Modeling Subtypes of Automatically Reinforced Self-Injurious Behavior with the Evolutionary Theory of Behavior Dynamics

Abstract

The subtypes of automatically reinforced self-injurious behavior (ASIB) delineated by Hagopian and colleagues (Hagopian et al., 2015; 2017) demonstrated how functional-analysis (FA) outcomes may predict the efficacy of various treatments. However, the mechanisms underlying the different patterns of responding obtained during FAs and corresponding differences in treatment efficacy have remained unclear. A central cause of this lack of clarity is that some proposed mechanisms, such as differences in the reinforcing efficacy of the products of ASIB, are difficult to manipulate. One solution may be to model subtypes of ASIB using mathematical models of behavior in which all aspects of the behavior can be controlled. In the current study, we used the evolutionary theory of behavior dynamics (ETBD; McDowell, 2019) to model the subtypes of ASIB, evaluate predictions of treatment efficacy, and replicate recent research aiming to test explanations for subtype differences. Implications for future research related to ASIB are discussed.

The development of functional analysis (FA) methodology (Iwata et al., 1982/1994) allowed clinicians and researchers to identify the functional reinforcer for problem behavior before selecting a course of clinical action. As a result, functional-analysis outcomes have been shown to strongly predict what types of treatments are most likely to be effective (see Beavers et al., 2013, for a review of FA). In a relatively large-scale epidemiological study in which FAs were conducted with 152 participants, Iwata et al. (1994) found that self-injurious behavior (SIB) was maintained by socially mediated reinforcement in the majority (i.e., 64%) of cases. That is, the functional reinforcer was some change in the behavior of others (e.g., delivery of attention or tangible items, removal of aversive stimuli like instructions). In these cases, the occurrence of SIB can be reduced by delivering that functional reinforcer contingent on another response (e.g., Kunnavatana et al., 2018) or on a time-based schedule (e.g., Fritz et al., 2017). However, in a subset (i.e., 20%–25%) of cases included in Iwata et al. (1994), SIB was found to persist in the absence of socially mediated reinforcement. In these cases, SIB was determined to be automatically reinforced (e.g., Querim et al., 2013). That is, the behavior appeared to produce its own source of maintaining reinforcement (e.g., pain relief, sensory stimulation). Automatically reinforced self-injurious behavior (ASIB) is necessarily more difficult to treat because, unlike identifying that the functional reinforcer is socially mediated, identifying that behavior is automatically reinforced does not implicitly suggest effective treatments. Moreover, treating ASIB is more difficult because it is relatively difficult to identify the stimuli that evoke the behavior and to observe or manipulate its functional reinforcer (LeBlanc et al., 2000; Vollmer, 1994). However, some researchers have developed methods of identifying items or activities that result in the suppression of problem behavior, presumably by providing functionally similar reinforcement that abolishes motivation for the reinforcers produced by ASIB (Fisher et al., 1998; Hagopian et al., 2020; Leif et al., 2020; Piazza et al., 1998; Vollmer et al., 1994).

FA outcomes that suggest SIB is automatically reinforced are primarily characterized by the persistence of behavior in the absence of socially mediated consequences but are otherwise quite diverse. Thus, the occurrence of the behavior in other contexts or conditions and the occurrence of behavior other than SIB may vary greatly across individuals displaying ASIB. Researchers have recently utilized these differences to delineate three subtypes of ASIB, each of which predicts the efficacy of different intervention approaches (Hagopian et al., 2015; Hagopian et al., 2017). The different subtypes can be identified by calculating a subtype quotient, the formula for which has been described in detail by Hagopian and colleagues. In essence, the subtype quotient quantifies the degree of overlap between the alone condition and the play or similar time-based reinforcement condition of a functional analysis.

Subtype 1 is characterized by little overlap between these two conditions. That is, SIB occurs at relatively high rates when the individual is alone but occurs at relatively low rates in the play condition. For Subtype 1, providing competing reinforcers as a treatment strategy has been shown to be sufficient to decrease the occurrence of ASIB (e.g., Hagopian et al., 2020; Leif et al., 2020). Subtype 2 is characterized by a high degree of overlap in responding across the alone and play conditions or a high rate (i.e., 50 response per min) of SIB in the play and alone conditions. That is, SIB occurs at similar or generally high rates in both conditions and is seemingly unaffected by the availability of reinforcers in the play condition. For Subtype 2, reinforcement alone is unlikely to be sufficient in reducing SIB, so additional components such as response blocking, restraint, or punishment are often necessary to bring about behavior reduction (e.g., Berg et al., 2016; Verriden & Roscoe, 2019). Subtype 3 is characterized by the occurrence of self-restraint during the alone condition along with SIB meeting the criteria of either of the other two subtypes. Subtype 3 is less common, and thus, the treatment predictions are less clear, but additional treatment components have often been found to be necessary to obtain reductions in SIB (Hagopian et al., 2017).

Thus, response patterns within an FA serve as good predictive behavioral markers (i.e., objective measures that predict responsiveness to treatment; Hagopian et al., 2018). However, despite these improvements in assessment and treatment, the mechanisms underlying differences across subtypes of ASIB have remained unclear. From this point forward, we will focus on Subtypes 1 and 2 because they have been more thoroughly described, are more directly comparable (i.e., only SIB included in criteria), and have been the focus of previous research on explaining subtype differences (e.g., Rooker et al., 2019). Three potential explanations have been put forth in explaining the differences between Subtypes 1 and 2. First, many researchers have hypothesized that, relative to Subtype 1, Subtype 2 ASIB produces higher magnitude or higher quality automatic reinforcement (Cataldo & Harris, 1982) or produces automatic reinforcers for which there are stronger establishing operations (Hagopian et al., 2017; Ringdahl et al., 1997; Shore et al., 1997; Sprague et al., 1997; Vollmer, 1994). Thus, in the initial description of Subtypes 1 and 2, Hagopian et al. (2015) described them as producing sensory and strong sensory reinforcement, respectively.

