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Within-session changes in responding during concurrent variable interval variable ratio schedules
Behavioural Processes 55 (2001) 163– 179 www.elsevier.com/locate/behavproc
Within-session changes in responding during concurrent variable interval variable ratio schedules Frances K. McSweeney *, Eric S. Murphy, Benjamin P. Kowal Department of Psychology, Washington State Uni6ersity, Pullman, WA 99164 -4820, USA Received 18 January 2001; received in revised form 8 May 2001; accepted 24 May 2001
Abstract Rats (Experiment 1) and pigeons (Experiment 2) responded on several concurrent variable interval (VI) variable ratio (VR) schedules. The rate of, but not the time spent, responding in each component usually changed within-sessions. The bias and sensitivity parameters of the generalized matching law (GML) did not change systematically within-sessions. The fit of the GML to the data did not change within-sessions for pigeons, but it was better in the middle than at the beginning or end of the session for some for rats. Both over- and under-matching occurred. These results imply that within-session changes in responding do not usually cause problems for assessing the validity of the GML when subjects respond on concurrent VI VR schedules. The results also suggest that underand over-matching are not produced by different factors, but rather lie on a continuum. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Concurrent schedule; Matching law; Pigeons; Rats; Variable interval schedule; Variable ratio schedule
1. Introduction The generalized matching law (GML) has provided the leading description of operant choice behavior for more than 25 years (Baum, 1974). It appears in Eq. (1). The rates of responding emitted on, the time spent responding on, and the values of the reinforcers obtained from, one schedule (component) of a concurrent schedule are symbolized by P1, T1, and V1, respectively. The same variables for the other component are * Corresponding author. Tel.: + 1-509-335-3508; fax: +1509-335-5043. E-mail address: [email protected] (F.K. McSweeney).
symbolized by P2, T2, and V2. Many factors contribute to reinforcer value including the size of the reinforcers, the immediacy of their delivery, and their rate of delivery (e.g. Baum, 1974). The a and b parameters are ‘bias’ and ‘sensitivity to reinforcement’, respectively. Bias represents preference for an alternative that is not explained by differences in the values of the reinforcers provided by the alternatives. Sensitivity represents the degree to which preference changes with changes in reinforcer ratios.
P1 T1 V = =a 1 P2 T2 V2
0376-6357/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 6 - 6 3 5 7 ( 0 1 ) 0 0 1 7 9 - 6
b
(1)
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Recently, it has been reported that the ability of reinforcers to support instrumental responding (reinforcer value) changes systematically with their repeated presentation during an experimental session (McSweeney et al., 1996b). These changes in reinforcer value might cause problems for the GML. Suppose, for example, that the changes are produced by a factor that contributes multiplicatively with other reinforcer variables to the overall value of the reinforcer. If this multiplier changes in the same way within-sessions for the two components of a concurrent schedule, then its effect would cancel when the ratios of the GML were calculated. As a result, the parameters and fit of the GML would be constant across the session. If, however, the multipliers differed for the two components or if the interaction was not multiplicative, then the parameters and fit of the GML might change within the session and, therefore, depend on the time within the session at which they were measured. Because longer sessions would sample different values of the parameters and fit than shorter sessions (McSweeney, 1992; McSweeney et al., 1994), the parameters and fit would also vary with session length, an undesirable result. To date, the parameters and fit of the GML have remained constant within the session as long as the components provide the same type of reinforcer. This conclusion holds regardless of whether the reinforcers are provided by similar (McSweeney et al., 1996c) or different operanda (McSweeney et al., 1995), and by similar (e.g. McSweeney et al., 1996c) or different simple schedules (McSweeney et al., 1999). The parameters and fit of the GML do change within the session when the components provide qualitatively different reinforcers (e.g. food and water; McSweeney et al., 1996a). The present experiments examined whether within-session changes in responding distort the interpretation of the GML when rats (Experiment 1) and pigeons (Experiment 2) respond on concurrent variable interval (VI) variable ratio (VR) schedules. The ratio of the programmed rates of reinforcement changed across conditions so that the GML could be fit to the data. Two species of subjects were used to examine the generality of
the results. Concurrent VI VR schedules were studied because conformity to the GML is often different for these schedules than for other schedules. For example, although under-matching (sensitivity parameter B1.0) is usually reported when subjects respond on concurrent VI VI schedules (e.g. Baum, 1979) over-matching (sensitivity parameter \ 1.0) is often found when subjects respond on concurrent VI VR schedules (e.g. Herrnstein and Heyman, 1979; Ziriax and Silberberg, 1984; Baum and Aparicio, 1999). Therefore, conclusions about the GML that are based on data obtained from other concurrent schedules may not generalize to the concurrent VI VR schedule.
2. Experiment 1
2.1. Materials and method 2.1.1. Subjects The subjects were five experimentally naive male rats, bred from Sprague–Dawley stock. They were maintained at approximately 85% of their free-feeding weights by post-session feedings given when all rats had completed their daily sessions. Weights were established immediately before the experiment, which began when the rats were approximately 120-days old. Rats were housed individually and were exposed to a 12:00/ 12:00 h light/dark cycle. 2.1.2. Apparatus The apparatus was a two-lever experimental enclosure, measuring 20.0×24.5× 24.5 cm. A 5.0× 5.5-cm opening, which allowed access to reinforcers, was centered on the front panel, 0.5 cm above the floor. Two 4.0 ×1.5-cm levers appeared 2.5 cm from this opening, one on each side. The levers were 5.0 cm above the floor and extended 1.5 cm into the enclosure. A 2.0-cm diameter light was located 2.5 cm above each lever. A third, 2.0-cm diameter, light was centered on the front panel, 4.0 cm from the ceiling. The houselight was another 2.0-cm light, located in the center of the ceiling. The apparatus was enclosed in a sound-attenuating chamber. An exhaust fan masked noises from outside. Experimental events
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were presented and data were recorded by MED Associates software run by an IBM-compatible 486 computer, located in another room.
2.1.3. Procedure Each rat was placed in the apparatus until the left and right levers had each been pressed 100 times on a continuous reinforcement schedule. Then the experiment began. In the first condition, rats responded on a concurrent VI 30 s VR 30 schedule. Pressing the left lever produced reinforcers (one 45 mg Noyes pellet per reinforcer) according to the VI schedule; pressing the right lever produced reinforcers according to the VR schedule. Reinforcers for each schedule were programmed by a 25-interval Fleshler and Hoffman (1962) series. The interreinforcer timer for the VI schedule operated throughout the session, stopping only when a reinforcer was scheduled for delivery. That is, the clock advanced regardless of whether the subject responded on the VR or VI schedule. A 3-s changeover delay (COD), during which responses were not reinforced, followed all changes from one operandum to the other. The houselight and the lights above the left and right levers were illuminated throughout the 60-min sessions. Sessions were conducted daily, five to six times per week. When rats had responded on this schedule for 30 sessions, they were exposed to the following schedules in the following order, concurrent VR 30 VI 15 s, concurrent VI 40 s VR 30, concurrent VR 45 VI 40 s, concurrent VI 40 s VR 60 and concurrent VR 30 VI 30 s. The schedule presented on the left lever is listed first. Each schedule was conducted for 30 sessions. These schedule values were selected because they were used by Herrnstein and Heyman (1979). Therefore, subjects should respond frequently enough on each component of these schedules to allow fitting of the GML. 2.2. Results and discussion Fig. 1 presents rates of responding (responses per minute) during successive 5-min intervals in the session for each component of each concurrent schedule. Rates were calculated by dividing
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the number of responses in a component during a 5-min interval by 5 min. Rates were averaged over the last five sessions for which each concurrent schedule was available and over all rats. Fig. 2 presents the proportion of total-session responses during successive 5-min intervals in the session for each component of each concurrent schedule. Proportions were calculated by dividing the rate of responding on each component during a 5-min interval for the mean of all rats by the sum of the rates of responding on that component across all 12, 5-min intervals in the session for the mean of all rats. Each graph in each figure presents the results for a concurrent schedule. Figs. 1 and 2 suggest that rates of responding often changed within-sessions. Although withinsession changes are difficult to see when response rate is slow in Fig. 1, the changes appear more clearly when proportions are plotted in Fig. 2. As in past studies (e.g. McSweeney, 1992), response rates usually increased and then decreased within the session. Occasionally, response rates only decreased. Two-way (component × 5-min interval) repeated-measures analyses of variance (ANOVAs) showed that response rates changed significantly within-sessions for all schedules except the final VR 30 VI 30 s (significant main effect of time, F(11, 44)= 9.363, first concurrent VI 30 s VR 30; F(11, 44)= 6.011, concurrent VR 30 VI 15 s; F(11, 44)= 5.445, concurrent VI 40 s VR 30; F(11, 44)= 2.300, concurrent VR 45 VI 40 s; F(11, 44)= 3.740, concurrent VI 40 s VR 60; F(11, 44)= 1.707, final concurrent VR 30 VI 30 s). Here and throughout this paper, results were significant when PB 0.05. Fig. 3 presents the time spent responding on the VR component (seconds) during successive 5-min intervals in the session for each concurrent schedule. Time spent was measured by a timer that started when the subject responded on the VR component and stopped when the subject switched to the VI component. Results are presented only for the VR component because the time spent responding on the two components summed to the 300 total seconds available for all 5-min intervals except the first. The time to the first response in the session was not included in the time spent responding for either component.
