Competitive integration of time and reward explains value-sensitive foraging decisions and frontal cortex ramping dynamics.

Patch foraging is a ubiquitous decision-making process in which animals decide when to abandon a resource patch of diminishing value to pursue an alternative. We developed a virtual foraging task in which mouse behavior varied systematically with patch value. Behavior could be explained by models integrating time and rewards antagonistically, scaled by a slowly varying latent patience state. Describing a mechanism rather than a normative prescription, these models quantitatively captured deviations from optimal foraging theory. Neuropixels recordings throughout frontal areas revealed distributed ramping signals, concentrated in the frontal cortex, from which multiple integrator models' decision variables could be decoded equally well. These signals reflected key aspects of decision models: they ramped gradually, responded oppositely to time and rewards, were sensitive to patch richness, and retained memory of reward history. Together, these results identify integration via frontal cortex ramping dynamics as a candidate mechanism for solving patch-foraging problems.