Second, and more recently, Rooker et al. (2019) suggested that Subtypes 1 and 2 ASIB might also be explained in terms of generalized differences in sensitivity to changes in environmental stimuli or contingencies. That is, Subtype 2 ASIB persists across conditions because individuals who display Subtype 2 ASIB are less sensitive to changes in their environment than individuals who display Subtype 1 ASIB. To test this possibility, Rooker et al. compared the responding of three individuals with Subtype 2 ASIB and three individuals with socially reinforced SIB on a single-operant, button-pressing task in which reinforcement contingencies varied (i.e., switched between continuous reinforcement, extinction, and a progressive-ratio schedule of reinforcement). The results of their study provided preliminary evidence against the explanation that individuals displaying Subtype 2 ASIB exhibit a generalized response tendency toward insensitivity and instead suggested that subtype differences were specific to the response class of SIB.

Third, some researchers have suggested that the differences between Subtypes 1 and 2 may not be explainable solely in terms of operant conditioning and instead require the consideration of biological processes. Vollmer (1994) suggested that reflexive processes may contribute to the persistence of ASIB. That is, SIB may be elicited by stimuli in the individual’s environment, whether those stimuli are publicly available or private (i.e., within the skin; Skinner, 1945). Others have suggested that the persistence of Subtype 2 ASIB may be partially explained in terms of movement disorders or sensory dysfunction (Hagopian & Frank-Crawford, 2018).

The relative contributions and validity of each of these possible explanations remains unclear because the stimuli evoking or eliciting ASIB and the consequences reinforcing ASIB are difficult to observe and manipulate. The subtypes provide an accurate description and categorization of patterns of responding within functional analyses, and they predict the efficacy of different methods of behavior reduction. However, despite this descriptive accuracy and utility, the subtypes alone cannot explain why the different patterns of responding emerge. For example, knowing that an individual’s SIB has been identified as Subtype 2 does not tell us why their ASIB persists across conditions, only that it is persistent. It remains unclear if more persistence across conditions is caused by the establishing operations for, or reinforcing efficacy of, the consequences of ASIB because we are currently unable to manipulate those consequences. Likewise, although individuals can be compared in terms of the degree to which their behavior is sensitive to changes in their environment, that type of sensitivity seems similarly difficult, or perhaps impossible, to change. Finally, the contribution of processes such as elicitation or sensory dysfunction will remain difficult to elucidate as long as potential operant processes remain unclear.

Perhaps because of these difficulties, the behavioral mechanisms that give rise to the distinct response patterns that characterize the subtypes have remained unclear and research aiming to elucidate these mechanisms has yet to progress beyond speculation. Thus, new approaches may be beneficial in furthering our understanding of the subtypes and potential causes for their characteristic difference in response pattern and response to treatment. One new approach could be to develop and evaluate mathematical models of the subtypes of ASIB, which may have the benefit of avoiding many difficulties inherent in aiming to understand underlying behavioral mechanisms of ASIB occurring in live organisms. Moreover, developing and evaluating mathematical models of the subtypes of ASIB could further our understanding of ASIB, clarify the need for different explanations of subtype differences, and guide future research aimed at explaining the differences across subtypes of ASIB. Finally, and most important, a better understanding of the mechanisms underlying subtype differences could suggest novel treatments or methods of improving existing treatments.

One mathematical model that could be used to model the subtypes of ASIB is the evolutionary theory of behavior dynamics (ETBD). The ETBD is a complexity theory, meaning that it consists of the repeated operation of simple rules that result in the emergence of complex outcomes (McDowell, 2019). The ETBD may be thought of as the algorithmic instantiation of selection by consequences (e.g., Skinner, 1981) that extends Darwinian rules of phylogenetic selection (Darwin, 1859) to ontogenetic or operant selection. In operant selection, behaviors are selected within the lifetime of the organism from operant variability. In particular, operant classes are made more or less likely to occur in the future if they produce reinforcement or punishment, respectively. Each of these aspects of operant selection are represented within the ETBD in the form of three simple rules: selection, reproduction, and mutation. The operation of these rules animates an artificial organism (AO) that consists of a repertoire of behavioral phenotypes which changes as algorithmic time moves forward (i.e., as the rules operate). Each generation (a) a behavior is emitted and either (b) produces a benefit (e.g., reinforcement) or does not. Next, (c) parent behaviors are selected based on whether or not a benefit was produced and then (d) selected parent behaviors are combined to produce the population of behaviors that may be emitted at the onset of the next generation. However, before the onset of the next generation, (e) this population of behaviors is potentially modified through mutation. Finally, (f) the next generation behavior is selected and emitted. How the parent behaviors are selected (i.e., selection), how parent behaviors are combined to produce the child or next-generation behavior (i.e., reproduction), and whether or not any additional changes (e.g., mutation) occur prior to the onset of the next generation is determined by each of the rules. This process is illustrated by Fig. 1. This process and each of the rules have been described in detail elsewhere (McDowell, 2004, 2013, 2019). Thus, no further description will be included here outside of those pertinent to the method of the current study. We suggest readers unfamiliar with the ETBD read a recent summary of the theory and its findings (McDowell, this issue; McDowell, 2019) prior to continued reading of this article.

Fig. 1.

A flowchart demonstrating the rules of the ETBD

Some readers may question whether the ETBD is a better candidate to model the subtypes of ASIB than older, more familiar mathematical models such as the matching law (Herrnstein, 1961). There are two main reasons why the ETBD may be a better candidate than the matching law for developing models of the subtypes of ASIB. First, and most important, although the matching equations have been consistently shown to account for variance in behavior, the theoretical implications of those equations (i.e., matching theory) have been demonstrated to be untenable (McDowell, 2013; McDowell, this issue). Second, the matching equations account well for steady-state phenomena but are not designed to account for more dynamic phenomena observed at smaller time scales. A model that can account for both steady-state and dynamic phenomena may be more useful in the initial development and evaluation of models of ASIB subtypes and in future research based on those models. As described next, the ETBD can account for both steady-state and dynamic phenomena.

