Evidence for a Mixed Timing and Counting Strategy in Mice Performing a Mechner Counting Task

Abstract

Numerosity, or the ability to understand and distinguish between discrete quantities, was first formalized for study in animals by Mechner (1958a). Rats had to press one lever (the counting lever) n times to arm food release from pressing a second lever (the reward lever). The only cue that n presses had been made to the counting lever was the animal's representation of how many times it had pressed it. In the years that have passed since, many researchers have modified the task in meaningful ways to attempt to tease apart timing-based and count-based strategies. Strong evidence has amassed that the two are fundamentally different and separable skills but, to date, no study has effectively examined the differential contributions of the two strategies in Mechner's original task. By examining performance mid-trial and correlating it with whole-trial performance, we were able to identify patterns of correlation consistent with counting and timing strategies. Due to the independent nature of these correlation patterns, this technique was uniquely able to provide evidence for strategies that combined both timing and counting components. The results show that most mice demonstrated this combined strategy. This provides direct evidence that mice can and do use numerosity to complete Mechner's original task. A rational agent with fallible estimates of both counts made and time elapsed in making them should use both estimates when deciding when to switch to the second lever.

Keywords: counting; mice; numerosity; operant conditioning; timing.

Figure 1

Top: schematic plots of press count vs. elapsed run time. The black line is the average across many trials. The colored lines portray individual runs that are found to be slower or faster than the average at 1/2 the mean terminal time [1/2 $\overline{T}$ and red (A) and green (B) lines/dots] or at 1/2 the mean terminal count [1/2 $\overline{C}$ and blue (A) and purple (B) lines/dots]. Lines equal in slope to the average slope extend from these drop-in points to the mean terminal time $\overline{T}$ and mean terminal count $\overline{C}$. Bottom: the correlations obtained from simulated data. The colors of the lines/dots in the top panel denote the predicted correlations, as portrayed in the bottom panel by bars of the same color. Thus, for example, a low count at 1/2 $\overline{T}$ predicts a low terminal count if the run is time terminated (panel B, lower green line/dots) and a long terminal time if the run is count terminated (panel A, lower red line/dots) The first prediction is the positive correlation—low with low and high with high—that was in fact observed in our simulation (green bar on the right side of the lower panel). The second prediction is the negative correlation—low with long and high with short—that was in fact observed in our simulation (red bar on the left side of the lower plot).

Figure 2

Performance across the last five sessions of a Mechner counting task. Average efficiency is plotted as a function of session for both 10 and 20 count requirements. Error bars indicate standard errors of the mean.

Figure 3

Comparison of coefficient of variation (CV) across task strategies. Average CV of terminal values across the last five sessions of training is plotted as a function of three possible strategies. Error bars indicate standard errors of the mean. Asterisks indicate statistically significant LSD post hoc comparisons (p < 0.05).

Figure 4

Analysis of counting and trial timing strategies. Top: predicted correlations based on counting (left) and trial timing (right) strategies. When one drops in at a fixed count, only elapsed trial time varies; likewise, when one drops in at a fixed trial time, only elapsed count varies. Bottom: computed correlation coefficients for all four mice with a 20-count requirement (left) and all four mice with a 10-count requirement (right). The horizontal dotted lines mark alpha = 0.01; bars that cross these lines indicate correlations significant at beyond the 0.01 level.

Figure 5

Analysis of counting and run-time timing strategies. Top: predicted correlations based on counting (left) and run-time timing (right) strategies. When one drops in at a fixed count, only elapsed run time varies; likewise, when one drops in at a fixed run time, only elapsed count varies. Bottom: computed correlation coefficients for all four mice with a 20 count requirement (left) and all four mice with a 10 count requirement (right). The horizontal dotted lines mark alpha = 0.01; bars that cross these lines indicate correlations significant at beyond the 0.01 level.

Figure 6

Relationship between efficiency and bias towards one strategy. Strategy Bias (difference between contribution of timing and counting) is plotted as a function of Overall Efficiency (number of rewards earned/number of trials for all five sessions). Positive values of contributor bias indicate counting bias while negative values indicate timing bias. The trend line indicates the regression line.