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Each graph presents the results for a different concurrent schedule. The results were averaged over all rats, during the final five sessions for which each schedule was available. Fig. 3 shows that time spent responding on the VR component (and therefore the VI component) changed little within-sessions. One-way (5-min intervals) repeated-measures ANOVAs showed that the time spent responding in the VR component did not change significantly within-sessions for any schedule except the concurrent VR 30 VI 15 s (F(11, 44)=1.666, first concurrent VI 30 s VR 30;
F(11, 44)= 2.545, concurrent VR 30 VI 15 s; F(11, 44)= 1.852, concurrent VI 40 s VR 30; F(11, 44)= 1.083, concurrent VR 45 VI 40 s; F(11, 44)= 1.683, concurrent VI 40 s VR 60; F(11, 44)= 1.183, final concurrent VR 30 VI 30 s). Time spent responding on the VR component increased and then decreased within the session when it changed significantly. Table 1 (top) presents the parameters and fit of the GML when the equation was fitted to results averaged over the session. The left side presents the results when the GML was fitted to the ratios
Fig. 1. Rates of responding (responses per minute) during successive 5-min intervals in the session for the mean of all rats responding on each component of each concurrent schedule in Experiment 1. Each graph presents the results for a concurrent schedule. The solid line represents responding on the VI component; the dashed line represents responding on the VR component.
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Fig. 2. Proportion of total-session responding during successive 5-min intervals in the session for the mean of all rats responding on each component of each concurrent schedule in Experiment 1. Each graph presents the results for a concurrent schedule. The solid line represents responding on the VI component; the dashed line represents responding on the VR component.
of response rates (response matching). The right side presents the results when the GML was fitted to the ratios of the times spent responding (time matching). The rates of reinforcement obtained from the two components were used to represent the values of the components. A leastsquares procedure was used to fit the GML to the logarithms of the ratios of the appropriate variables for each subject (see Eq. (1)). This procedure was used because it was used in the studies to which the present results will be compared (e.g. Herrnstein and Heyman, 1979; Ziriax
and Silberberg, 1984; McSweeney et al., 1996a, 1999; Baum and Aparicio, 1999). Results for the VR component were divided by those for the VI component. The GML was not fitted to rat 308’s data because this subject exhibited exclusive preference for the VI component during the last three conditions. As a result, the twoparameter GML would have been fit to only three points for this subject. Exclusive preference has been reported in the past when subjects respond on concurrent VI VR schedules (e.g. Herrnstein and Heyman, 1979).
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Table 1 shows that the GML fit the data well, accounting for 86.5– 99.2% of the variance. All rats showed a bias towards the VR component (bias parameter \1.0). Both over- (sensitivity parameter \ 1.0) and under-matching (sensitivity parameter B1.0) occurred for response matching. Under-matching occurred for time matching. Figs. 1 and 2 showed that the within-session patterns of responding were similar for the two components of the concurrent schedules but that differences also occurred. Figs. 4 and 5 ask whether the differences produced systematic
changes in the parameters and fit of the GML within the session. Notice that even large withinsession changes in the ratios of the rates of responding would not alter the parameters and fit of the GML if those changes were accompanied by similar changes in the ratios of rates of reinforcement. Fig. 4 presents the parameters and fit (r 2) of the GML during successive 5-min intervals in the session averaged over the four rats. Fig. 5 presents the same results for individual rats. The left graphs present the results for response matching.
Fig. 3. The time spent responding on the VR component during successive 5-min intervals for the mean of all rats responding on each concurrent schedule in Experiment 1. Each graph presents the results for a concurrent schedule.
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Table 1 The parameters of, and the percentage of the variance accounted for by (r 2), the GML for individual subjects when data were averaged over the entire session Subject
Responses
Time
Bias
Sensitivity
r2
Bias
Sensitivity
r2
Rats 306 307 309 310
1.908 1.621 1.710 1.893
0.973 1.171 0.715 1.065
86.5 99.1 93.0 91.7
1.111 1.205 1.122 1.196
0.633 0.751 0.839 0.894
96.0 99.2 92.3 97.7
Pigeons 19 20 2560
1.133 2.456 1.704
1.059 1.045 0.803
93.6 99.1 98.3
0.559 0.500 1.073
1.185 0.818 0.852
70.0 99.5 92.9
Results on the left are those for response matching; those on the right are for time matching.
The right graphs present the results for time matching. The GML was fitted to the data as for Table 1 except that the data that entered the calculations were averaged over 5-min intervals rather than over the entire session. As would be expected when results are calculated over intervals as short as 5 min, there is some variance in Figs. 4 and 5. However, the GML provided a good description of the data. The GML usually accounted for more than 90% of the variance for both response and time matching. The fit of the GML was somewhat better during the middle of the session than it was early or late in the session. One-way (5-min intervals) repeated-measures ANOVAs showed that the percentage of variance accounted for changed significantly within the session for both response (F(11, 33) = 2.472) and time (F(11, 33)=2.191) matching. Although some individual rats showed relatively good fits throughout the session (rats 307 and 309 for response matching; rat 310 for time matching), others showed relatively good fits towards the middle of the session, but poorer fits at either the beginning (e.g. rats 306 and 307 for time matching) or end (e.g. rat 310 for response matching; rat 309 for time matching) of the session or both (e.g. rat 306 for response matching). For the mean of all rats, behavior was biased toward the VR schedule (bias \1.0) but the bias parameter changed unsystematically within the
session. Rats 306, 309 and 310 showed a bias towards the VR component for both response and time matching that was maintained across most of the session. Rat 307 was sometimes biased toward the VI (bias B 1.0) and sometimes toward the VR schedule. The within-session changes in bias were inconsistent across subjects. One-way (5-min interval) repeated-measures ANOVAs showed that the bias parameter did not change significantly within the session for either response (F(11, 33)= 0.961) or time (F(11, 33)= 0.751) matching. The sensitivity parameters were usually less than 1.0 for time matching. They were both greater than and less than 1.0 for response matching. Again, sensitivity parameters did not change systematically within the session for the mean of all subjects or in a way that was consistent across individual rats. One-way (5-min interval) repeated-measures ANOVAs showed that the sensitivity parameters did not change significantly within the session for either response (F(11, 33)= 1.058) or time (F(11, 33)= 0.941) matching.
3. Experiment 2
3.1. Materials and method 3.1.1. Subjects The subjects were four experimentally experienced pigeons, maintained at approximately 85%
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of their free-feeding body weights by post-session feedings delivered when all pigeons had completed the daily session. Pigeons were housed individually and were exposed to a 12:00/12:00 h light/dark cycle.