Since its initial description (McDowell, 2004) the ETBD has been demonstrated to produce AO behavior similar to existing live-organism data (McDowell, 2019). In particular, the ETBD has been shown to produce AO behavior on single interval reinforcement schedules (McDowell & Calvin, 2015; McDowell & Caron, 2007; McDowell & Klapes, 2020), concurrent interval reinforcement schedules (McDowell et al., 2008; McDowell & Popa, 2010; Popa & McDowell, 2016), concurrent ratio reinforcement schedules (McDowell & Klapes, 2018), and concurrent interval reinforcement schedules with superimposed punishment schedules (McDowell & Klapes, 2019) that closely resemble data produced by live organisms. Support for the ETBD has been found with steady-state (e.g., slight undermatching; McDowell et al., 2008) and dynamic (e.g., effect of successive reinforcers on a response-by-response basis; Kulubekova & McDowell, 2013) phenomena. As discussed by McDowell (2019), the ETBD has also made several predictions that go beyond data currently available with live organisms. For example, the theory has made predictions about the behavior of parameters within single-alternative, concurrent, and bivariate matching equations, the rate of change-over responses when reinforcement rate and magnitude are varied, as well as choice under concurrent ratio schedules. These predictions have yet to be evaluated with live organisms, and this is an important direction for future research on the ETBD. Given this large body of support for the ETBD, it may be well suited to model subtypes of ASIB.

Researchers have demonstrated that the occurrence of SIB maintained by socially mediated reinforcement is well described by single-alternative (Herrnstein, 1970; McDowell, 1982; McDowell, 1986, 1988) and generalized matching equations (Baum, 1974; Borrero et al., 2010; Borrero & Vollmer, 2002). Similar demonstrations do not exist for ASIB because of the aforementioned difficulties; we currently do not possess the technology to manipulate the availability of automatic reinforcers for the behavior of live organisms. However, assuming that automatic reinforcers do not affect behavior in a manner that is distinct from socially mediated reinforcers (MacCorquodale, 1969; Vollmer, 1994), similar relations likely exist with behavior maintained by automatic reinforcement. Such manipulations may only be possible with the ETBD or similar models. The relations characteristic of the single-alternative and generalized matching equations have been shown to be emergent properties of the ETBD (McDowell et al., 2008; McDowell & Klapes, 2020). Therefore, the ETBD may be well-suited to model the subtypes of ASIB as a response occurring in a single-alternative arrangement, in which the magnitude of background reinforcement or available environmental stimulation varies across conditions (e.g., more in the play condition, less in test conditions, and least in the alone condition). The ETBD would allow for a manipulation of the magnitude of reinforcement for the target response (i.e., ASIB) and level of sensitivity or sustained operant variability (i.e., mutation rate) that could provide a test of proposed explanations for differences across subtypes and whether or not these differences can be explained in purely operant terms. Thus, the purpose of the current study was to use the ETBD to (1) model functional-analysis outcomes that characterize Subtypes 1 and 2 ASIB, (2) test these models by evaluating interventions aimed at decreasing the target response, and (3) test for differences in sensitivity between ETBD’s model of the subtypes using procedures similar to those described by Rooker et al. (2019).

Method

General Procedure

Across all three phases of the current study, AOs were placed in a single-alternative arrangement in which the target response served as the model for ASIB. Each AO was created with of an initial population of 100 potential behaviors chosen randomly from the phenotype range, 0–1,023. The target class consisted of 41 phenotypes from the range, 471–511. This target-class range has been used frequently in previous research (e.g., McDowell & Klapes, 2020). Any phenotype emitted from this range counted as a target response. The background class consisted of 200 phenotypes selected at random from the range of possible phenotypes (0–1,023), not including the target range. Any phenotype emitted from this class counted as a background response. The background phenotypes were chosen separately for each AO.

The general operation of the selection, reproduction, and mutation rules is depicted in Fig. 1. These rules were implemented as described in previous research (e.g., McDowell & Klapes, 2020). When phenotypes emitted produced reinforcement, the parent behaviors for the next generation were selected according to a linear fitness-density function (FDF). The FDF mean was one parameter that was manipulated in the current study, smaller FDF means result in stronger selection strength and affect behavior in a manner consistent with increases in reinforcement magnitude (e.g., McDowell et al., 2012). When the phenotype emitted did not produce reinforcement, the parent behaviors for the next generation were selected randomly. Once the parent phenotypes were selected, they were combined through bitwise recombination. That is, bits from each of the parent genotypes (i.e., binary strings corresponding to each phenotype) were randomly selected from each parent to produce the child behavior’s genotype (e.g., 111011000) and to obtain its corresponding phenotype (e.g., 472). After all parent behaviors were combined, a population of 100 child behaviors that could be emitted at the onset of the next generation was complete. Prior to the emission of the child or next-generation behavior, there was some chance that mutation would occur. That is, a randomly selected percentage of the created child behaviors underwent bit-flip mutation in which one bit of their genotype was changed (i.e., from 1 to 0 or from 0 to 1). The percentage of child behaviors that underwent mutation is referred to as the mutation rate, which has been described as a diffusion process (e.g., McDowell, 2004). This was the second parameter that was manipulated in the current study. Higher levels of mutation may be thought of as forcing more sustained operant variability or less sensitivity to moment-to-moment changes in the environment. After the population of potential child behaviors undergoes mutation, one behavior is randomly selected for emission, and the process begins again. The computational experiments were run on commercially available off-the-shelf desktop and notebook computer hardware. The code that created the AOs, animated them by means of the evolutionary theory, arranged the virtual experimental environments, and collected the data was written by the second author in VB.NET 2015, a popular programming language. The code was written, compiled, and run in the Microsoft® Visual Studio 2015 Integrated Development Environment. A more complete, general description of the ETBD and its findings can be found in this issue (McDowell, this issue). For all phases, the ETBD was implemented as described by McDowell and Klapes (2020), and a more complete descriptions of the theory can be found there. For each phase, only the procedural details pertinent to the purpose of that phase are included.

