Median reinforcements to acquisition plotted against the C/T ratio

Note. Asterisks show the data from Gibbon and Balsam’s (1981) metanalysis of acquisition in pigeon acquisition. The two open circles are from Jenkins, Barnes and Barrera (1981) who used even bigger C/T ratios in some of their groups. The log of the informativeness is the mutual information, I, between the CS and the expected wait for reinforcement (λR; lower x axis). The learning rate (right axis, reversed) is the reciprocal of reinforcements to acquisition (thus the axis increases towards zero). The regression model was fit only to the asterisks, but it also predicts the Jenkins et al. data. The value k is the x intercept, the informativeness that produces one-trial learning. The regression model curves upward to infinity as informativeness goes to 1 and mutual information to 0 because, when the CS rate does not differ from the contextual rate of reinforcement, differential responding to the CS does not emerge (Rescorla, 1967, 1968).

Summary of groups.

Mean response rate for each group across Sessions or across time since CS onset.

Note. There were 10 (groups with C/T ≤ 72) or 3 (groups with C/T ≥ 110) trials per session. Plot 15 (bottom right) shows the mean response rate per second during the CS, averaged from the last 5 sessions. Each group is identified by the length of the mean CS-US interval (T).

Number of trials for acquisition of responding to the CS, plotted against CS informativeness (C/T ratio).

Note. Number of trials to reach acquisition criterion for each group (filled orange circles) and each rat (unfilled orange diamonds) plotted against informativeness of the CS, superimposed onto the data (black asterisks) from Gibbon & Balsam (1981) and the regression line shown in Figure 1. The different plots show trials to acquisition using different acquisition criteria. A plots the trial after which the cumulative response rate during the CS is permanently greater than cumulative ITI response rate (not applying any statistical threshold for significance). B plots the trial on which the CS response rate is greater than the ITI response rate by a non-parametric signed-rank test with probability 0.3125 (equivalent to 3 out of 4 trials). C plots the trial on which the nDKL is greater than 2.2, corresponding to odds more than 27:1 that the CS response rate was greater than the ITI rate. D is a tile plot of the same data as in C and includes the learning rate (right axis; reciprocal of the number of trials to acquisition) plotted against the mutual information (log2 of informativeness) for the 14 groups. The number of trials to acquisition has been divided into 14 bins of approximately equal width on a logarithmic scale represented by the 14 rows of tiles. The darkness of each tile shows the number of rats that reached criterion within that range of trials (see greyscale bar on right).

Response metrics, averaged over the final 5 conditioning sessions, plotted against T.

Note: Open grey circles show data for individual rats. Black filled circles show mean data for each group. The dashed orange lines are the best-fitting regression lines.

Terminal response rates (final 5 sessions) of individual rats as a function of the reinforcement rate on double-logarithmic coordinates.

Note: Red circles show response rates during the CS (number of pokes after the first poke divided by the remaining CS time when the rat’s head was out of the magazine) plotted against the CS reinforcement rate (1/T). Black circles show response rates during the inter-trial interval (ITI; calculated as number of pokes in the pre-CS interval divided by the pre-CS time with head out of the magazine) plotted against the baseline reinforcement rate (1/C). Filled circles show data of rats given 420 reinforced trials (Groups with C/T ratios of 72 or less), and open circles show data of rats given 126 reinforced trials (Groups with C/T ratios of 110 or more). The Model gives the equation for the solid black regression line (R2 = 0.80). The slope of this line is virtually indistinguishable from 1 (R2 = 0.80, when slope fixed at 1). The dashed red and grey lines show the regression lines fitted separately to the CS response rates and ITI responses rates.

Response rate and trials to criterion for an individual rat.

Note. The grey line in A shows the response rate on each trial for an individual rat (Rat 10 from Group C/T = 9). The response rate was calculated as the number of responses during the CS divided by the total time out of the magazine but excluding the latency to first response (i.e., the total time across which the animal could respond). In B, the cumulative response count across trials for the same rat is plotted against the cumulative opportunity to respond (cumulative time out of the magazine). The slope of this cumulative function was used to identify the trial on which the rat’s response rate reached each decile (from 10% to 90%) of its peak response rate, as shown in C. These trials are also marked as circles on the response plots in A and B.

Number of trials to each decile of peak response rate.

Note. The coloured line plots show the mean number of trials to each decile for each rat in each of the 14 groups (identified by the C/T ratio). The thick black line in each plot is the average for that group. The slopes of those black lines for each group are plotted against each group’s T in the rightmost plot of the third row. The final plot in the bottom right corner of the figure plots the Bayesian Information Criterion (BIC) for an exponential function against the BIC for a straight line when each was fitted to the trials-to-criterion data of individual rats (each open black circle shows the BICs for one rat). For each point in the top left of the plot (above the solid orange line), BICline < BICexponential, meaning that the data were better accounted for by the line than the exponential function (and vice versa for points in the bottom right half of the plot). The two dashed orange lines mark where the difference in BICs equals 4.6 which equates to odds of 10:1 in favour of the function with the lower BIC.

The parsed response rates during the CS (solid lines) and during the ITI (dashed lines) for the first 6 rats in the group with the lowest informative-ness (ι = 1.5).

The parsed response rates during the CS (solid lines) and during the ITI (dashed lines) for the first 6 rats in the group with the highest informativeness (ι = 299).

Cumulative distributions of the nDKL for the difference between the CS reinforcement rate and the contextual rate.

Note. The cumulative distributions are plotted as of the reinforcement after which the behavioural evidence for acquisition satisfied increasingly stringent criteria (Earliest evidence, and Odds of 10:1, 100:1 and 1,000:1 in favour of the trustworthiness of the observed mutual information). The informativeness (l) increases from left to right within a row of panels and top to bottom between panels.

Note. In panels a & c, the rate of poking during the CS, denoted λr|CS, (solid black line), during pre-CS ITIs, λr|Pre (dashed black line), and the contextual rate, λr|C(dotted black line), plotted as functions of the number of reinforcements (1 R/trial). The red curve is the signed nDKL plotted against the right axis. The x-axis in a has been right-cropped to better reveal early changes. Panels b & d show the parsed estimates of λr|CS and λr|CS. In all plots, the vertical red lines mark different estimates of when CS-conditional responding appeared (see text).

Note. Second example: from a subject in the group with the maximally informative protocol. The average pokes/min plots for the CS in Panels a and c (solid black curves) are cumulative poke count divided by cumulative CS duration; they include the single pokes made during CS 3 and CS 5. These first pokes were ignored by the parse algorithm.