3.1.2. Apparatus The apparatus was a three-key experimental enclosure, measuring 30.0×36.0 ×27.0 cm. Three 2.5-cm diameter keys were positioned 21.5 cm above the floor and 7.5 cm apart. The left key was 7.0 cm from the left wall; the right key, 7.5 cm
from the right wall. A 4.5× 5.0-cm opening allowed access to a food magazine. It was 7.5 cm above the floor and 15.0 cm from the right wall. A 4.0-cm diameter houselight was located 1.5 cm from the ceiling and 0.5 cm from the right wall. The experimental panel was housed in a sound-attenuating chamber. A ventilating fan masked noises from outside the chamber. Experimental events were programmed and data were recorded by MED Associates Software run by an IBMcompatible 486 computer, located in another room.
Fig. 4. The bias (top graphs) and sensitivity (middle graphs) parameters of, and the percentage of the variance accounted for (bottom graphs) by, the GML for the mean of all rats in Experiment 1. The left graphs present the results for response matching; the right graphs for time matching.
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Fig. 5. The bias (top graphs) and sensitivity (middle graphs) parameters of, and the percentage of the variance accounted for (bottom graphs) by, the GML for individual rats in Experiment 1. The left graphs present the results for response matching; the right graphs for time matching.
3.1.3. Procedure The pigeons had pecked keys in previous experiments. Therefore, they were placed directly on the experimental procedure. The procedure was identical to that used for rats with the following exceptions. First, reinforcers were 5-s access to mixed grain. The time for which reinforcement was available was excluded from the timing of the session and of the 5-min intervals. Second, the components of the concurrent schedule were available on the left and right keys rather than on the left and right levers. Both keys were illuminated with white light except that they were dark when a reinforcer was presented.
3.2. Results and discussion Fig. 6 presents rates of responding (responses per minute) during successive 5-min intervals in the session for the mean of all pigeons responding on each concurrent schedule. Fig. 7 presents the proportion of total-session responding during successive 5-min intervals in the session for the mean of all pigeons responding on each concurrent schedule. Results were calculated and presented as in Figs. 1 and 2. Figs. 6 and 7 show that response rates changed within-sessions. As in past studies, response rates
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usually increased and then decreased within the session (e.g. McSweeney, 1992). This impression was confirmed by two-way (component × 5-min interval) repeated measures ANOVAs. The main effect of time was significant for all schedules except the concurrent VI 40 s VR 60 (F(11, 33)=1.941) and even for that schedule the results approached significance (P B 0.070; F(11, 33)= 3.025 first concurrent VI 30 s VR 30 F(11, 33)= 3.424, concurrent VR 30 VI 15 s; F(11, 33) =3.718, concurrent VI 40 s VR 30; F(11, 33)= 3.368, concurrent VR 45 VI 40 s; F(11,
33)= 2.774, final concurrent VR 30 VI 30 s). Fig. 8 presents time spent responding on the VR component during successive 5-min intervals for each concurrent schedule. Results were calculated and presented as in Fig. 3. Fig. 8 shows that time spent responding on the VR component was relatively constant within-sessions. The results of one-way (5-min interval) repeated-measures ANOVAs applied to the time spent responding on the VR schedule were significant for the concurrent VR 45 VI 40 s (F(11, 33)= 2.400) and the second concurrent VR 30 VI 30 s schedules (F(11,
Fig. 6. Rates of responding (responses per minute) during successive 5-min intervals in the session for the mean of all pigeons responding on each component of each concurrent schedule in Experiment 2. Each graph presents the results for a concurrent schedule. The solid line represents responding on the VI component; the dashed line represents responding on the VR component.
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Fig. 7. Proportion of total-session responding during successive 5-min intervals in the session for the mean of all pigeons on each component of each concurrent schedule in Experiment 2. Each graph presents the results for a concurrent schedule. The solid line represents responding on the VI component; the dashed line represents responding on the VR component.
33)=2.353), but not for the other schedules (F(11, 33)= 1.039, concurrent VI 30 s VR 30; F(11, 33)= 0.995,concurrent VR 30 VI 15 s; F(11, 33) =1.085, concurrent VI 40 s VR 30; F(11, 33)=1.656, concurrent VI 40 s VR 60). Again, the time spent responding on the VR component increased and then decreased within the session when it changed significantly. Table 1 (bottom) presents the parameters and fit of the GML when it was fit to data averaged over the session. Figs. 9 and 10 present the parameters and fit of the GML during successive
5-min intervals in the session for the mean of all pigeons and for individual pigeons, respectively. Results were analyzed and presented as they were for Table 1 (top) and Figs. 4 and 5. Results are presented for only three subjects because pigeon 10 showed close to exclusive preference for the VI component of most schedules and exclusive preference for that component during the concurrent VI 40 s VR 30 and concurrent VR 45 VI 40 s schedules. The figures present results for only the first 50-min of the session (10 5-min intervals) because pigeons often failed to obtain reinforcers
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late in the session from the VR component of several schedules. Although the GML usually accounted for more than 90% of the variance in the data when results were averaged over the entire session (Table 1, bottom), the GML did not describe the data as well when results were averaged over only 5-min intervals. Because of the high variance visible for individual subjects in Fig. 10, the fit of the GML did not change significantly within the session. One-way (5-min interval) repeated-measures
ANOVAs applied to r 2 were not significant for response (F(9, 18)= 1.634) or for time (F(9, 18)=0.525) matching. Behavior was usually biased toward the VR schedule (bias \ 1.0) for response matching and towards the VI schedule for time matching. The exceptions were pigeon 2560 who was often biased toward the VR schedule for time matching and pigeon 19 who was occasionally biased toward the VI schedule for response matching. Oneway (5-min interval) ANOVAs showed that the
Fig. 8. The time spent responding on the VR component during successive 5-min intervals for the mean of all pigeons responding on each concurrent schedule in Experiment 2. Each graph presents the results for a concurrent schedule.
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Fig. 9. The bias (top graphs) and sensitivity (middle graphs) parameters of, and the percentage of the variance accounted for (bottom graphs) by, the GML for the mean of all pigeons in Experiment 2. The left graphs present the results for response matching; the right graphs for time matching.
bias parameter did not change significantly within the session for response (F(9, 18)=1.489) or for time (F(9, 18)=0.430) matching. The sensitivity parameters were sometimes greater than 1.0 (over-matching) and sometimes less than 1.0 (under-matching) depending on the subject and the time in the session. Negative sensitivity parameters were observed for pigeon 20 during the ninth and tenth 5-min intervals for time matching. One-way (5-min interval) repeated-measures ANOVAs showed that the sensitivity parameters did not change significantly within the session for response (F(9, 18)= 1.314) or for time (F(9, 18)= 0.400) matching.
4. General discussion Within-session changes in response rates were observed for both rats (Experiment 1) and pigeons (Experiment 2) responding on both components of most schedules. As in past studies (e.g. McSweeney, 1992), rate of responding usually increased and then decreased within the session. This finding extends the generality of within-session changes in responding to concurrent VI VR schedules. In contrast to the large changes in response rates, the time spent responding on a component was relatively constant within the session for both rats and pigeons (Figs. 3 and 8). Significant
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within-session changes in time spent responding on the VR components were reported for only one schedule for rats and for two schedules for pigeons. Relatively constant time allocation was also reported by McSweeney et al. (1999) when subjects responded on concurrent VI FI schedules. Time spent responding on the FI component changed significantly within the session for only one of the five (rats) or six (pigeons) schedules that they conducted. In contrast, McSweeney et al. (1996a) reported systematic within-session changes in time spending when subjects responded on concurrent VI VI schedules that provided different reinforcers in the two components (e.g. food and water). Therefore, the time allocated to
each component of a concurrent schedule is relatively constant within the session as long as the components provide the same reinforcers. When the components provide qualitatively different reinforcers, systematic within-session changes in time allocation may occur. It is not clear why the time spent responding on the VR component changed within the session in the few cases that it did. The significant changes do not follow any obvious pattern. For example, in the present experiment, significant changes occurred for the concurrent schedule that provided the highest total reinforcement for rats, but for schedules that provided the second and third lowest total reinforcers for pigeons. Significant
Fig. 10. The bias (top graphs) and sensitivity (middle graphs) parameters of, and the percentage of the variance accounted for (bottom graphs) by, the GML for individual pigeons in Experiment 2. The left graphs present the results for response matching; the right graphs for time matching.