Phase 1: Modeling Subtypes

Phase 1 Method

The purpose of Phase 1 was to evaluate if and how parameters of the ETBD could be manipulated to bring about patterns of responding that meet the criteria for Subtypes 1 and 2 ASIB. Eight models were evaluated, 10 AOs were animated in accordance with each model. All models were evaluated in a single-alternative arrangement in which the target response served as the model for ASIB. The FDF mean and mutation rate were manipulated and evaluated in different combinations in an attempt to produce response patterns characteristic of Subtypes 1 and 2 ASIB. In particular, models in which ASIB produced high-magnitude reinforcement (i.e., an FDF mean of 10) and low-magnitude reinforcement (i.e., an FDF mean of 100) were evaluated in AOs whose behavior had mutation rates of 1%, 3%, 10%, and 20% (i.e., ranging from highly sensitive to more insensitive). Table 1 summarizes the different values for each parameter and how they were combined to produce each of the 8 distinct models. ASIB produced reinforcement according to a random-interval (RI) 20- schedule in all models. Each model was evaluated in three different conditions. The alone, test (i.e., attention or escape), and play conditions of an FA were modeled by varying the magnitude of background reinforcement. In the alone conditions, an FDF mean of 200 (very low magnitude) was used. In the test condition an FDF mean of 100 (low magnitude) was used. In the play condition an FDF mean of 50 (moderate magnitude) was used. Background reinforcement was produced according to an RI 20 schedule in all conditions. Each condition was conducted for 10,000 generations. The occurrence of ASIB was evaluated in 1,000 generation bins (termed “Sessions”). For each model, we evaluated the pattern of responding across conditions that resulted from averaging all 10 AO’s behavior. We also evaluated each individual AO’s pattern of responding by calculating subtype quotients, comparing the session-by-session occurrence of ASIB in the alone and play conditions according to the method described by Hagopian et al. (2015). We considered the best models of Subtype 1 to be those with subtype quotients greater than .5 (i.e., high differentiation between alone and play conditions) and lower levels of ASIB in the play condition. We considered the best models of Subtype 2 to be those with subtype quotients less than .5 (i.e., high differentiation between alone and play conditions) and higher levels of ASIB in the play condition.

Table 1.

Parameters values and resulting combinations for each model

	MR 1% (most sensitive)	MR 3%	MR 10%	MR 20% (least sensitive)
FDF 100 (low-reinforcement magnitude)	Model 1	Model 2	Model 3	Model 4
FDF 10 (high-reinforcement magnitude)	Model 5	Model 6	Model 7	Model 8

FDF = fitness density function, MR = mutation rate

Phase 1 Results

Figure 2 depicts the models of Subtypes 1 and 2 that were produced by the Phase 1 analyses. For each panel, the averaged data of all 10 AOs is depicted in the alone, play, and test conditions. The top panel depicts the aggregate results for the AOs animated according to Model 1, with a 1% mutation rate (i.e., highly sensitive) and a target response that produced low-magnitude reinforcement (i.e., had an FDF mean of 100). The data produced by AOs animated according to Model 1 look similar to the results of a multielement FA conducted with individuals with Subtype 1 ASIB (cf. Hagopian et al., 2015). As is characteristic of Subtype 1 ASIB, there was a high level of differentiation between the occurrence of ASIB in the alone and play conditions. In particular, this model produced the highest rate of responding in the alone condition with little responding in the play condition.

Fig. 2.

Models for Subtypes 1 and 2 ASIB (Aggregate Data; BG = background reinforcement)

The bottom panel of Fig. 2 depicts the aggregate results for the AOs animated according to Model 8, with a 20% mutation rate (i.e., insensitive) and a target response that produced high-magnitude reinforcement (i.e., had an FDF mean of 10). The data produced by AOs animated according to Model 8 look similar to the results of a multielement FA conducted with individuals with Subtype 2 ASIB (cf. Hagopian et al., 2015). As is characteristic of Subtype 2 ASIB, there was little differentiation between ASIB response rates in the alone and play conditions. It is important to note that the level of responding in the play condition was much higher for Subtype 2 than Subtype 1, which is also characteristic of the subtypes. Note that the y-axes have different maximum values and scaling across the panels.

Figure 3 depicts the results of the parametric analysis of the effects of various mutation rates across the two FDF means. For each panel, the averaged data of all 10 AOs are depicted in the alone, play, and test conditions. The mutation rate and FDF mean used to animate the AOs’ behavior shown in each panel can be found across the top and right of Fig. 3, and the model number corresponding to Table 1 can be found in each panel. Note that the y-axes have different maximum values and scaling across the panels. Figure 3 indicates that mutation rate is the primary variable affecting the degree of differentiation between the alone and play conditions. Moving from left to right across both top and bottom panels, the level of differentiation decreases systematically with increases in mutation rate. It is important to note that mutation rate seems to primarily affect the level of responding in the alone condition, whereas the level of responding in the play condition remains relatively consistent. Figure 3 also indicates that the FDF mean primarily affects how much responding occurs. When comparing the top and bottom row of panels, it is clear that the level of responding in a given condition is consistently higher in the bottom panels across all mutation rates. Thus, mutation rate (i.e., level of sensitivity or sustained variability) seems primarily responsible for the difference between conditions within each model, whereas FDF mean (i.e., reinforcer magnitude) seems primarily responsible for how the level of responding varies across models.

Fig. 3.

All models evaluated (Aggregate Data)

Figure 4 depicts the individual data for each of the 10 AOs animated according to each model. Each white data point represents a summary of one AO’s behavior. The top panels display subtype quotients calculated from each AO’s session-by-session data. The bottom panels display the average number for responses per session in the play condition for each AO. Left panels and right panels depict models that were animated with FDF means of 100 and 10, respectively. Subtype quotients decreased systematically as mutation rate increased. For models with an FDF mean of 100, subtype quotients may have decreased slightly more quickly with increases in mutation rate relative to models with an FDF mean of 10. The average number of responses in the play condition was higher for models with an FDF mean of 10 relative to those with an FDF mean of 100. This difference remained consistent across changes in mutation rate, although there was more variability in the average number of responses in the play condition for those models with an FDF mean of 10.

Fig. 4.

Subtype quotients and responding in play condition for individual AOs

In summary, mutation rate primarily affected the level of differentiation between play and alone conditions, and thus, their subtype quotients. FDF mean was primary responsible for the variance in the amount of responding across models and resulted in higher rates of responding in the play condition at smaller FDF means (i.e., stronger reinforcers). Thus, given that Subtype 1 is characterized by high differentiation between the play and alone condition (i.e., a subtype quotient greater than or equal to .5), the best model for Subtype 1 was Model 1, in which the AO’s target response produced reinforcement with an FDF mean of 100 and whose behavior had a mutation rate of 1% (see Fig. 2, top panel). In terms of ASIB, this would mean that response patterns indicative of Subtype 1 ASIB are obtained when ASIB produces relatively weak reinforcement, and the individual is relatively sensitive to environmental changes. Given that Subtype 2 is characterized by little to no differentiation between the play and alone condition (i.e., a subtype quotient less than .5), the best model for Subtype 2 would be Model 8, in which AO’s target response produced reinforcement with an FDF mean of 10 and whose behavior had a mutation rate of 20% (see Fig. 2, bottom panel). In terms of ASIB, this would mean that response patterns indicative of Subtype 2 ASIB are obtained when ASIB produces relatively strong reinforcement, and the individual is relatively insensitive to environmental changes. Although other models met the criteria for Subtypes 1 and 2, the two identified here most clearly meet the criteria and represent the extremes of response patterns obtained. Thus, they may be well suited for the initial test of the model’s correspondence with each subtype’s predictions of treatment efficacy.

