Evidence for a Latent Bottleneck After Extensive Dual-Task Practice of a Visual-Manual and an Auditory-Verbal Task

Abstract

Practicing two simultaneous tasks in an extensive manner reduces the performance impairments (i.e., dual-task costs) that occur in dual-task situations compared to single-task situations. The present study provides empirical tests of the latent bottleneck model to explain this reduction and thus the practice-related improvement in dual-task performance. To do so, in three experiments, participants practiced a visual-manual and an auditory-verbal task in single-task and dual-task trials for several sessions. In these experiments, we changed the duration of the response selection stages of the two tasks after practice and analyzed the resulting effects on the reaction times (RTs) during subsequent transfer. The results showed a pattern of selective prolongations of the RTs in the two tasks, which depends on the location of the manipulated process relative to a presumed latent processing bottleneck. The manipulation of the time at bottleneck stages in the longer (auditory-verbal) task did not propagate into the RTs of the shorter task, while prolongations of bottleneck stages of a shorter (visual-manual) task propagated into longer task RTs after practice. These results are consistent with a latent bottleneck model of dual-task practice.

Keywords

dual tasks practice latent bottleneck response selection

Introduction

Usually, participants produce longer reaction times (RTs) and/or increased error rates if they perform two tasks simultaneously in dual tasks as compared to the tasks’ separate performance in single tasks (i.e., dual-task costs). A popular assumption for explaining these dual-task costs holds that a basic capacity limitation of the cognitive system exists (Koch et al., 2018; Pashler, 1994), which prevents central cognitive processes from being processed simultaneously in two tasks. Instead, these processes are subject to an unavoidable (i.e., structural) bottleneck and must be processed serially, leading to dual-task costs. The response selection bottleneck (RSB) model assumes that this bottleneck is located at a central response selection stage (between a perception stage and a motor response stage), and this model represents a theoretical hallmark of research on dual-task processing (Welford, 1952).

The RSB model allows predicting basic findings in elementary dual-task research of the psychological refractory period (PRP) paradigm (Pashler, 1994; Welford, 1952). This PRP paradigm typically consists of two sensorimotor tasks for which RTs are the primary dependent measure. Both tasks are performed in combination in each trial of a dual-task block through the presentation of two stimuli; the stimuli are presented with a variable interval between their onsets (stimulus onset asynchrony; SOA). Participants are asked to perform different responses to these stimuli with a priority to respond to the first task stimulus. The typical finding is that RTs to the first task stimulus (RT1) are usually independent of the SOA (i.e., RT1s are relatively constant across SOA levels), while RTs to the second task stimulus (RT2) increase with decreasing SOA levels. The RT pattern of increasing RT2s with decreasing SOAs is referred to as the “PRP effect,” reflecting dual-task costs in the PRP paradigm. To explain the PRP effect, the RSB model assumes an interruption in the processing chain of the second task if the response selection in that task cannot start because of ongoing response selection in the first task. This interruption is longer for shorter SOA conditions compared with longer SOA conditions, so that RTs in the second task and the dual-task costs increase from the latter to the former conditions.

Despite its success in explaining basic empirical findings, several critical observations have been reported (Logan & Gordon, 2001; Meyer & Kieras, 1997; Miller et al., 2009) (see Fischer & Plessow, 2015, for a review), which raise doubts about the validity of the RSB model. One of these findings concerns the observation that practice may lead to a strong reduction or even to a complete elimination of dual-task costs in a situation in which participants perform two choice RT tasks simultaneously. Such findings are often used to question the assumption of a structural bottleneck because practice seems to have resolved the serial processing of the response selection processes in two tasks. For example, in one of the most famous dual-task practice studies, Schumacher et al. (2001) asked participants in Experiment 1 to perform a dual-task paradigm that consisted of a visual-manual (i.e., the visual task) and an auditory-verbal choice RT task (i.e., the auditory task). In the visual task, participants responded manually with key presses of the fingers of the right hand to the spatial position of visually presented circles. In the auditory task, a low, middle, or high tone was presented, and participants responded by saying “ONE,” “TWO,” or “THREE,” respectively. The two-component tasks were presented separately in single-task trials and simultaneously in dual-task trials (with an SOA of 0 ms). Dual-task costs, as measured by RTs in dual-task trials minus RTs in single-task trials, were observed at the beginning of practice. After practice and with appropriate incentives, however, dual-task costs were statistically eliminated, consistent with the assumption of a disappearing bottleneck. In particular, the RT difference between dual-task and single-task trials amounted to 4 and 11 ms in the visual and auditory tasks at the end of practice, respectively (for similar findings with this paradigm, see also Anderson et al., 2005; Göthe et al., 2016; Hartley et al., 2011; Hazeltine et al., 2002; Israel & Cohen, 2011; Liepelt, Strobach, et al., 2011; Schubert & Strobach, 2018; Schubert et al., 2017; Strobach & Huestegge, 2021; Strobach & Schubert, 2017b; Strobach, Frensch, Müller, et al., 2012a, 2012b; Strobach, Frensch, Soutschek, et al., 2012; Strobach et al., 2013, 2015; Strobach, Salminen, et al., 2014).