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changes also occurred when the VR component of the concurrent VR 30 VI 30 s schedule appeared on the left, but not on the right, key McSweeney et al. (1999) reported similar results for concurrent VI FI schedules. Their two significant withinsession changes in time allocation occurred for different schedules for rats and pigeons. Therefore, the factors that produce these changes in time allocation are not known. Shurtleff and Silberberg (1990) reported that the relative response and time allocation to the VI alternative of a concurrent VI VR schedule increased as session duration increased from 10 to 30 min. A shift in behavior away from the VR schedule is not apparent in the figures across the first 30 min of the session. For example, if anything, time spent responding shifts to the VR schedule when it changes at all. However, two procedural differences between our study and that of Shurtleff and Silberberg (1990) may have contributed to the difference in results. First, the present experiment did not explicitly manipulate session duration. To compare our results to those of Shurtleff and Silberberg’s, it must be assumed that the results reported for 10 and 30 min into our 60 min sessions are equivalent to the results for 10 and 30 min sessions. Although some data support this assumption (McSweeney, 1992; McSweeney et al., 1994), our results would be more comparable if we had manipulated session duration. Second, Shurtleff and Silberberg’s subjects obtained all of their food during the experimental session. The present subjects were given post-session feedings if they failed to obtain enough food during the session to maintain their body weights. As argued by Shurtleff and Silberberg, their subjects may have shifted their behavior to the VR schedule when sessions were short in order to obtain enough food to sustain themselves. Our subjects did not need to shift their behavior in this way. Therefore, at present, our conclusion that time allocation is relatively constant within the session should not be generalized to studies, such as that of Shurtleff and Silberberg, that employ closed economies. The parameters and fit of the GML reported in Table 1 were consistent with those reported in past studies of responding on concurrent VI VR
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schedules. Similar to results reported by Baum and Aparicio (1999) and by Herrnstein and Heyman (1979), the GML provided a good description of the data. It accounted for more than 90% of the variance for 12 of the 14 fits in Table 1. Rats usually showed a bias towards the VR component (bias parameter \ 1.0). Pigeons showed a bias towards the VR for response matching, but two of three pigeons showed a bias toward the VI for time matching (bias parameter B 1.0). Herrnstein and Heyman (1979) also reported that pigeons were biased towards the VR schedule for response matching and toward the VI schedule for time matching. Both over- (sensitivity parameter \ 1.0) and under-matching (sensitivity parameter B 1.0) occurred for response rate. Under-matching occurred for all rats and for two of three pigeons for time matching. Over- and undermatching have also been reported in the past (e.g. Baum and Aparicio, 1999). Finding both over- and under-matching, sometimes for the same subject at different times in the session (Figs. 4, 5, 9 and 10) or for different behavioral measures (Table 1), sheds some light on the factors that control the sensitivity parameter. According to some theories, over- and undermatching are produced by distinctively different processes. For example, because under-matching is the usual finding in studies of concurrent VI VI schedule performance (e.g. Baum, 1979), it has been argued that exact matching (sensitivity parameter= 1.0) is the true state of behavior. Under-matching results if procedural details prevent the animal from exact matching. For example, performance would depart from matching towards indifference (under-matching) if the subject could not discriminate which component produced a reinforcer. According to this thinking, over-matching is a statistical error when it is reported. According to other theories, over- and under-matching lie on a continuum. For example, Baum (1982) argued that animals respond predominantly on the richer component of the concurrent schedule with brief visits to the leaner one. Altering the cost associated with switching from one alternative to the other can determine whether under- or over-matching is observed. When costs are high, subjects visit the leaner
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alternative infrequently, yielding over-matching. That is, relatively more time is spent on the richer alternative than is justified by the reinforcers it produces. When costs are small, subjects visit the leaner alternative frequently, yielding undermatching. That is, relatively more time is spent on the leaner alternative than is justified by the reinforcers it produces. Because under- and overmatching were found for the same subject at different times in the session, the present results are more consistent with the idea that over- and under-matching lie on a continuum than that they are produced by qualitatively different variables. Fig. 10 shows that negative sensitivity parameters were reported late in the session for pigeon 20. Negative parameters have been reported in the past, but only when subjects respond on schedules that provide qualitatively different reinforcers in the two components (e.g. Hursh, 1978; McSweeney et al., 1996a). As in the present experiment, the negative parameters appeared late in the session when responding was examined withinsessions (McSweeney et al., 1996a). If these negative parameters were replicated for subjects responding on concurrent VI VR schedules, they would challenge the leading explanation for why negative sensitivity occurs (Hursh, 1980, 1984). This explanation predicts negative sensitivity only when the components of the concurrent schedule provide qualitatively different reinforcers. However, because negative sensitivity was observed for only one subject in the present experiment, these negative parameters should be replicated before strong conclusions are drawn. The parameters of the GML did not change significantly within-sessions (Figs. 4, 5, 9 and 10). Because the parameters were relatively constant within-sessions, these parameters should not differ at different times in the session or for sessions of different lengths. Therefore, within-session changes in responding do not create problems for assessing the parameters of the GML when subjects respond on concurrent VI VR schedules. To date, within-session changes in response rates do not create problems for interpreting the GML as long as the components provide the same type of reinforcer. This conclusion holds even when the components are provided on different types of
operanda (McSweeney et al., 1995) or by different types of simple schedules (McSweeney et al., 1999; present experiments). As a final point, the fit of the GML was poorer at the beginning and end of the session than in the middle when rats served as subjects. As a result, researchers who study the GML might examine their data separately for the entire session and for the session with the first and last 10 min eliminated. They might want to report the later statistics if the two differ substantially.
Acknowledgements The present experiments were partially supported by grant RO 1 MH61720 from the National Institute of Mental Health. The results were presented at the 2001 meeting of the Association for Behavior Analysis in New Orleans, LA.
References Baum, W.M., 1974. On two types of deviation from the matching law: bias and undermatching. J. Exp. Anal. Behav. 22, 231 – 242. Baum, W.M., 1979. Matching, undermatching, and overmatching in studies of choice. J. Exp. Anal. Behav. 32, 269 – 281. Baum, W.M., 1982. Choice, changeover, and travel. J. Exp. Anal. Behav. 38, 35 – 49. Baum, W.M., Aparicio, C.F., 1999. Optimality concurrent variable-interval variable-ratio schedules. J. Exp. Anal. Behav. 71, 75 – 89. Fleshler, M., Hoffman, H.S., 1962. A progression for generating variable-interval schedules. J. Exp. Anal. Behav. 5, 529 – 530. Herrnstein, R.J., Heyman, G.M., 1979. Is matching compatible with reinforcement maximization on concurrent variable interval, variable ratio? J. Exp. Anal. Behav. 31, 209 – 223. Hursh, S.R., 1978. The economics of daily consumption controlling food- and water-reinforced responding. J. Exp. Anal. Behav. 29, 475 – 491. Hursh, S.R., 1980. Economic concepts for the analysis of behavior. J. Exp. Anal. Behav. 34, 219 – 238. Hursh, S.R., 1984. Behavioral economics. J. Exp. Anal. Behav. 42, 435 – 452. McSweeney, F.K., 1992. Rate of reinforcement and session duration as determinants of within-session patterns of responding. Anim. Learn. Behav. 20, 160 – 169.