Phase 2: Treatment Evaluation

Phase 2 Method

The primary utility of the subtypes of ASIB is their ability to predict treatment efficacy (e.g., Hagopian et al., 2015; Hagopian et al., 2017; Hagopian et al., 2018). Thus, an important test of the validity of the ETBD’s models of the subtypes is to evaluate the efficacy of different interventions in decreasing ASIB within each model. The purpose of Phase 2 was to evaluate the efficacy of time-based reinforcement in decreasing ASIB within each model. When time-based reinforcement was shown to be ineffective, we evaluated the effects of adding a punishment contingency. Although other, less-intrusive interventions would typically be evaluated prior to the implementation of punishment (e.g., response blocking), these cannot currently be implemented in the ETBD in a straightforward manner. In addition, mild forms of negative (e.g., response cost; Berg et al., 2016) and positive (e.g., contingent demands; Verriden & Roscoe, 2019) punishment have been shown to be necessary to bring about reductions in ASIB in some cases. In an applied setting, reinforcement-based interventions should always be evaluated prior to punishment-based procedures, and punishment should never be evaluated in the absence of reinforcement-based procedures (Behavior Analyst Certification Board, 2014, Guideline 4.08). A punishment-alone condition was included only for the purposes of facilitating comparisons between reinforcement alone and reinforcement plus punishment.

The first interventions evaluated with both models were time-based reinforcement conditions. These conditions were similar to the play condition of the functional analyses described in Phase 1. Assuming that the play condition includes the most efficacious reinforcers available, we did not increase the FDF mean (i.e., reinforcement efficacy) beyond 50 because this may not be possible or may not have any clear analogue to the clinical setting. Instead, we increased the rate of background reinforcement (i.e., time-based reinforcement) to random time (RT) 10, 5, and 1 schedules. This allowed us to evaluate whether more dense or continuous schedules of background reinforcement would be sufficient to decrease target responding.

We also evaluated the effects of punishment alone and in combination with reinforcement when reinforcement alone was found to be ineffective. Within the ETBD, when a behavior produces punishment, all members of the operant class have some probability of undergoing forced mutation. This forced mutation operates in the same manner as, and occurs in addition to, the normally occurring rate of mutation described in the General Procedure section. In particular, the forced mutation that occurs when a behavior produces punishment decreases responding by sometimes causing members in the target phenotype range to mutate into a phenotype that is no longer in the target range. Thus, by causing some phenotypes to “mutate out” of the target range of phenotypes, the target response becomes less likely. The probability that members of the target class undergo forced mutation is governed by the reinforcing value of the context (i.e., target and alternative responses) in which punishment is delivered. The magnitude or strength of punishment can also be increased by increasing the number of times the target class is “scanned” with a given probability of forced mutation per scan. At a higher number of scans, the likelihood of mutation is greater, and therefore, so are the effects of punishment. All aspects of the implementation of punishment within the ETBD were developed and described in more detail by McDowell and Klapes (2018). We evaluated a total of four punishment conditions: (1) RI 20 schedule of punishment, (2) RI 20 schedule of punishment with RT 5 reinforcement, (3) RI 20 schedule of punishment with RT 1 reinforcement, and (4) RI 20 schedule of punishment in which five additional scans for mutation were added (i.e., a higher magnitude punisher) with RT 5 reinforcement.

Phase 2 Results

Figure 5 displays the results of the treatment evaluation. Across all panels, the alone data paths (white circles) are the same data that were included for the specified models during Phase 1. The upper left panel depicts the treatment evaluation for Subtype 1. For Subtype 1, all three time-based reinforcement interventions resulted in an almost 80% reduction in the occurrence of the target response. Percentage reductions from the alone condition were 78%, 86%, and 87% for RT 10, 5, and 1 schedules, respectively. Thus, in the model for Subtype 1, reinforcement alone was sufficient to decrease the occurrence of ASIB, and the denser the schedule of reinforcement implemented, the greater the reduction obtained.

Fig. 5.

Treatment evaluation conducted with the models of Subtypes 1 and 2

The lower left panel depicts the evaluation of interventions consisting of reinforcement alone for Subtype 2. For Subtype 2, all three time-based reinforcement interventions resulted in small reductions (i.e., < 50% of the alone condition) of ASIB, none of which achieved clinical significance (e.g., 80%). Thus, for Subtype 2, we also evaluated the effects of punishment with and without reinforcement. Each of these interventions was more effective than reinforcement alone in reducing Subtype 2 ASIB. Punishment alone resulted in a 60% reduction. Punishment with RT 5 reinforcement resulted in a 71% reduction. Punishment with RT 1 reinforcement resulted in a 79% reduction. Finally, higher magnitude punishment with RT 1 reinforcement resulted in a 91% reduction.

Thus, in the model for Subtype 2, reinforcement alone was insufficient to decrease the occurrence of ASIB, but punishment in conjunction with continuous reinforcement was sufficient to bring about significant reductions in ASIB, and higher magnitudes of punishment were more effective.

In summary, Phase 1 provided 8 models in which sensitivity (i.e., mutation rate) of AO behavior and magnitude of reinforcement (i.e., the FDF mean) produced by ASIB (i.e., the target response) varied. From the models evaluated, the two that most clearly fit the criteria for Subtypes 1 and 2 ASIB were selected. Phase 2 tested the models’ validity by evaluating whether each model predicted the response to treatment that is characteristic of each subtype. Hagopian et al. (2015) and Hagopian et al. (2017) demonstrated that reinforcement alone is often sufficient in reducing Subtype 1 ASIB; whereas reinforcement alone is unlikely to be effective, and more intrusive, additive components are likely required to reduced Subtype 2 ASIB. Each of these predictions was verified during Phase 2. The ETBD’s model for Subtype 1 was effectively reduced by approximately 80% or greater with reinforcement alone. In contrast, the ETBDs model for Subtype 2 was not significantly reduced with reinforcement alone but was reduced by greater than 80% only with a higher magnitude punisher and a dense schedule of reinforcement. These findings provide support for the validity of the ETBD’s models of subtypes and suggest using them as a basis to evaluate differences between subtypes.