The implications of the finding of eliminated dual-task costs as demonstrated by Schumacher et al. (2001) and others for the RSB assumption are still not yet clear and debated (see Hartley et al., 2011; Levy & Pashler, 2001; Ruthruff, Pashler, et al., 2001; Tombu & Jolicœur, 2003). One reason for the debate is that there might be theoretical models that can explain dramatic practice-related reductions of dual-task costs in dual-task situations while still assuming a capacity limitation at the central cognitive stage. One example of such a theoretical model is the latent bottleneck model (Anderson et al., 2005; Ruthruff et al., 2006; Strobach & Schubert, 2017b).

The Latent Bottleneck Model

According to the latent bottleneck model, a practice-related elimination of dual-task costs may occur in a situation in which practice leads to a scheduling of the processing stages in a way that the response selection in one component task has finished before the response selection in the other task starts. As illustrated in Figure 1A, in such a situation, the bottleneck stages may operate serially, one after the other, and there is no interruption of the processing chains. Such a pattern of stage scheduling may result from a number of reasons. First, the two-component tasks may involve pre-bottleneck/bottleneck stages with a different basic duration, for example, a component task with a very short perception and response selection stage in combination with a component task with a time-consuming perception stage (Lien et al., 2005; Van Selst et al., 1999). Second, extended practice has led to a non-symmetric shortening of the durations of initially (time-wise) overlapping processing stages in the two tasks, which may result in a latent bottleneck-like scheduling of the response selection stages (Ruthruff et al., 2006).

Importantly, the particular situation in the Schumacher et al. (2001, Experiment 1) study seems susceptible to a latent bottleneck-like scheduling of processing stages because, first, participants performed the tasks for several practice sessions. Second, a relatively short visual task (M = 283 ms in dual tasks) was combined with a relatively long auditory task (M = 456 ms in dual tasks) at the end of practice, which might have resulted from combining tasks with different difficulty levels, such as a spatially highly compatible and an arbitrary stimulus-response mapping in the visual and the auditory tasks, respectively (Ruthruff et al., 2006). Finally, the particular combination of input and output modalities in the paradigm of Schumacher et al. avoided any kind of peripheral interference between the perceptual and motor systems of the component tasks (Göthe et al., 2016; Hazeltine et al., 2006; Meyer & Kieras, 1997; Wickens, 2014). In summary, these characteristics may have caused participants to perform the two component tasks in a latent bottleneck-like scheduling after practice.

In the present study, we tested the possibility of a latent bottleneck for explaining the practice-related reduction of dual-task costs when participants perform a visual and an auditory choice RT task simultaneously, as in Schumacher et al. (2001, Experiment 1). Testing the latent bottleneck assumption in this situation is essential because this situation represents (a) all prerequisite elements of optimal dual-task performance (Hartley et al., 2011; Meyer & Kieras, 1997; Strobach, Frensch, Müller, et al., 2012a, 2012b; Tombu & Jolicœur, 2004), and (b) one of the first dual-task situations with eliminated dual-task costs at the end of long-lasting practice, in both component tasks, on the group mean level, and with replications in some following studies (Hartley et al., 2011; Hazeltine et al., 2002). Note that Anderson et al. (2005) proposed a production-based model that can simulate practice effects in tasks like those in Schumacher et al. (2001) by assuming serially ordered response selection processes. The findings of these simulations provide valuable clues about practice-related changes in systems with serial central stages. However, elaborated empirical tests of the latent bottleneck model in the context of task situations like that in Schumacher et al. are still lacking (see also Strobach & Schubert, 2017a).

Experimental Rationale to Test the Latent Bottleneck Model

Because the practice effects reported for task situations of Schumacher et al. (2001) are most challenging for the RSB assumption, we relate the findings of the current study primarily to predictions of the latent bottleneck model. Testing specific predictions of this model empirically can be realized by the locus of slack logic (Hazeltine et al., 2002; Meyer & Kieras, 1997; Pashler, 1994, 1998; Pashler & Johnston, 1989, 1998). This logic is based on the prolongation of the duration of certain processes in the two-component tasks after practice and on the application of assumptions by the latent network theory (McCann & Johnston, 1992; Schubert, 1999; Schweickert, 1983) for the interpretation of the resulting effects on the RTs. The idea of that approach is that a prolongation of a stage after practice should have different effects depending on the specific location of that stage relative to a presumed latent bottleneck. The predictions about these different effects are illustrated in Figure 1B (prolongation of processing stage in shorter task) and Figure 1C (prolongation of processing stage in longer task). For a better understanding of this figure, we label the shorter and longer of the two tasks Task 1 and Task 2, respectively.

