Short communicationRapid acquisition in concurrent chains: Effects of initial-link duration
Introduction
Most previous studies on concurrent chains have used steady-state procedures in which training continues with a given pair of terminal-link schedules until response allocation in the initial links has stabilized. Typically this requires 20 or more sessions, after which the terminal-link schedules are changed and training begins in a new condition (e.g., Fantino and Davison, 1983, Grace, 2002). However, recent studies have shown that subjects’ response allocation can adjust rapidly when terminal-link schedules are changed frequently across sessions (Grace et al., 2003, Grace and McLean, 2006). For example, Kyonka and Grace (2007) exposed pigeons to a concurrent chains procedure in which the terminal-link schedules in each session were either fixed-interval (FI) 10 s FI 20 s or FI 20 s FI 10, determined by a pseudorandom binary series, and the initial-link was a variable-interval (VI) 8-s schedule that arranged equal access to the terminal links. After pigeons had received about 50 sessions of training, response allocation stabilized about midway through each session, showing strong sensitivity to the terminal-link delays in the current session with virtually no influence of prior sessions.
Grace and McLean (2006) proposed a model to account for performance in such rapid acquisition experiments in which the terminal links are frequently changed. They assumed that a process similar to categorical discrimination underlies the acquisition of choice. According to their model, when reinforcement is obtained in a terminal-link, subjects make a ‘decision’ whether the delay to food in the terminal-link was short or long relative to the history of reinforcer delays experienced in both terminal links. If the delay was short, the response strength for the associated initial-link increases, whereas if the delay was long the response strength for the initial-link decreases.
Reinforcement history is represented by a log normal distribution with a mean equal to the log geometric mean of the prior delays associated with both terminal links (the ‘criterion’), and standard deviation σ. This contrasts with theories that assume separate ‘memories’ for delays from each alternative (e.g. Gallistel and Gibbon, 2000, Gibbon et al., 1988). The probability of a ‘short’ decision is determined by calculating the inverse of the cumulative density for reinforcement history, with the percentage of values that are greater than the delay giving the probability that the delay is judged ‘short’. Grace and McLean showed that the decision model provided a good account of their data, and was able to predict initial-link responding that approximated generalized matching or categorical, ‘all or none’ preference. When σ was relatively large, log response allocation was a linear function of the log immediacy ratio (generalized matching), whereas log response allocation was a nonlinear function of the log immediacy ratio (categorical preference) when σ was relatively small.
One limitation of Grace and McLean's model is that it does not address effects of initial-link duration on response allocation. Such effects are well known in steady-state research: preference between a constant pair of terminal links becomes less extreme as the initial-link duration is increased (e.g., Fantino, 1969). Models for choice, such as delay-reduction theory (DRT; Fantino and Romanowich, 2007, Squires and Fantino, 1971), the contextual choice model (CCM; Grace, 1994) and the hyperbolic value-added model (HVA; Mazur, 2001) all predict that preference decreases towards indifference as initial-link duration increases. However, relatively little is known about effects of initial-link duration on acquisition of preference (but cf. Berg and Grace, 2006), and no previous experiments using procedures in which terminal-link schedules are changed unpredictably across sessions have manipulated initial-link duration.
A simple way to extend Grace and McLean's (2006) model to include effects of initial-link duration is to view reinforcement history as a series of transitions between stimuli correlated with reward, of which the onset of the terminal links and reinforcer delivery are only two examples. Specifically, we assume that the reinforcement history distribution includes delays between onset of the initial links and terminal-link entry, as well as between terminal-link onset and food delivery. As a result, the criterion (i.e., the mean of the reinforcement history distribution) varies directly with initial-link duration. Fig. 1 shows representative predictions of the decision model for preference between FI 10 s and FI 20 s terminal links, as the initial-link duration increases from 5 s to 30 s.1 Over most of the range of initial-link durations – between 10 s and 30 s – the predicted preference becomes less extreme as the initial links increase. The reason is that the relative probability of a ‘short’ decision for the terminal links, that is, p(‘short’|10 s)/p(‘short’|20 s), decreases as the initial-link duration increases (for a detailed explanation of the model's predictions, see Appendix A). As a result, including the time spent in the initial links in the calculation of the criterion allows the decision model to account for the initial-link effect. However, Fig. 1 also shows that for short initial-link durations, there is a range over which preference becomes less extreme as the initial links decrease. This decrease occurs because the relative probability of a ‘short’ decision for the FI 10-s terminal-link decreases as the criterion becomes less than the terminal-link delays. Thus, the overall function relating preference to initial-link duration is bitonic. This bitonic function is robust with respect to variation in the parameter values, and represents a novel prediction of the decision model: existing models for steady-state choice such as CCM (Grace, 1994), HVA (Mazur, 2001), and DRT (Fantino, 1969) predict that choice is a monotonic decreasing function of initial-link duration.
The plan of the current study was to train pigeons in a rapid-acquisition concurrent chains procedure with a constant pair of terminal-link schedules (FI 10 s and FI 20 s). Once pigeons were showing sensitivity to the immediacy ratio in the current session, we varied the initial-link schedule across sessions, between 0.01 s and 30 s, in ascending and descending series. The major question was whether the stable level of response allocation reached within sessions would vary with initial-link duration, and whether that function would be monotonic decreasing (as predicted by current models for steady-state choice), or a bitonic function as predicted by the extension of the Grace and McLean decision model.
Section snippets
Subjects
Six pigeons of mixed breed, numbered 181–186 served as subjects and were maintained at 85% of their free-feeding weight ± 15 g through appropriate post-session feeding. Subjects were housed individually in a vivarium with a 12 h:12 h light/dark cycle (lights on at 06:00 h), with water and grit freely available in the home cages. All pigeons were experienced with a variety of experimental procedures.
Apparatus
Four standard three-key operant chambers, 32 cm deep × 34 cm wide × 34 cm high, were used. The keys were 21 cm
Results
To assess the relationship between response allocation and the immediacy ratios in the current and prior sessions, we used a generalized-matching model:where B and D refer to initial-link response rate and terminal-link delay, respectively, subscripted for choice alternative (L and R) and lag (0–4; 0 = current session). The parameters a0, ⋯, a4 quantify sensitivity to reinforcer immediacy (i.e., reciprocal of delay) at each
Discussion
Our goal was to explore how response allocation in a rapid acquisition concurrent chains procedure varied when initial-link duration was changed according to an ascending and descending sequence. In particular, we were interested to test whether the relationship between response allocation and initial-link duration was monotonic, as predicted by steady-state models for choice (Fantino, 1969, Grace, 1994, Mazur, 2001), or bitonic, as predicted by an extension of Grace and McLean's (2006)
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2016, Behavioural ProcessesCitation Excerpt :However, its generality is uncertain. Kyonka and Grace (2009) did not find evidence of a bitonic function when initial-link duration was varied unpredictably across sessions over the same range as Christensen and Grace (2008). In addition, to our knowledge no research has tested for a bitonic effect over short initial-link durations using a steady-state design.
Acquisition of choice in concurrent chains: Assessing the cumulative decision model
2016, Behavioural ProcessesCitation Excerpt :MacEwen (1972) found that preference became more extreme as overall terminal-link duration increased with the ratio held constant (see also Grace, 2004; Grace and Bragason, 2004; White and Pipe, 1987). Christensen and Grace (2008, 2009a) showed that both the initial- and terminal-link effects could be predicted by the decision model if the criterion were calculated as the average interval between all stimuli, not just terminal-link delays to reinforcement. Two aspects of this assumption are worth noting.
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