Phase 3: Test of Generalized Sensitivity Differences

Phase 3 Method

The ETBD can model the functional-analysis and treatment outcomes characteristic of Subtypes 1 and 2 ASIB. Thus, it may now be useful to consider how these models can help elucidate the differences between the subtypes that have not yet been entirely possible to examine. Phase 1 demonstrated that mutation rate was primarily responsible for the degree of differentiation in the occurrence of ASIB during the play and alone conditions. Mutation rate has been described as a diffusion process (McDowell, 2004) and within the context of ASIB may be thought of as sensitivity to changes in the environment. At low mutation rates, any instance of reinforcement can exert its full effects and is only minimally dampened by the ongoing mutation rate. In contrast, at high mutation rates, the effects of any instance of reinforcement are at least somewhat dampened, because some percentage of potential next-generation behaviors that could have occurred within the target class may undergo mutation and no longer fall within the target class. As a result, AOs animated with high mutation rates are less affected by, or less sensitive to, any instance of reinforcement than those animated with lower mutation rates. On a molar scale, this results in responding that is more consistent across time and across AOs at higher mutations rates whereas responding is more variable across time and AOs at lower mutation rates (see Figure 3). Thus, higher mutation rates may result in less sensitivity to momentary changes in the environment. That being said, the ETBD’s models of subtypes of ASIB suggest that the primary difference between Subtypes 1 and 2 is sensitivity. It is the variable primarily affecting the degree of differentiation between the play and alone conditions.

These conclusions are somewhat inconsistent with those drawn by Rooker et al. (2019) from their study with humans. Rooker et al. aimed to evaluate whether the insensitivity seemingly characteristic of Subtype 2 ASIB was a general response tendency (i.e.,evident across response classes) or if it applied only to the response class of ASIB only. Rooker et al. compared the responding of three individuals with Subtype 2 ASIB and three individuals with socially reinforced SIB on a button-pressing task in which preferred food items were used as reinforcers. As the contingencies for button pressing varied (i.e., switched between continuous reinforcement, extinction, and a progressive-ratio schedule of reinforcement), all individuals displayed some level of sensitivity. As a result, the authors concluded that individuals displaying Subtype 2 ASIB are not characterized by a general (i.e., across response classes) insensitivity to their environment; instead, differences must be related to ASIB in particular (e.g., sensitivity to that response class alone). In the current implementation of the ETBD, mutation rate applies to all behaviors emitted by the AOs (i.e., alternative or background responses, as well as the target response). Thus, the ETBD’s models are seemingly inconsistent with the conclusion of Rooker et al. (i.e., they are built with general insensitivity). Evaluating how the behavior of AOs change with changes in the contingencies of reinforcement similar to those evaluated by Rooker et al. may provide a useful test of the ETBD’s models of the subtypes of ASIB. In particular, the purpose of Phase 3 was to evaluate the independent and relative sensitivity of the ETBD’s models of the subtypes of ASIB under changing reinforcement contingencies. This evaluation was designed to clarify how the difference in sensitivity (i.e., mutation rate) built into the ETBD’s models would manifest in an arrangement similar to that employed by Rooker et al. and how it may inform future research on subtype differences.

Thirty AOs animated according to the model for Subtype 1 and 30 AOs animated according to the model for Subtype 2 were placed in a single-alternative arrangement in which the target response (i.e., button pressing) produced reinforcement according to contingencies that varied during the experiment. In previous phases, the models differed in the magnitude of reinforcement for the target response (i.e., the magnitude of reinforcement for ASIB); whereas, in this phase, the magnitude of reinforcement was equated (i.e., simulating the delivery of highly preferred foods for button pressing). In particular, an FDF mean of 50 was used for the target response in both models, so the only difference was their mutation rate (i.e., 1% for Subtype 1 and 20% for Subtype 2). Intervals of continuous reinforcement and extinction were presented in alternation for a total of three times each. We evaluated two different interval durations to evaluate whether some differences were only discriminable at larger or smaller time scales. In one experiment, each interval consisted of 5,000 generations that were analyzed in 500 generation bins. In a second experiment, each interval consisted of 1,000 generations that were analyzed in 100 generation bins. In addition, each experiment was conducted in two contexts: one with background reinforcement occurring on an RI 20 schedule with an FDF mean of 200 (i.e., the alone condition) and one with background reinforcement occurring on an RI 20 schedule with an FDF mean of 100 (i.e., the test condition). Unlike our initial evaluation of the models of ASIB, this experiment allowed for a comparison of sensitivity when both models produced reinforcement with similar magnitudes, the contingencies of reinforcement varied, and the time scale of analysis varied.

Phase 3 Results

Figure 6 displays the results for Phase 3. Data produced when the contingencies of reinforcement alternated on a smaller time scale (i.e., every 1,000 generations) are presented in the left panels. Data produced when the contingencies of reinforcement alternated on a larger time scale (i.e., every 5,000 generations) are presented in the right panels. The top panels show data produced when background reinforcement was programmed with an FDF mean of 100 (i.e., the test condition of Phase 1). The bottom panels show data produced when background reinforcement was programmed with an FDF mean of 200 (i.e., the alone condition of Phase 1). Dashed black lines depict the mean cumulative responses for AOs animated according to the Subtype 1 model. Solid black lines depict the mean cumulative responses for AOs animated according to the Subtype 2 model. In both cases, grey lines depict the standard deviation of the number of responses within each bin of time. Note that the y-axes have different maximum values and scaling across the left and right panels.

Fig. 6.

