Interresponse Time Structures in Variable‐ratio and Variable‐interval Schedules

Abstract

The interresponse-time structures of pigeon key pecking were examined under variable-ratio, variableinterval, and variable-interval plus linear feedback schedules. Whereas the variable-ratio and variableinterval plus linear feedback schedules generally resulted in a distinct group of short interresponse times and a broad distribution of longer interresponse times, the variable-interval schedules generally showed a much more continuous distribution of interresponse times. The results were taken to indicate that a log survivor analysis or double exponential fit of interresponse times may not be universally applicable to the task of demonstrating that operant behavior can be dichotomized into bouts of engagement and periods of disengagement.Key words: interresponse time, variable-ratio, variable-interval, yoked schedules, Shull machine, key peck, pigeonsIn the past, the conceptualization of behavior as two-state (Gilbert, 1958) has not enjoyed widespread research interest because of the difficulty in validly dichotomizing the behavior stream into visits and nonvisits by simply specifying some specific interresponse time (IRT) duration as a criterion. The split between within-visit IRTs and visit-initiation IRTs is unlikely to be at the same value across individuals, or even within an individual across procedures.Shull, Gaynor, and Grimes (2001) described one possible solution for resolving the categorization problem. They displayed the total distribution of obtained IRTs as a survivor plot with a logarithmically scaled y axis. In this semilogarithmic plot, the slope between any two points on the x axis is an indicator of the relative decrease in the frequency of the IRTs per opportunity between those points. If a single exponential decay governed the occurrence of all responding, then the IRT distribution would appear as a single straight line. If, on the other hand, behavior occurred in short bouts of responding separated by longer delays, then the short IRTs governed by one exponential decay process would result in an initial steep slope, while the longer delays between response bouts characterized by a different exponential would be spread across a broad range of values and would generate a second shallower slope.Shull and his colleagues (Shull et al., 2001) found that the log survivor plots of the output of their explicitly two-state emulator had two relatively straight lines intersecting at an angle less than 180u, or had a ''broken-stick'' appearance, such that the function and therefore the two classes of behavior were easily dichotomized by simple inspection. Figure 1 provides example log survivor plots of the output of Shull's model. The ratio of the within-visit response rate to the between-visit response rate and the probability of disengaging are given above each frame. The columns of frames illustrate how increasing the relative value of the probability of entering the engaged state, p(V), with respect to the probability of a response during a visit, p(R), (i.e., larger ratios of within-visit to the be...

Concurrent VR VI schedules: Primacy of molar control of preference and molecular control of response rates

“…As a consequence, rate emission may lower more, leading to still longer IRIs. Indeed, Bowers, Hill, and Palya (2008) recently reported such behavior patterns on a VI schedule.…”

Bouts, Changeovers, and Units of Operant Behavior

“…Such patterns have been evident with key-poking and lever-pressing by rats, as described above, and with nose-poking by mice (Johnson et al, 2009(Johnson et al, , 2011. But attempts to find evidence of broken-stick log survivor plots with key pecking by pigeons have largely failed (Bennett, Hughes, & Pitts, 2007;Bowers et al, 2008). In at least one case (Bowers et al) a likely source of the problem is that virtually all the IRTs were shorter than 5 s whereas with rats and mice, a substantial proportion of the distribution-mostly in the right tail-has usually extended beyond 30 s (and sometimes beyond 200 s).…”

“…This kind of plot shows the proportion of IRTs in a sample that are longer than any particular duration, t. For a wide range of species and activities, log survivor plots of response times often have an odd shape that has been described as looking like a "broken stick" (Clifton, 1987;Fagen & Young, 1978;Johnson, Bailey, & Newland, 2011;Langston, Collett, & Silby, 1995;Machlis, 1977;Slater, 1974;Staddon & Zanutto, 1997; for some exceptions see Bowers, Hill, & Palya, 2008;Tolkamp & Kyriazakis, 1999). The top panel in Figure 5 shows an idealized (although not unrealistic) example of a broken-stick log survivor plot.…”

The copyist model of response emission

“…There is some debate as to whether this assumption is true. For example, Shull (2004) has shown that behavior often seems discontinuous, alternating between periods of action and inaction, while Bowers et al (2008) have argued that response emission on some schedules seems well characterized by assuming that emission is continuous. Evaluation of the integrity of the copyist model's assumption that response emission is continuous awaits further work.…”

“…The finding of a rate difference between VR and VI schedules that provide the same rate of reinforcement has generated considerable interest among operant-oriented researchers (Baum, 1973(Baum, , 1981(Baum, , 1993Bowers, Hill, & Palya, 2008;Catania et al, 1977;Cole, 1994Cole, , 1999Dawson & Dickinson, 1990;Ferster & Skinner, 1957;Morse, 1966;Peele et al, 1984;Reed, Hildebrandt, DeJongh, & Soh, 2003;Reed, Soh, Hildebrandt, DeJongh, & Shek, 2000). Empirical and theoretical reasons drive this interest.…”