F.K. McSweeney et al. / Beha6ioural Processes 55 (2001) 163–179 McSweeney, F.K., Roll, J.M., Cannon, C.B., 1994. The generality of within-session patterns of responding: rate of reinforcement and session length. Anim. Learn. Behav. 22, 252 – 266. McSweeney, F.K., Weatherly, J.N., Roll, J.M., 1995. Within-session changes in responding during concurrent schedules that employ two different operanda. Anim. Learn. Behav. 23, 237 – 244. McSweeney, F.K., Swindell, S., Weatherly, J.N., 1996a. Within-session changes in responding during concurrent schedules with different reinforcers in the components. J. Exp. Anal. Behav. 66, 369 – 390. McSweeney, F.K., Weatherly, J.N., Swindell, S., 1996b. Reinforcer value may change within experimental sessions. Psychonom. Bull. Rev. 3, 372 –375.
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McSweeney, F.K., Weatherly, J.N., Swindell, S., 1996c. Within-session changes in responding during concurrent variable-interval schedules. J. Exp. Anal. Behav. 66, 75 – 95. McSweeney, F.K., Swindell, S., Weatherly, J.N., 1999. Within-session changes in responding during concurrent fixed interval variable interval schedules. Anim. Learn. Behav. 27, 236 – 248. Shurtleff, D., Silberberg, A., 1990. Income maximization on concurrent ratio-interval schedules of reinforcement. J. Exp. Anal. Behav. 53, 273 – 284. Ziriax, J.M., Silberberg, A., 1984. Concurrent variable-interval variable-ratio schedules can provide only weak evidence for matching. J. Exp. Anal. Behav. 41, 83 – 100.
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Within-session changes in responding during concurrent variable interval variable ratio schedules Frances K. McSweeney *, Eric S. Murphy, Benjamin P. Kowal Department of Psychology, Washington State Uni6ersity, Pullman, WA 99164 -4820, USA Received 18 January 2001; received in revised form 8 May 2001; accepted 24 May 2001
Abstract Rats (Experiment 1) and pigeons (Experiment 2) responded on several concurrent variable interval (VI) variable ratio (VR) schedules. The rate of, but not the time spent, responding in each component usually changed within-sessions. The bias and sensitivity parameters of the generalized matching law (GML) did not change systematically within-sessions. The fit of the GML to the data did not change within-sessions for pigeons, but it was better in the middle than at the beginning or end of the session for some for rats. Both over- and under-matching occurred. These results imply that within-session changes in responding do not usually cause problems for assessing the validity of the GML when subjects respond on concurrent VI VR schedules. The results also suggest that underand over-matching are not produced by different factors, but rather lie on a continuum. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Concurrent schedule; Matching law; Pigeons; Rats; Variable interval schedule; Variable ratio schedule
1. Introduction The generalized matching law (GML) has provided the leading description of operant choice behavior for more than 25 years (Baum, 1974). It appears in Eq. (1). The rates of responding emitted on, the time spent responding on, and the values of the reinforcers obtained from, one schedule (component) of a concurrent schedule are symbolized by P1, T1, and V1, respectively. The same variables for the other component are * Corresponding author. Tel.: + 1-509-335-3508; fax: +1509-335-5043. E-mail address: [email protected] (F.K. McSweeney).
symbolized by P2, T2, and V2. Many factors contribute to reinforcer value including the size of the reinforcers, the immediacy of their delivery, and their rate of delivery (e.g. Baum, 1974). The a and b parameters are ‘bias’ and ‘sensitivity to reinforcement’, respectively. Bias represents preference for an alternative that is not explained by differences in the values of the reinforcers provided by the alternatives. Sensitivity represents the degree to which preference changes with changes in reinforcer ratios.
P1 T1 V = =a 1 P2 T2 V2
0376-6357/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 6 - 6 3 5 7 ( 0 1 ) 0 0 1 7 9 - 6
b
(1)
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Recently, it has been reported that the ability of reinforcers to support instrumental responding (reinforcer value) changes systematically with their repeated presentation during an experimental session (McSweeney et al., 1996b). These changes in reinforcer value might cause problems for the GML. Suppose, for example, that the changes are produced by a factor that contributes multiplicatively with other reinforcer variables to the overall value of the reinforcer. If this multiplier changes in the same way within-sessions for the two components of a concurrent schedule, then its effect would cancel when the ratios of the GML were calculated. As a result, the parameters and fit of the GML would be constant across the session. If, however, the multipliers differed for the two components or if the interaction was not multiplicative, then the parameters and fit of the GML might change within the session and, therefore, depend on the time within the session at which they were measured. Because longer sessions would sample different values of the parameters and fit than shorter sessions (McSweeney, 1992; McSweeney et al., 1994), the parameters and fit would also vary with session length, an undesirable result. To date, the parameters and fit of the GML have remained constant within the session as long as the components provide the same type of reinforcer. This conclusion holds regardless of whether the reinforcers are provided by similar (McSweeney et al., 1996c) or different operanda (McSweeney et al., 1995), and by similar (e.g. McSweeney et al., 1996c) or different simple schedules (McSweeney et al., 1999). The parameters and fit of the GML do change within the session when the components provide qualitatively different reinforcers (e.g. food and water; McSweeney et al., 1996a). The present experiments examined whether within-session changes in responding distort the interpretation of the GML when rats (Experiment 1) and pigeons (Experiment 2) respond on concurrent variable interval (VI) variable ratio (VR) schedules. The ratio of the programmed rates of reinforcement changed across conditions so that the GML could be fit to the data. Two species of subjects were used to examine the generality of
the results. Concurrent VI VR schedules were studied because conformity to the GML is often different for these schedules than for other schedules. For example, although under-matching (sensitivity parameter B1.0) is usually reported when subjects respond on concurrent VI VI schedules (e.g. Baum, 1979) over-matching (sensitivity parameter \ 1.0) is often found when subjects respond on concurrent VI VR schedules (e.g. Herrnstein and Heyman, 1979; Ziriax and Silberberg, 1984; Baum and Aparicio, 1999). Therefore, conclusions about the GML that are based on data obtained from other concurrent schedules may not generalize to the concurrent VI VR schedule.
2. Experiment 1
2.1. Materials and method 2.1.1. Subjects The subjects were five experimentally naive male rats, bred from Sprague–Dawley stock. They were maintained at approximately 85% of their free-feeding weights by post-session feedings given when all rats had completed their daily sessions. Weights were established immediately before the experiment, which began when the rats were approximately 120-days old. Rats were housed individually and were exposed to a 12:00/ 12:00 h light/dark cycle. 2.1.2. Apparatus The apparatus was a two-lever experimental enclosure, measuring 20.0×24.5× 24.5 cm. A 5.0× 5.5-cm opening, which allowed access to reinforcers, was centered on the front panel, 0.5 cm above the floor. Two 4.0 ×1.5-cm levers appeared 2.5 cm from this opening, one on each side. The levers were 5.0 cm above the floor and extended 1.5 cm into the enclosure. A 2.0-cm diameter light was located 2.5 cm above each lever. A third, 2.0-cm diameter, light was centered on the front panel, 4.0 cm from the ceiling. The houselight was another 2.0-cm light, located in the center of the ceiling. The apparatus was enclosed in a sound-attenuating chamber. An exhaust fan masked noises from outside. Experimental events
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were presented and data were recorded by MED Associates software run by an IBM-compatible 486 computer, located in another room.
