Resurgence as Choice

Abstract

Resurgence is typically defined as an increase in a previously extinguished target behavior when a more recently reinforced alternative behavior is later extinguished. Some treatments of the phenomenon have suggested that it might also extend to circumstances where either the historic or more recently reinforced behavior is reduced by other non-extinction related means (e.g., punishment, decreases in reinforcement rate, satiation, etc.). Here we present a theory of resurgence suggesting that the phenomenon results from the same basic processes governing choice. In its most general form, the theory suggests that resurgence results from changes in the allocation of target behavior driven by changes in the values of the target and alternative options across time. Specifically, resurgence occurs when there is an increase in the relative value of an historically effective target option as a result of a subsequent devaluation of a more recently effective alternative option. We develop a more specific quantitative model of how extinction of the target and alternative responses in a typical resurgence paradigm might produce such changes in relative value across time using a temporal weighting rule. The example model does a good job in accounting for the effects of reinforcement rate and related manipulations on resurgence in simple schedules where Behavioral Momentum Theory has failed. We also discuss how the general theory might be extended to other parameters of reinforcement (e.g., magnitude, quality), other means to suppress target or alternative behavior (e.g., satiation, punishment, differential reinforcement of other behavior), and other factors (e.g., non- contingent versus contingent alternative reinforcement, serial alternative reinforcement, and multiple schedules).

Keywords: Behavioral momentum; Choice; Extinction; Matching law; Relative value; Resurgence.

Copyright © 2016 Elsevier B.V. All rights reserved.

Figures

Fig. 1

The top panel shows sample weighting functions generated by Eq. (6) (i.e., the Temporal Weighting Rule). Functions are presented after every five sessions. The bottom panel shows the same functions with a logarithmic y-axis.

Fig. 2

The top panel shows arranged reinforcement rates for the target and alternative options in a sample resurgence experiment. The middle panel shows sample weighting functions as in Fig. 1. The bottom panel shows the value functions for the target and alternative options across sessions resulting from the application of Eq. (8). P1 = Phase 1, P2 = Phase 2, and P3 = Phase 3.

Fig. 3

The top panel shows value functions for the target and alternative options across Phases 2 & 3 as presented in Fig. 2. The bottom panel shows changes in the probability of the target response across sessions generated by using these daily values in Eq. (3).

Fig. 4

The top panel shows weighting functions generated by Eq. (9) (i.e., the scaled temporal weighting rule; sTWR). Functions are presented for three different values of the currency term (i.e., c). The bottom panel shows the same functions with a logarithmic y-axis.

Fig. 5

The top panel shows value functions from Eq. (8) for the target and alternative options across Phases 2 & 3 generated by application of Eq. (9) (sTWR with c = 2) to the reinforcement rates across conditions depicted in the top panel of Fig. 2. The bottom panel shows changes in the probability of the target response across sessions generated by using these daily values in Eq. (3).

Fig. 6

The top panel shows the relation between average running reinforcement rate for an option (i.e., r) and the value of the currency term (i.e., c) as determined by Eq. (10). Functions are presented for three different λ parameters. The middle panel shows value functions during 10 sessions of extinction following reinforcement on a VI15-s or VI60-s schedule with λ = 0.006. The bottom panel shows the same value functions presented as a proportion of the value at the end pre-extinction training (i.e., x = 0 in the middle panel).

Fig. 7

The top panel shows value functions generated by the sTWR (Eq. (9)) using a currency term (i.e., c) determined by reinforcement rates according to Eq. (10) with λ = 0.006. Phase 1 target = VI15, Phase 2 alternative = VI15. The middle panel shows absolute response rates based on this value functions generated by Eq. (11). The bottom panel provides a zoomed view of the last day of Phase 2 and five Phase 3 resurgence sessions.

Fig. 8

The relation between target response rates in the first session of Phase 3 (resurgence) and asymptotic baseline response rates (i.e., k in Eq. (11)). Functions are shown for three different a parameter values relating arousal to overall value of the options in Eq. (12).

Fig. 9

Target response rates across 5 sessions of Phase-3 (resurgence) test sessions generated with different a parameter values in Eq. (12).

Fig. 10

Summary of the major components of the RaC model.

Fig. 11

The top panels show data replotted data from Craig and Shahan (2016). The bottom panels show simulations generated by RaC. Details in text.

Fig. 12

Simulations of RaC across a range of alternative reinforcement rates following either VI10-s or VI120-s reinforcement of the target in Phase 1.

Fig. 13

Value functions (top panels), probability of the target (middle panels), and arousal (bottom panels) associated with the simulations shown in Fig. 12.

Fig. 14

The top panels show data from Sweeney and Shahan (2013b) in Phase 2 (left) and Phase 3 (right). The bottom panels show a simulation generated by RaC. Last P2 and First P3 refer to the last session of Phase 2 and the first session of Phase 3, respectively.

Fig. 15

The top panels show data from Schepers and Bouton (2015, Experiment 2) in Phase 2 (left) and Phase 3 (right). The bottom panels show a simulation generated by RaC. Last P2 and First P3 refer to the last session of Phase 2 and the first session of Phase 3, respectively.

Fig. 16

The top panels show data from Schepers and Bouton (2015, Experiment 3) in Phase 2 (left) and Phase 3 (right). The bottom panels show a simulation generated by RaC. Last P2 and First P3 refer to the last session of Phase 2 and the first session of Phase 3, respectively.

Fig. 17

Simulations of the effects of different durations of exposure to Phase-2 alternative reinforcement generated by RaC. The two panels use different λ parameters for Eq. (10).

Fig. 18

Simulations of the effects of different magnitudes of alternative reinforcement during Phase 2 generated by RaC.

Fig. 19

Simulations generated by RaC of the effects of different sized downshifts in reinforcement rate with the transition from Phase 2 to Phase 3. Reinforcement in both Phases 1 & 2 was on VI15-s schedule. Last P2 and First P3 refer to the last session of Phase 2 and the first session of Phase 3, respectively.

Fig. 20

The left panels show data replotted data from Podlesnik and Shahan (2010). The right panels show a simulation generated by RaC. The top panels are expressed in absolute response rates and the bottom panels in terms of proportion of Phase-1 (baseline) rates.

Fig. 21

The top panels shows simulations of absolute rates of target responding in Phases 2 and 3 following Phase 1 reinforcement in a multiple schedule with equal rates of contingent reinforcement in both components and added non-contingent reinforcement in one component. The bottom panels are expressed in terms of proportion of Phase-1 (baseline) rates. Parameter values are the same as in Fig. 20 with the addition of the p parameter in the simulations in the right-hand panels. See text for details.