Sensitivity to changes in contingencies for models of each subtype

Taking all four panels together, some general conclusions can be drawn. First, at both time scales and contexts, AOs animated according to both models displayed sensitivity to changes in environmental contingencies. That is, much larger increases in the cumulative number of responses were observed during the reinforcement periods than during the extinction periods. Second, at both time scales and contexts, there was little difference in the rate of responding during periods of extinction across AOs animated according to the different models. Third, at both time scales and contexts, AOs animated according to the Subtype 1 model responded at higher rates during the reinforcement intervals, and as a result, had responded much more by the end of the experiment. This effect was exacerbated when background reinforcement was weaker (i.e., had an FDF mean of 200) and especially at larger time scales (i.e., the difference between the models was larger the longer the periods of reinforcement). Thus, AOs animated according to both models displayed sensitivity to changes in the contingencies of reinforcement. These data demonstrate that AOs animated according to the model for Subtype 1 may be somewhat more sensitive than those animated according to the model for Subtype 2. Moreover, the difference between subtypes was clearer with weaker background reinforcement and longer reinforcement periods. In terms of ASIB, Phase 1 suggested that sensitivity was a key difference between the subtypes. The results of Phase 3 suggest that the level of insensitivity (i.e., mutation rate) required to obtain high degrees of overlap within an FA (i.e., across conditions with different levels of background reinforcement) does not result in complete insensitivity to changes in the environment and reinforcement contingencies but may only affect behavior outside of the response class of ASIB in more nuanced ways (e.g., less responding during periods of reinforcement).

Discussion

In Phase 1, we aimed to evaluate if and how the parameters of the ETBD could be manipulated to bring about patterns of responding characteristic of Subtypes 1 and 2 ASIB. This produced two candidate models. As is the case for Subtype 1 ASIB in humans (Hagopian et al., 2015; Hagopian et al., 2017), the ETBD’s model was characterized by a high degree of differentiation, the highest subtype quotients, and with low response rates in the play condition. These patterns of responding were obtained by AOs animated according to Model 1, with 1% mutation rates (i.e., high sensitivity) and target responses that produced reinforcement with an FDF mean of 100 (i.e., relatively low-magnitude reinforcement). As is the case for Subtype 2 ASIB in humans (Hagopian et al., 2015; Hagopian et al., 2017), the ETBD’s model was characterized by a low degree of differentiation, nearly the lowest subtype quotients, and higher response rates in the play condition. These patterns of responding were obtained by AOs animated according to Model 8, with 20% mutation rates (i.e., low sensitivity) and target responses that produced reinforcement with an FDF mean of 10 (i.e., relatively high-magnitude reinforcement). Parametric analysis of different mutation rates across the two FDF means clarified that mutation rate was the primary variable responsible for, and was negatively correlated with, the degree of differentiation. The parametric analyses clarified that FDF mean primarily affected the rate of responding, with higher response rates occurring across all conditions at lower FDF means (i.e., higher magnitude reinforcers).

In Phase 2 we tested these models by evaluating the efficacy of different behavior-reduction procedures. Variation in treatment efficacy across models was consistent with the findings of Hagopian and colleagues (Hagopian et al., 2015; Hagopian et al., 2017) and supported the validity of the models of both subtypes. For the model of Subtype 1, ASIB was reduced by reinforcement alone, with denser schedules of reinforcement resulting in greater reduction. This finding may be analogous to the manner in which qualitatively similar or “matched” stimulation and more preferred stimuli have been found to result in greater reduction in the occurrence of ASIB (e.g., Hagopian et al., 2020; Leif et al., 2020). For the model of Subtype 2, reinforcement alone was ineffective and resulted in only minor decreases in ASIB. As a result, we evaluated the efficacy of superimposing punishment onto reinforcement-based interventions. The addition of punishment brought about greater reductions in ASIB, but higher magnitude punishers, in conjunction with continuous reinforcement, were required to bring ASIB to near-zero levels. These findings parallel those of Verriden and Roscoe (2019) in which multiple punishers were evaluated to identify which exerted the strongest effects on behavior.

The results of Phases 1 and 2 support the ETBD’s models of the subtypes of ASIB and suggest that these models may be beneficial in understanding the mechanisms underlying differences between Subtypes 1 and 2. One proposed explanation for the difference between Subtypes 1 and 2 was that Subtype 2 produces qualitatively superior (i.e., higher magnitude) reinforcers or reinforcers for which there is a stronger establishing operation (Cataldo & Harris, 1982; Hagopian et al., 2017; Ringdahl et al., 1997; Shore et al., 1997; Sprague et al., 1997; Vollmer, 1994). The ETBD’s models of the subtypes of ASIB suggest that differences in reinforcer magnitude primarily affect the general level of responding but not the level of differentiation between conditions. Thus, differences in reinforcer magnitude may be pertinent to cases in which high rates of ASIB in the alone and play conditions result in categorization as Subtype 2 ASIB, regardless of the level of differentiation (Hagopian et al., 2015). Moreover, differences in reinforcer magnitude may play an important role in resistance to solely reinforcement-based treatment procedures, but this cannot be determined from the current study.

Another proposed explanation for the differences between Subtypes 1 and 2 is that Subtype 2 may persist across all conditions because it is, at least in part, the product of elicitation, sensory dysfunction, or movement disorders (Hagopian & Frank-Crawford, 2018; Vollmer, 1994). Although the current study can certainly not rule out these variables as playing a role in the persistence of Subtype 2 ASIB, the ETBD’s models of the subtypes suggest that the differences between them are possible to explain solely in terms of operant conditioning. Thus, references to biological processes outside of behavior–environment relations may not be necessary to explain the differences between subtypes in all cases. However, the current study offers no insight as to when or how often the inclusion of other processes is needed.

The final proposed explanation for the differences between Subtypes 1 and 2 is that individuals displaying Subtype 2 ASIB have a general response tendency toward insensitivity (Rooker et al., 2019). Such general (i.e., across-response-class) differences are inherent in the ETBD’s models of the subtypes, and mutation rate was primarily responsible for the degree of differentiation across conditions in the different models. Thus, our results suggest that sensitivity is an important part of the difference between subtypes. In particular, our data suggest that some degree of insensitivity is necessary to dampen the increased efficacy of automatic reinforcement in the presence of very weak levels of background reinforcement. This is evident in Fig. 4. The level of responding in the play condition remains relatively stable as the subtype quotients decrease more rapidly, so the primary change as mutation rates increase is the level of responding in the alone condition.

