A Multidimensional Framework for Behavioral Persistence: Dissociable Dimensions of Effort, Endurance, and Sequence Stability in Mice
Persistence has five separate parts—measure all of them, not just one.
01Research in Context
What this study did
Cao and team watched mice press levers for food. They tested five ways to measure how long the mice keep pressing.
The five ways are effort (how hard they press), endurance (how long they keep going), extinction resistance (how long they press when food stops), consistency (same pattern every time), and sequence stability (same order of moves).
They used different food schedules to see which one made the mice most persistent.
What they found
The mice kept pressing longest when they had to work hard for food that then stopped coming.
Getting food was not what kept them going. The frustration of not getting food made them press more.
Each of the five persistence measures changed in its own way. They did not all move together.
How this fits with other research
This builds on Glover et al. (1976) who first showed that variable-ratio schedules create pauses after food. Cao adds that the same schedules also create five separate kinds of persistence.
Gaucher et al. (2020) showed autistic children can learn timing under DRL schedules. Cao shows mice can learn persistence under many schedules. Both prove schedule effects work across species.
KELLEHER (1961) said conditioned reinforcers slow extinction. Cao agrees but adds that the real driver is frustration from non-reward, not the conditioned cues themselves.
Why it matters
Stop using one score for persistence. Use the PERCS model to track all five dimensions. When a learner keeps working after you stop reinforcement, check which of the five is driving it. This tells you if you need to change effort demands, add breaks, or fade extinction more slowly.
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02At a glance
03Original abstract
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 2×2 and 5×5, 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, 2×2, and 5×5 (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 2×2 (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; 2×2 and 5×5 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.
bioRxiv, 2026 · doi:10.64898/2026.03.02.709169