Figure 1.
(A) The decision making network consists of two populations of sensory neurons Ni, corresponding to the two targets, and two populations of premotor neurons Mi, corresponding to the two actions. Choice is determined by comparing the activities of the two populations of premotor neurons (see text). (B) The effect of the synaptic plasticity rule on synaptic efficacy. The decision making model was simulated in a concurrent VI reward schedule (see Materials and Methods) with equal baiting probabilities, and the efficacy of one of the synapses is plotted as a function of trial number. During the first 300 trials (blue), the synaptic efficacies evolved according to Eq. (2) with α = 0 and β = 1 (and thus γ = 0), resulting in small fluctuations of the efficacy around the initial conditions. A 10% mistuning of the mean subtraction after 300 trials (red arrow) to β = 0.9 (γ = 0.1) resulted in a linear divergence of the efficacy (red line). The addition of a linear decay term to the plasticity rule (Eq. (4) with ρ = 1) after 600 trials (black arrow) resulted in small fluctuations of the efficacy around 0.04 (black line).
Figure 2.
Incomplete mean subtraction and deviations from matching behavior.
(A) The probability of choice as a function of fractional income. Each point corresponds to one simulation of the model, Eq. (4), in a concurrent VI reward schedule with fixed baiting probabilities. The level of deviation from matching behavior (black line) depends on the level of incomplete mean subtraction, γ and synaptic saturation stiffness, ρ. Red squares, γ = 0.05, ρ = 1; blue diamonds, γ = 0.5, ρ = 1; gray triangles γ = 0.5, ρ = 4; colored lines are the analytical approximations, Eq. (7). (B) Susceptibility of behavior as a function of γ. In order to quantify the effect of γ on deviation from matching behavior, we repeated the simulations of A for many values of γ and measured the susceptibility of behavior (the slope of the resultant curve, see text and Materials and Methods). Blue dots, ρ = 5; red dots, ρ = 1; black dots, ρ = 0.2. Lines correspond to the expected slope from the analytical approximation, Eq. (7).
Figure 3.
Bias in the winner-take-all mechanism and deviations from matching behavior.
(A) The probability of choice as a function of fractional income. Each point corresponds to one simulation of the model (Eq. (4) with ρ = 1) in a concurrent VI reward schedule with fixed baiting probabilities. The level of deviation from matching behavior (black line) depends on the bias in the winner-take-all mechanism. Red squares, ε = −3σ; blue diamonds, ε = 0; gray triangle, ε = 3σ; γ = 0.05; colored lines are the analytical approximation, Eq. (8). (B) Choice bias. The simulation of A was repeated for different values of ε for two values of γ (blue dots, γ = 0.5; red dots, γ = 0.05), and the probability of choosing alternative 1 for a fractional income of r1 = 0.5 was measured. Lines correspond to the expected probability of choice from the analytical approximation, Eq. (8).