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

Patch foraging presents 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. Mouse behavior could be explained by a model integrating time and rewards antagonistically, scaled by a latent patience state. The model accounted for deviations from predictions of optimal foraging theory. Neural recordings throughout frontal areas revealed encoding of decision variables from the integrator model, most robustly in frontal cortex. Regression modeling followed by unsupervised clustering identified a subset of ramping neurons. These neurons' firing rates ramped up gradually (up to tens of seconds), were inhibited by rewards, and were better described as a continuous ramp than a discrete stepping process. Together, these results identify integration via frontal cortex ramping dynamics as a candidate mechanism for solving patch foraging problems.