, phenotypic adaptations based on that prediction, and the deleterious consequences of incorrect predictions. Despite their popularity, these ideas remain poorly defined. To remedy this, we provide mathematical definitions for DC, PARs, and related concepts, and develop statistical tests derived from these definitions. We use simulations to demonstrate that PARs are more readily detected by tests based on quadratic regressions than by tests based on more commonly used interaction regression models. Specifically, quadratic regression-based tests on simulated data yield 90.7% sensitivity and 71.5% specificity in detecting PARs, while interaction-based tests yield sensitivity and specificity roughly equal to chance. We demonstrate that the poor performance of interaction models stems from two problems: first, they are mathematically incapable of detecting a central prediction of PAR, and second, they conceptually conflate PARs with DC. Our results emphasize the value of formal statistical modeling to reveal the theoretical underpinnings of verbal and visual models, and their importance for helping resolve conflicting and ambiguous results in this field of research. We conclude by providing recommendations for how researchers can make use of explicit definitions and properly-aligned visualizations and statistical tests to make progress in this important research area.