2.1.3. Procedure Each rat was placed in the apparatus until the left and right levers had each been pressed 100 times on a continuous reinforcement schedule. Then the experiment began. In the first condition, rats responded on a concurrent VI 30 s VR 30 schedule. Pressing the left lever produced reinforcers (one 45 mg Noyes pellet per reinforcer) according to the VI schedule; pressing the right lever produced reinforcers according to the VR schedule. Reinforcers for each schedule were programmed by a 25-interval Fleshler and Hoffman (1962) series. The interreinforcer timer for the VI schedule operated throughout the session, stopping only when a reinforcer was scheduled for delivery. That is, the clock advanced regardless of whether the subject responded on the VR or VI schedule. A 3-s changeover delay (COD), during which responses were not reinforced, followed all changes from one operandum to the other. The houselight and the lights above the left and right levers were illuminated throughout the 60-min sessions. Sessions were conducted daily, five to six times per week. When rats had responded on this schedule for 30 sessions, they were exposed to the following schedules in the following order, concurrent VR 30 VI 15 s, concurrent VI 40 s VR 30, concurrent VR 45 VI 40 s, concurrent VI 40 s VR 60 and concurrent VR 30 VI 30 s. The schedule presented on the left lever is listed first. Each schedule was conducted for 30 sessions. These schedule values were selected because they were used by Herrnstein and Heyman (1979). Therefore, subjects should respond frequently enough on each component of these schedules to allow fitting of the GML. 2.2. Results and discussion Fig. 1 presents rates of responding (responses per minute) during successive 5-min intervals in the session for each component of each concurrent schedule. Rates were calculated by dividing
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the number of responses in a component during a 5-min interval by 5 min. Rates were averaged over the last five sessions for which each concurrent schedule was available and over all rats. Fig. 2 presents the proportion of total-session responses during successive 5-min intervals in the session for each component of each concurrent schedule. Proportions were calculated by dividing the rate of responding on each component during a 5-min interval for the mean of all rats by the sum of the rates of responding on that component across all 12, 5-min intervals in the session for the mean of all rats. Each graph in each figure presents the results for a concurrent schedule. Figs. 1 and 2 suggest that rates of responding often changed within-sessions. Although withinsession changes are difficult to see when response rate is slow in Fig. 1, the changes appear more clearly when proportions are plotted in Fig. 2. As in past studies (e.g. McSweeney, 1992), response rates usually increased and then decreased within the session. Occasionally, response rates only decreased. Two-way (component × 5-min interval) repeated-measures analyses of variance (ANOVAs) showed that response rates changed significantly within-sessions for all schedules except the final VR 30 VI 30 s (significant main effect of time, F(11, 44)= 9.363, first concurrent VI 30 s VR 30; F(11, 44)= 6.011, concurrent VR 30 VI 15 s; F(11, 44)= 5.445, concurrent VI 40 s VR 30; F(11, 44)= 2.300, concurrent VR 45 VI 40 s; F(11, 44)= 3.740, concurrent VI 40 s VR 60; F(11, 44)= 1.707, final concurrent VR 30 VI 30 s). Here and throughout this paper, results were significant when PB 0.05. Fig. 3 presents the time spent responding on the VR component (seconds) during successive 5-min intervals in the session for each concurrent schedule. Time spent was measured by a timer that started when the subject responded on the VR component and stopped when the subject switched to the VI component. Results are presented only for the VR component because the time spent responding on the two components summed to the 300 total seconds available for all 5-min intervals except the first. The time to the first response in the session was not included in the time spent responding for either component.
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Each graph presents the results for a different concurrent schedule. The results were averaged over all rats, during the final five sessions for which each schedule was available. Fig. 3 shows that time spent responding on the VR component (and therefore the VI component) changed little within-sessions. One-way (5-min intervals) repeated-measures ANOVAs showed that the time spent responding in the VR component did not change significantly within-sessions for any schedule except the concurrent VR 30 VI 15 s (F(11, 44)=1.666, first concurrent VI 30 s VR 30;
F(11, 44)= 2.545, concurrent VR 30 VI 15 s; F(11, 44)= 1.852, concurrent VI 40 s VR 30; F(11, 44)= 1.083, concurrent VR 45 VI 40 s; F(11, 44)= 1.683, concurrent VI 40 s VR 60; F(11, 44)= 1.183, final concurrent VR 30 VI 30 s). Time spent responding on the VR component increased and then decreased within the session when it changed significantly. Table 1 (top) presents the parameters and fit of the GML when the equation was fitted to results averaged over the session. The left side presents the results when the GML was fitted to the ratios
Fig. 1. Rates of responding (responses per minute) during successive 5-min intervals in the session for the mean of all rats responding on each component of each concurrent schedule in Experiment 1. Each graph presents the results for a concurrent schedule. The solid line represents responding on the VI component; the dashed line represents responding on the VR component.
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Fig. 2. Proportion of total-session responding during successive 5-min intervals in the session for the mean of all rats responding on each component of each concurrent schedule in Experiment 1. Each graph presents the results for a concurrent schedule. The solid line represents responding on the VI component; the dashed line represents responding on the VR component.
of response rates (response matching). The right side presents the results when the GML was fitted to the ratios of the times spent responding (time matching). The rates of reinforcement obtained from the two components were used to represent the values of the components. A leastsquares procedure was used to fit the GML to the logarithms of the ratios of the appropriate variables for each subject (see Eq. (1)). This procedure was used because it was used in the studies to which the present results will be compared (e.g. Herrnstein and Heyman, 1979; Ziriax
and Silberberg, 1984; McSweeney et al., 1996a, 1999; Baum and Aparicio, 1999). Results for the VR component were divided by those for the VI component. The GML was not fitted to rat 308’s data because this subject exhibited exclusive preference for the VI component during the last three conditions. As a result, the twoparameter GML would have been fit to only three points for this subject. Exclusive preference has been reported in the past when subjects respond on concurrent VI VR schedules (e.g. Herrnstein and Heyman, 1979).
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Table 1 shows that the GML fit the data well, accounting for 86.5– 99.2% of the variance. All rats showed a bias towards the VR component (bias parameter \1.0). Both over- (sensitivity parameter \ 1.0) and under-matching (sensitivity parameter B1.0) occurred for response matching. Under-matching occurred for time matching. Figs. 1 and 2 showed that the within-session patterns of responding were similar for the two components of the concurrent schedules but that differences also occurred. Figs. 4 and 5 ask whether the differences produced systematic
changes in the parameters and fit of the GML within the session. Notice that even large withinsession changes in the ratios of the rates of responding would not alter the parameters and fit of the GML if those changes were accompanied by similar changes in the ratios of rates of reinforcement. Fig. 4 presents the parameters and fit (r 2) of the GML during successive 5-min intervals in the session averaged over the four rats. Fig. 5 presents the same results for individual rats. The left graphs present the results for response matching.
Fig. 3. The time spent responding on the VR component during successive 5-min intervals for the mean of all rats responding on each concurrent schedule in Experiment 1. Each graph presents the results for a concurrent schedule.
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Table 1 The parameters of, and the percentage of the variance accounted for by (r 2), the GML for individual subjects when data were averaged over the entire session Subject
Responses
Time
Bias
Sensitivity
r2
Bias
Sensitivity
r2
Rats 306 307 309 310
1.908 1.621 1.710 1.893
0.973 1.171 0.715 1.065
86.5 99.1 93.0 91.7
1.111 1.205 1.122 1.196
0.633 0.751 0.839 0.894
96.0 99.2 92.3 97.7
Pigeons 19 20 2560
1.133 2.456 1.704
1.059 1.045 0.803
93.6 99.1 98.3
0.559 0.500 1.073
1.185 0.818 0.852
70.0 99.5 92.9
Results on the left are those for response matching; those on the right are for time matching.