Therefore, individuals who respond in the alone condition, but not in the play condition, (i.e., Subtype 1) may do so because their behavior is sensitive to the decrease in the relative reinforcing efficacy of the products of ASIB as the magnitude of background or alternative reinforcement increases. In contrast, individuals who respond at similar rates across both conditions (i.e., Subtype 2) may do so because their behavior is not sensitive to the decrease in the relative reinforcing efficacy of the products of ASIB as the magnitude of background or alternative reinforcement increases. It is important to note that this interpretation is distinct from the description that behavior does not decrease with an increase in background reinforcement or environmental stimulation alone. Instead, the models evaluated here suggest that this relation is the product of insensitivity to changes in the relative efficacy of ASIB as the level of background reinforcement changes.

In Phase 3, we used procedures similar to Rooker et al. (2019) to test whether the ETBD’s models supported their preliminary conclusion that differences in the subtypes of ASIB could not be described in terms of generalized (i.e., repertoire-spanning) differences in sensitivity. This is an important test of the ETBD’s models of the subtypes because they were built with general differences in sensitivity (i.e., mutation rate) and thus may seem inconsistent with the conclusions of Rooker et al. There are several differences between our procedures and those of Rooker et al. that limit the strength of our conclusions; however, we obtained comparable findings and conducted additional analyses that ultimately led us to draw slightly different conclusions. In Rooker et al., individuals who engaged in Subtype 2 ASIB displayed sensitivity to changes in contingencies of reinforcement that was comparable to the sensitivity displayed by individuals with socially reinforced SIB. Likewise, in the current study, we found that the models for Subtype 1 and 2 both displayed sensitivity to changes in contingencies of reinforcement. However, AOs animated according to the model for Subtype 1 responded more rapidly during periods of reinforcement, suggesting they were somewhat more sensitive than AOs animated according to the model for Subtype 2. This effect was larger with longer periods of reinforcement and lower rates of background reinforcement. The results of Phase 3 suggest, as did Rooker et al., that individuals displaying Subtype 2 are sensitive to changes in the contingencies for responses outside of the response class of ASIB. However, in contrast to Rooker et al., the results of Phase 3 also suggest that there are generalized differences in sensitivity between the subtypes, but that these differences are more nuanced and may only be evident after more fine-grained analyses.

The current study suggests several directions for future research with humans. As with all predictions of the ETBD that go beyond data currently available with live organisms, evaluating the validity of these predictions with live organisms is a crucial next step (McDowell, 2019). It may be useful to replicate Phase 3 of the current study with humans who meet criteria for Subtypes 1 and 2 ASIB. The results of Phase 3 suggest that longer periods of reinforcement and conditions more similar to the alone condition than the play condition of a functional analysis may make differences in sensitivity of responses outside of the class of ASIB more apparent. In addition, one aspect that will be important to control is the value of reinforcers across individuals. This could be accomplished in the sensitivity analysis by using reinforcers with similar breakpoints on progressive-ratio schedules across individuals to ensure that differences in reinforcer magnitude do not obscure differences in sensitivity.

Hagopian et al. (2018) applied the methods of precision medicine to the assessment and treatment of ASIB and found that both the level of differentiation and subtype classification served as good to excellent predictive behavioral markers. They also noted a large amount of heterogeneity in the findings for Subtype 2 ASIB, suggesting that it may be possible to further delineate predictions of treatment efficacy based on the identification of additional behavior markers. In Phase 1, many AOs animated according to the different models met criteria for Subtype 2 in that their data generated subtype quotients less than .5 or they responded at high rates in the play and alone conditions. These different models were similar in their level of differentiation and would have obtained the same subtype classification but also varied considerably in the rate of occurrence of ASIB in the play condition (see Fig. 4). This suggests that in future research, one variable that could be considered as a possible predictive behavioral marker is the level of occurrence of ASIB in the play condition of functional analyses, independent of level of differentiation. The current study did not clarify the extent to which level of differentiation, subtype classification, or response rate in the play condition would predict the efficacy of different behavior-reduction interventions because the treatment evaluation was conducted with only two models, and these more detailed analyses were outside the scope of the current study.

The current study also suggests several directions for future research on the ETBD as it is related to ASIB. One important next step will be to extend the parametric analysis included in Phase 1. Evaluating the response patterns obtained from AOs whose behavior produces reinforcement with greater variations in FDF mean (i.e., reinforcer magnitude) and are animated with mutation rates smaller and larger than those evaluated in the current study could further elucidate the differences between subtypes and the variables underlying different response patterns. Another important next step would be to apply the procedures of Hagopian et al. (2018) to the responding of AOs animated according to many different models. This could serve to more thoroughly characterize the relation between different behavioral markers and treatment efficacy by filling in the gaps where little data are available from live organisms. In particular, the extent to which subtype classification, level of differentiation, and rate of responding in the play condition predict treatment efficacy could be evaluated by conducting a treatment evaluation with all models. This may be especially useful if it is done with models animated with a wider range of mutation rates and FDF means than those included in the current study.

In summary, the current study demonstrates that the ETBD can model the well-documented assessment results used to characterize subtypes of ASIB (Phase 1) and that the model’s subtype classifications predict treatment efficacy just as they do in humans (Phase 2). Finally, the ETBD replicated the results of a study with humans aimed at understanding differences between subtypes but predicted that a different conclusion could be drawn with modification to the procedures and analyses (Phase 3). Taken together, these results demonstrate the utility of quantitative models of behavior (Dallery & Soto, 2013). The ETBD provided precise predictions about behavioral mechanisms that may give rise to the different patterns of responding characteristic of the subtypes and the correlated differences in treatment efficacy. The ETBD has a long history of accurately modeling the behavior of live organisms and making predictions about experimental arrangements that have yet to be conducted. The current study adds to the small body of research demonstrating how the ETBD can model behavior problems of applied importance and make predictions about their causes and occurrence (e.g., attention-deficit hyperactivity disorder, depression, bipolar disorder; see discussion in McDowell, 2019). Moreover, this is the first instance in which the ETBD has modeled differences in contingencies and behavior (i.e., automatic reinforcement of SIB) that go beyond our current technological capacity. The current study demonstrates the potential of utilizing the ETBD to model behaviors of applied importance and suggests that future research could further our understanding of ASIB and other social significant behaviors by continuing to apply the ETBD.

Declarations

Conflict of interest

The authors report no conflicts of interest. This research was conducted in accordance with ethical standards.