Figure 1.
An example of the empirical choice patterns and the mean choice percentage of consumed pellets by food location, flavor, and rank.
(A) The foraging behavior of a representative rat for two days, day 5 and day 14, illustrating the choice dynamics. The ordinate represents each food location/type and the abscissa represents the hour of the day. The light and dark cycles are denoted as yellow and black bars above each day's choice plot, with overall choice plotted per hour below the choice plot. The histogram to the right shows the total choices for the entire experiment. For subject 2, the rank 1 flavor (red color) was chocolate, located at the far right [RR]; the rank 2 (orange color) was coffee, middle left [ML]; the rank 3 (green color) was banana, middle right [MR]; finally, the rank 4 (blue color) was cinnamon, at the far left [LL]. (B) Entropy changes of representative data over trials. Black and red solid lines represent the entropy changes of the empirical and randomly shuffled data, respectively. (C) Mean choice percentage for specific food locations (LL, ML, MR, and RR) across subjects. (D) Mean choice percentage by flavor across subjects. (E) The mean choice percentage across subjects for each rank is shown in a log-linear scale. Choice percentage linearly decreases as a function of log(rank order). The dotted line is the log-linear fit (the slope = −70.7±4.95 [mean ± s.e.m], adj. R2 = 0.994). For all figures, error bars are standard errors of the mean (s.e.m). In C, D and E, a Dunnett-T3 post hoc test was conducted: *p<0.05, **p<0.01, ***p<0.001.
Figure 2.
Temporal features of the foraging behavior.
(A) The variation of intake percentage during a day averaged over all rats. (B) The autocorrelogram of the time series of foraging behavior over all rats. The period of the foraging behavior is measured by extracting the pitch of the average autocorrelogram. The time interval between peaks is 24 hours, which is consistent with the animals' circadian rhythm. (C) The inter-choice interval (ICI) sequence for an example rat (subject 4). Short ICIs are abundant while long ICIs are intermittently observed. (D–F) display example results for the same rat. (D) The cumulative distribution of ICIs longer than a given ICI is heavy-tailed in a log-log scale. The distribution of the empirical data (black solid line) is compared to what would be predicted from a homogeneous Poisson process (HPP) (green solid line). The red and blue solid lines denote the cumulative ICI distribution for the light and dark cycles, respectively. (E) The probability density function of the bimodal ICI distribution. The power-law fitted to the probability density function for short ICIs is shown in a log-log scale (the red line in the inset) (F) Separate cumulative ICI distributions for short and longer ICIs in the light (red) and dark (blue) cycles. Squares and triangles denote short and longer ICIs, respectively. For short ICIs, the magenta and cyan lines represent synthetic power-law distributions with the upper bound fitted to the empirical data for the light and dark cycles, respectively. For longer ICIs, the magenta and cyan lines represent synthetic Weibull distributions fitted to the empirical data for the light and dark cycles, respectively. (D–F) The black dotted line represents the time constant
, which separates events into independent bursts. All the exponents were obtained by maximum likelihood estimation (MLE).
Table 1.
Parameter estimates of the bimodal ICI distributions.
Figure 3.
Sequential features of the empirical choice patterns.
(A) A trial-dependent change of run lengths for one example rat is shown both for all runs together and separated by rank. Short runs are frequent while a few long runs are intermittently observed. (B) Cumulative distribution of runs longer than a given length of run in a log-log scale for one example rat (subject 5). The cumulative run distribution of the empirical data compared to randomly shuffled data with no trial-by-trial dependencies. (C) Cumulative run distribution of each rank for the same rat (subject 5). (D) The hazard rate for ending a run with respect to the number of preceding choices in a run averaged over all rats.
Figure 4.
Comparison of the simulation of the dual-state model with the empirical data.
(A) Schematic diagram for the dual-state model. (B–C) Cumulative ICI distributions of the empirical data (black squares) from two example rats and the simulated data from the dual-state model (red circles) in a log-log scale. (D) Autocorrelograms of the empirical and the simulated data averaged across rats. The black and red lines denote the empirical and the simulated data, respectively. The time interval between peaks of the simulated data is 24 hours, which is consistent with that of empirical data.
Table 2.
Parameter estimates of the dual-state temporal model.
Table 3.
Parameter estimates of the dual-control choice model.
Table 4.
Comparisons among choice models.
Figure 5.
Comparison of a choice sequence generated from the dual-control model with the empirical data from two representative rats.
(A–B) Cumulative run distributions of the empirical data for the two representative rats and the simulated data in a log-log scale. The black squares denote the empirical data and the blue circles the simulated data. (C–D) Cumulative choice frequency graphs for each rank for both the empirical data (solid lines) and simulation (dashed lines). Red, orange, green, and blue represent the rank order from rank 1 to rank 4, respectively.