The effects of reinforcer magnitude on timing in rats

Abstract

The relation between reinforcer magnitude and timing behavior was studied using a peak procedure. Four rats received multiple consecutive sessions with both low and high levels of brain stimulation reward (BSR). Rats paused longer and had later start times during sessions when their responses were reinforced with low-magnitude BSR. When estimated by a symmetric Gaussian function, peak times also were earlier; when estimated by a better-fitting asymmetric Gaussian function or by analyzing individual trials, however, these peak-time changes were determined to reflect a mixture of large effects of BSR on start times and no effect on stop times. These results pose a significant dilemma for three major theories of timing (SET, MTS, and BeT), which all predict no effects for chronic manipulations of reinforcer magnitude. We conclude that increased reinforcer magnitude influences timing in two ways: through larger immediate after-effects that delay responding and through anticipatory effects that elicit earlier responding.

Fig 1. Mean wait time (s) as a function of reinforcer magnitude and previous trial type.

For data in the left columns, the previous trial was reinforced, and for data in the right columns, the previous trial was nonreinforced (peak).

Fig 2. Mean response rate as function of time into peak trial for each rat in each reinforcer condition in 1-s bins.

Each column presents data from an individual rat. Each row presents averaged data from the final five sessions for each of the three levels of reinforcer magnitude (High 1, Low, and High 2). The curves plot the result from the best-fitting Gaussian model (DGKQ: Dual Gaussian with a Kurtosis factor and Quadratic tail; see Methods) to the response-rate data. The dotted line in each plot represents the time at which reinforcement was available to rats on nonpeak trials (20 s).

Fig 3. Evaluative criteria comparing the three different Gaussian models.

(A) Akaike Information Criteria (AIC) calculated across all rats and all reinforcer conditions for each of the models for both datasets. Lower AIC scores indicate better models. Note that the y-axis is inverted. (B) Durbin-Watson (DW) statistic calculated independently for each rat, averaged across reinforcement condition. Points below the dashed line denote significant autocorrelation at a .05 alpha level. SG  =  Single Gaussian; SGR  =  Single Gaussian plus linear Ramp; DGKQ  =  Dual Gaussian with a Kurtosis parameter plus Quadratic tail.

Fig 4. Fitted peak times, peak rates plus start and stop half-max times as a function of reinforcer magnitude for each rat from the model that best fit the data (DGKQ: Dual Gaussian with a single Kurtosis parameter and a Quadratic tail).

Error bars are 95% confidence intervals as calculated by a bootstrapped resampling method. Note that the parameters are plotted on different y-axes.

Fig 5. Frequency distributions of start and stop times from the single-trial analysis.

Each row plots the cumulated frequency in 1-s bins of starts (dashed curves) and stops (solid curves) across the final five sessions with each reinforcer magnitude condition (High 1, Low, and High 2). The dotted vertical line represents the time at which reinforcement became available to rats on nonpeak trials (20 s).

Fig 6. Median start and stop times (+ SEM) from the single-trial analysis, averaged across all 4 rats at each reinforcer magnitude condition (High 1, Low, and High 2).