Cao, T.; Johnston, W. R.; Christensen, S.; Crouse, S.; Sun, Q.-Q.

Behavioral persistence, the maintenance of goal-directed action despite obstacles, is a fundamental adaptive process, yet its scientific study remains fragmented across disciplines with disparate operational definitions. Here, we introduce the Persistence Spectrum (PERCS) framework, a five-dimensional model deconstructing persistence into Perseverance of Effort (P), Strategic Endurance (E), Resistance to Extinction (R), Temporal Consistency (C), and Repetitive Sequence Stability (S). Using programmable operant schedules via the FED3 system, we induced a continuum of persistent food-seeking in mice across four paradigms: Fixed Ratio (FR), Alternating 2 by 2 and 5 by 5, and Random Progressive Ratio (RPR). To objectively identify persistence periods, we developed a session-specific Gaussian mixture model, providing a data-driven alternative to arbitrary frequency thresholds. We found that persistence bouts were fundamentally driven by unrewarded effort, not reward delivery: instantaneous frequency for incorrect pokes significantly exceeded that for correct pokes in FR, 2 by 2, and 5 by 5 (all p < 0.05). This pattern was most pronounced in the high-demand RPR schedule, where high-rate poking continued unabated even after successes, directly challenging reinforcement-centric models and providing strong empirical support for frustration theory. Linear mixed-effects modeling revealed that frequency increased with consecutive unrewarded pokes across all paradigms, with a quadratic (inverted-U) relationship specific to FR and 2 by 2 (p < 0.001), suggesting effort invigoration followed by strategic disengagement in simpler tasks, whereas high-demand schedules maintained linear increases. Notably, the collapse of Sequence Stability (S) in RPR is partly constrained by the task's environmental contingency: random reward rules mathematically restrict stable sequence learning. Aggregate analysis showed total poke counts and unrewarded effort scaled with task difficulty (all p < 2e-16), yet pellet retrieval rates remained stable, indicating goal achievement despite increased challenge. Crucially, PERCS profiles were robust across independent and continuous training histories, demonstrating they reflect stable phenotypes shaped by current contingencies rather than training artifacts. Application of PERCS revealed distinct fingerprints: FR produced near-zero P, E, R, and C but maximal S, characteristic of an efficient habit; 2 by 2 and 5 by 5 elevated P, E, and R while reducing S; and RPR generated highest P and R, lowest S, and marked inter-individual variability. These findings demonstrate that operant schedules dissociably shape distinct persistence dimensions, with unrewarded effort acting as a key motivational trigger, positioning frustrative nonreward as a primary engine of persistent behavior. The PERCS framework provides a unified, quantitative language for characterizing persistent behavior across species and paradigms, offering a powerful tool for linking dimensions to neural circuits and understanding their breakdown in neuropsychiatric disorders.