The right graphs present the results for time matching. The GML was fitted to the data as for Table 1 except that the data that entered the calculations were averaged over 5-min intervals rather than over the entire session. As would be expected when results are calculated over intervals as short as 5 min, there is some variance in Figs. 4 and 5. However, the GML provided a good description of the data. The GML usually accounted for more than 90% of the variance for both response and time matching. The fit of the GML was somewhat better during the middle of the session than it was early or late in the session. One-way (5-min intervals) repeated-measures ANOVAs showed that the percentage of variance accounted for changed significantly within the session for both response (F(11, 33) = 2.472) and time (F(11, 33)=2.191) matching. Although some individual rats showed relatively good fits throughout the session (rats 307 and 309 for response matching; rat 310 for time matching), others showed relatively good fits towards the middle of the session, but poorer fits at either the beginning (e.g. rats 306 and 307 for time matching) or end (e.g. rat 310 for response matching; rat 309 for time matching) of the session or both (e.g. rat 306 for response matching). For the mean of all rats, behavior was biased toward the VR schedule (bias \1.0) but the bias parameter changed unsystematically within the
session. Rats 306, 309 and 310 showed a bias towards the VR component for both response and time matching that was maintained across most of the session. Rat 307 was sometimes biased toward the VI (bias B 1.0) and sometimes toward the VR schedule. The within-session changes in bias were inconsistent across subjects. One-way (5-min interval) repeated-measures ANOVAs showed that the bias parameter did not change significantly within the session for either response (F(11, 33)= 0.961) or time (F(11, 33)= 0.751) matching. The sensitivity parameters were usually less than 1.0 for time matching. They were both greater than and less than 1.0 for response matching. Again, sensitivity parameters did not change systematically within the session for the mean of all subjects or in a way that was consistent across individual rats. One-way (5-min interval) repeated-measures ANOVAs showed that the sensitivity parameters did not change significantly within the session for either response (F(11, 33)= 1.058) or time (F(11, 33)= 0.941) matching.
3. Experiment 2
3.1. Materials and method 3.1.1. Subjects The subjects were four experimentally experienced pigeons, maintained at approximately 85%
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of their free-feeding body weights by post-session feedings delivered when all pigeons had completed the daily session. Pigeons were housed individually and were exposed to a 12:00/12:00 h light/dark cycle.
3.1.2. Apparatus The apparatus was a three-key experimental enclosure, measuring 30.0×36.0 ×27.0 cm. Three 2.5-cm diameter keys were positioned 21.5 cm above the floor and 7.5 cm apart. The left key was 7.0 cm from the left wall; the right key, 7.5 cm
from the right wall. A 4.5× 5.0-cm opening allowed access to a food magazine. It was 7.5 cm above the floor and 15.0 cm from the right wall. A 4.0-cm diameter houselight was located 1.5 cm from the ceiling and 0.5 cm from the right wall. The experimental panel was housed in a sound-attenuating chamber. A ventilating fan masked noises from outside the chamber. Experimental events were programmed and data were recorded by MED Associates Software run by an IBMcompatible 486 computer, located in another room.
Fig. 4. The bias (top graphs) and sensitivity (middle graphs) parameters of, and the percentage of the variance accounted for (bottom graphs) by, the GML for the mean of all rats in Experiment 1. The left graphs present the results for response matching; the right graphs for time matching.
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Fig. 5. The bias (top graphs) and sensitivity (middle graphs) parameters of, and the percentage of the variance accounted for (bottom graphs) by, the GML for individual rats in Experiment 1. The left graphs present the results for response matching; the right graphs for time matching.
3.1.3. Procedure The pigeons had pecked keys in previous experiments. Therefore, they were placed directly on the experimental procedure. The procedure was identical to that used for rats with the following exceptions. First, reinforcers were 5-s access to mixed grain. The time for which reinforcement was available was excluded from the timing of the session and of the 5-min intervals. Second, the components of the concurrent schedule were available on the left and right keys rather than on the left and right levers. Both keys were illuminated with white light except that they were dark when a reinforcer was presented.
3.2. Results and discussion Fig. 6 presents rates of responding (responses per minute) during successive 5-min intervals in the session for the mean of all pigeons responding on each concurrent schedule. Fig. 7 presents the proportion of total-session responding during successive 5-min intervals in the session for the mean of all pigeons responding on each concurrent schedule. Results were calculated and presented as in Figs. 1 and 2. Figs. 6 and 7 show that response rates changed within-sessions. As in past studies, response rates
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usually increased and then decreased within the session (e.g. McSweeney, 1992). This impression was confirmed by two-way (component × 5-min interval) repeated measures ANOVAs. The main effect of time was significant for all schedules except the concurrent VI 40 s VR 60 (F(11, 33)=1.941) and even for that schedule the results approached significance (P B 0.070; F(11, 33)= 3.025 first concurrent VI 30 s VR 30 F(11, 33)= 3.424, concurrent VR 30 VI 15 s; F(11, 33) =3.718, concurrent VI 40 s VR 30; F(11, 33)= 3.368, concurrent VR 45 VI 40 s; F(11,
33)= 2.774, final concurrent VR 30 VI 30 s). Fig. 8 presents time spent responding on the VR component during successive 5-min intervals for each concurrent schedule. Results were calculated and presented as in Fig. 3. Fig. 8 shows that time spent responding on the VR component was relatively constant within-sessions. The results of one-way (5-min interval) repeated-measures ANOVAs applied to the time spent responding on the VR schedule were significant for the concurrent VR 45 VI 40 s (F(11, 33)= 2.400) and the second concurrent VR 30 VI 30 s schedules (F(11,
Fig. 6. Rates of responding (responses per minute) during successive 5-min intervals in the session for the mean of all pigeons responding on each component of each concurrent schedule in Experiment 2. Each graph presents the results for a concurrent schedule. The solid line represents responding on the VI component; the dashed line represents responding on the VR component.
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Fig. 7. Proportion of total-session responding during successive 5-min intervals in the session for the mean of all pigeons on each component of each concurrent schedule in Experiment 2. Each graph presents the results for a concurrent schedule. The solid line represents responding on the VI component; the dashed line represents responding on the VR component.
33)=2.353), but not for the other schedules (F(11, 33)= 1.039, concurrent VI 30 s VR 30; F(11, 33)= 0.995,concurrent VR 30 VI 15 s; F(11, 33) =1.085, concurrent VI 40 s VR 30; F(11, 33)=1.656, concurrent VI 40 s VR 60). Again, the time spent responding on the VR component increased and then decreased within the session when it changed significantly. Table 1 (bottom) presents the parameters and fit of the GML when it was fit to data averaged over the session. Figs. 9 and 10 present the parameters and fit of the GML during successive
5-min intervals in the session for the mean of all pigeons and for individual pigeons, respectively. Results were analyzed and presented as they were for Table 1 (top) and Figs. 4 and 5. Results are presented for only three subjects because pigeon 10 showed close to exclusive preference for the VI component of most schedules and exclusive preference for that component during the concurrent VI 40 s VR 30 and concurrent VR 45 VI 40 s schedules. The figures present results for only the first 50-min of the session (10 5-min intervals) because pigeons often failed to obtain reinforcers
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late in the session from the VR component of several schedules. Although the GML usually accounted for more than 90% of the variance in the data when results were averaged over the entire session (Table 1, bottom), the GML did not describe the data as well when results were averaged over only 5-min intervals. Because of the high variance visible for individual subjects in Fig. 10, the fit of the GML did not change significantly within the session. One-way (5-min interval) repeated-measures
ANOVAs applied to r 2 were not significant for response (F(9, 18)= 1.634) or for time (F(9, 18)=0.525) matching. Behavior was usually biased toward the VR schedule (bias \ 1.0) for response matching and towards the VI schedule for time matching. The exceptions were pigeon 2560 who was often biased toward the VR schedule for time matching and pigeon 19 who was occasionally biased toward the VI schedule for response matching. Oneway (5-min interval) ANOVAs showed that the
Fig. 8. The time spent responding on the VR component during successive 5-min intervals for the mean of all pigeons responding on each concurrent schedule in Experiment 2. Each graph presents the results for a concurrent schedule.
