Extended Data Fig. 7: Correlation between state duration and activity of dorsal raphe state neurons and exploration-state-encoding neurons, multimodal activation of the exploitation state, and stochastic model of trigger and state signals.

a, Top, peak activities of exploration state neurons are not correlated with the duration of exploration state. Bottom, peak activities of dorsal raphe exploitation state encoding neurons correlate with the duration of exploitation state. Activity is in units of z-scored fluorescence. b–d, The trigger network that is active at the transition from exploration to exploitation contains both modality-specific neurons (b, c), that are only active at either spontaneous transitions (b) or at stimulus-evoked transitions (c), as well as cross-modal neurons that are activated at all state transitions regardless of whether the transition is stimulus-evoked or spontaneous (d). e, Schematic of the stochastic model. Spontaneous and stimulus-evoked trigger events are represented by delta functions with variable (integrated) amplitudes. The spontaneous trigger events arrive according to a Poisson process during exploration state, triggering the exit from exploration state after an exponentially distributed waiting time. Each delta function causes the trigger signal to undergo an impulsive rise, followed by rapid exponential decay. The state signal integrates the trigger signal, and then undergoes a slow linear decay back to baseline. Exploitation state corresponds to the time intervals when the state signal is elevated above baseline. Spontaneous trigger amplitudes are exponentially distributed, which leads to a corresponding amplitude in the state signal, and effectively determines the duration of the ensuing exploitation state due to the slow linear decay of the state signal. f, Two examples of recorded trigger and state signals during long exploitation states, together with corresponding signals in the fitted model. Event amplitudes \({A}_{i}^{{\rm{spont}}}\) and times \({t}_{i}^{{\rm{spont}}}\) are fit individually for each transition. The shared model parameters (α, β, γ) were obtained by simultaneous least squares fitting of the equations for T(t) and S(t) to the dynamics of the population mean activity of trigger and exploitation state neurons during 14 exploitation states having a duration of at least 10 min (obtained from n = 17 fish). The joint fitting procedure yielded α = 1.5, β = 0.1 min⁻¹, and γ = 1.3 min⁻¹. These parameters, together with the fitted behavioural state distributions from Fig. 1d (obtained from n = 36 fish), comprise the conceptual model of the stochastic nonlinear dynamical system for exploration and exploitation.