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Fig. 9. The bias (top graphs) and sensitivity (middle graphs) parameters of, and the percentage of the variance accounted for (bottom graphs) by, the GML for the mean of all pigeons in Experiment 2. The left graphs present the results for response matching; the right graphs for time matching.
bias parameter did not change significantly within the session for response (F(9, 18)=1.489) or for time (F(9, 18)=0.430) matching. The sensitivity parameters were sometimes greater than 1.0 (over-matching) and sometimes less than 1.0 (under-matching) depending on the subject and the time in the session. Negative sensitivity parameters were observed for pigeon 20 during the ninth and tenth 5-min intervals for time matching. One-way (5-min interval) repeated-measures ANOVAs showed that the sensitivity parameters did not change significantly within the session for response (F(9, 18)= 1.314) or for time (F(9, 18)= 0.400) matching.
4. General discussion Within-session changes in response rates were observed for both rats (Experiment 1) and pigeons (Experiment 2) responding on both components of most schedules. As in past studies (e.g. McSweeney, 1992), rate of responding usually increased and then decreased within the session. This finding extends the generality of within-session changes in responding to concurrent VI VR schedules. In contrast to the large changes in response rates, the time spent responding on a component was relatively constant within the session for both rats and pigeons (Figs. 3 and 8). Significant
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within-session changes in time spent responding on the VR components were reported for only one schedule for rats and for two schedules for pigeons. Relatively constant time allocation was also reported by McSweeney et al. (1999) when subjects responded on concurrent VI FI schedules. Time spent responding on the FI component changed significantly within the session for only one of the five (rats) or six (pigeons) schedules that they conducted. In contrast, McSweeney et al. (1996a) reported systematic within-session changes in time spending when subjects responded on concurrent VI VI schedules that provided different reinforcers in the two components (e.g. food and water). Therefore, the time allocated to
each component of a concurrent schedule is relatively constant within the session as long as the components provide the same reinforcers. When the components provide qualitatively different reinforcers, systematic within-session changes in time allocation may occur. It is not clear why the time spent responding on the VR component changed within the session in the few cases that it did. The significant changes do not follow any obvious pattern. For example, in the present experiment, significant changes occurred for the concurrent schedule that provided the highest total reinforcement for rats, but for schedules that provided the second and third lowest total reinforcers for pigeons. Significant
Fig. 10. The bias (top graphs) and sensitivity (middle graphs) parameters of, and the percentage of the variance accounted for (bottom graphs) by, the GML for individual pigeons in Experiment 2. The left graphs present the results for response matching; the right graphs for time matching.
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changes also occurred when the VR component of the concurrent VR 30 VI 30 s schedule appeared on the left, but not on the right, key McSweeney et al. (1999) reported similar results for concurrent VI FI schedules. Their two significant withinsession changes in time allocation occurred for different schedules for rats and pigeons. Therefore, the factors that produce these changes in time allocation are not known. Shurtleff and Silberberg (1990) reported that the relative response and time allocation to the VI alternative of a concurrent VI VR schedule increased as session duration increased from 10 to 30 min. A shift in behavior away from the VR schedule is not apparent in the figures across the first 30 min of the session. For example, if anything, time spent responding shifts to the VR schedule when it changes at all. However, two procedural differences between our study and that of Shurtleff and Silberberg (1990) may have contributed to the difference in results. First, the present experiment did not explicitly manipulate session duration. To compare our results to those of Shurtleff and Silberberg’s, it must be assumed that the results reported for 10 and 30 min into our 60 min sessions are equivalent to the results for 10 and 30 min sessions. Although some data support this assumption (McSweeney, 1992; McSweeney et al., 1994), our results would be more comparable if we had manipulated session duration. Second, Shurtleff and Silberberg’s subjects obtained all of their food during the experimental session. The present subjects were given post-session feedings if they failed to obtain enough food during the session to maintain their body weights. As argued by Shurtleff and Silberberg, their subjects may have shifted their behavior to the VR schedule when sessions were short in order to obtain enough food to sustain themselves. Our subjects did not need to shift their behavior in this way. Therefore, at present, our conclusion that time allocation is relatively constant within the session should not be generalized to studies, such as that of Shurtleff and Silberberg, that employ closed economies. The parameters and fit of the GML reported in Table 1 were consistent with those reported in past studies of responding on concurrent VI VR
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schedules. Similar to results reported by Baum and Aparicio (1999) and by Herrnstein and Heyman (1979), the GML provided a good description of the data. It accounted for more than 90% of the variance for 12 of the 14 fits in Table 1. Rats usually showed a bias towards the VR component (bias parameter \ 1.0). Pigeons showed a bias towards the VR for response matching, but two of three pigeons showed a bias toward the VI for time matching (bias parameter B 1.0). Herrnstein and Heyman (1979) also reported that pigeons were biased towards the VR schedule for response matching and toward the VI schedule for time matching. Both over- (sensitivity parameter \ 1.0) and under-matching (sensitivity parameter B 1.0) occurred for response rate. Under-matching occurred for all rats and for two of three pigeons for time matching. Over- and undermatching have also been reported in the past (e.g. Baum and Aparicio, 1999). Finding both over- and under-matching, sometimes for the same subject at different times in the session (Figs. 4, 5, 9 and 10) or for different behavioral measures (Table 1), sheds some light on the factors that control the sensitivity parameter. According to some theories, over- and undermatching are produced by distinctively different processes. For example, because under-matching is the usual finding in studies of concurrent VI VI schedule performance (e.g. Baum, 1979), it has been argued that exact matching (sensitivity parameter= 1.0) is the true state of behavior. Under-matching results if procedural details prevent the animal from exact matching. For example, performance would depart from matching towards indifference (under-matching) if the subject could not discriminate which component produced a reinforcer. According to this thinking, over-matching is a statistical error when it is reported. According to other theories, over- and under-matching lie on a continuum. For example, Baum (1982) argued that animals respond predominantly on the richer component of the concurrent schedule with brief visits to the leaner one. Altering the cost associated with switching from one alternative to the other can determine whether under- or over-matching is observed. When costs are high, subjects visit the leaner
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alternative infrequently, yielding over-matching. That is, relatively more time is spent on the richer alternative than is justified by the reinforcers it produces. When costs are small, subjects visit the leaner alternative frequently, yielding undermatching. That is, relatively more time is spent on the leaner alternative than is justified by the reinforcers it produces. Because under- and overmatching were found for the same subject at different times in the session, the present results are more consistent with the idea that over- and under-matching lie on a continuum than that they are produced by qualitatively different variables. Fig. 10 shows that negative sensitivity parameters were reported late in the session for pigeon 20. Negative parameters have been reported in the past, but only when subjects respond on schedules that provide qualitatively different reinforcers in the two components (e.g. Hursh, 1978; McSweeney et al., 1996a). As in the present experiment, the negative parameters appeared late in the session when responding was examined withinsessions (McSweeney et al., 1996a). If these negative parameters were replicated for subjects responding on concurrent VI VR schedules, they would challenge the leading explanation for why negative sensitivity occurs (Hursh, 1980, 1984). This explanation predicts negative sensitivity only when the components of the concurrent schedule provide qualitatively different reinforcers. However, because negative sensitivity was observed for only one subject in the present experiment, these negative parameters should be replicated before strong conclusions are drawn. The parameters of the GML did not change significantly within-sessions (Figs. 4, 5, 9 and 10). Because the parameters were relatively constant within-sessions, these parameters should not differ at different times in the session or for sessions of different lengths. Therefore, within-session changes in responding do not create problems for assessing the parameters of the GML when subjects respond on concurrent VI VR schedules. To date, within-session changes in response rates do not create problems for interpreting the GML as long as the components provide the same type of reinforcer. This conclusion holds even when the components are provided on different types of
operanda (McSweeney et al., 1995) or by different types of simple schedules (McSweeney et al., 1999; present experiments). As a final point, the fit of the GML was poorer at the beginning and end of the session than in the middle when rats served as subjects. As a result, researchers who study the GML might examine their data separately for the entire session and for the session with the first and last 10 min eliminated. They might want to report the later statistics if the two differ substantially.
Acknowledgements The present experiments were partially supported by grant RO 1 MH61720 from the National Institute of Mental Health. The results were presented at the 2001 meeting of the Association for Behavior Analysis in New Orleans, LA.
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