Prolongation of Task 1 Processes

First, we focus on the prediction of the latent bottleneck model when prolonging presumed central bottleneck processes in Task 1. When prolonging the duration of these processes after the final practice session, these processes might then come into conflict (again) with the bottleneck processes of Task 2, according to the latent bottleneck model. This prediction is illustrated in Figure 1B. In this figure, it can be seen that, due to the prolongation, RTs in Task 1 increase for a certain amount of time, and this prolongation propagates into the processing time of Task 2 via the bottleneck mechanism between both tasks. In case bottleneck processes are scheduled close together at the end of practice, this propagation should cause an equal amount of RT increase in Task 1 and Task 2.

To prolong the response selection in Task 1, Hazeltine et al. (2002) increased the difficulty of response selection of this task during transfer after practice. However, they reported effects that were not consistent with the prediction of the latent bottleneck model but rather with a model assuming parallel processing of two tasks. In particular, participants of this study practiced the dual-task situation of Schumacher et al. (2001) for eight sessions in Experiment 1. After that first experiment, the same participants continued to work on three more experiments with manipulations of the component tasks’ perceptual and response selection stages as well as of the task timing conditions by introducing a small interval between the stimuli (see also Strobach & Schubert, 2017b); note that between the manipulations, participants conducted a number of re-practice sessions. In Experiment 3 of this series, participants were asked to give motor responses with spatially incompatible fingers to stimulus locations in the visual task, which represents a manipulation of the response selection stage (i.e., the presumed bottleneck stage) in Task 1. While this manipulation led to an increase of the RTs in the visual and the auditory tasks, the amount of that increase in the auditory Task 2 (18 ms) was far smaller than that in the visual Task 1 (65 ms).

Although, on first glance, these findings of Hazeltine et al. (2002) seem at odds with the predictions of a latent bottleneck (i.e., identical RT increases in Tasks 1 and 2 after Task 1 manipulation), the discrepancy between the predictions and the empirical findings may be caused by analytical aspects of the Hazeltine et al. study. First, the authors included all trials in the analysis of RTs in the manipulation session. Because of this inclusion procedure, a high number of trials were included in which participants responded first to the auditory task and second to the visual task. For these “reversed” trials, the difficulty-related effect on the visual task would not be carried over into the RTs of the auditory task in case of a structural (latent) bottleneck. Consequently, the difficulty-related effect on the auditory task should be far smaller than on the visual task. Second, the impact of the compatibility manipulation on the RTs in the visual task was relatively small (65 ms) in the study of Hazeltine et al.; this may have been a result of the unusual practice regime in that study. That is, Hazeltine et al. trained the same participants consecutively with flexible and changing task situations differing in difficulty and time regime and applied several subsequent transfer manipulations. As shown by Schubert et al. (2017, 2024), flexible and changing practice regimes may enhance the acquisition of dual-task coordination skills. These practice-related skills are associated with the improvement of task coordination mechanisms, which allow for a more efficient scheduling of the capacity limitations as well as the management and control of two independent task processing streams in dual-task situations. Importantly, the acquired dual-task coordination skills are transferable to alternative dual-task situations (Liepelt, Strobach, et al., 2011; Strobach, Frensch, Soutschek, et al., 2012). Among others, this may explain the relatively small manipulation effects in the visual task in Hazeltine et al. (2002).

Consequently, we included the following criteria in the present experimental design. First, we exclusively analyzed those dual-task trials in which participants responded first on the (shorter) visual task and second on the (longer) auditory task. This selection is based on the assumption that response execution processes of two tasks are scheduled in the order of preceding response selection processes (Ruthruff et al., 2006). Thus, the response execution order should reflect the order of response selections and also the manipulated response selection stages (e.g., manipulated response selection in Task 1 [visual task] is processed before the non-manipulated response selection in Task 2 [auditory task] and vice versa). As a second consequence of the Hazeltine et al. (2002) study, we conducted a series of separate and isolated practice experiments. That is, at the end of each experiment in this series, we exclusively introduced one single-task manipulation and analyzed the resulting effects on dual-task performance. Due to this experimental regime, we were able to analyze these effects separately in different experiments and in different groups of participants while avoiding potential confounding impacts on the effects due to different previous manipulations, which may have caused transfer effects in later situations. We assume that the experimental procedure in the current study allows for a systematic and diagnostic analysis of the manipulation effects when contrasted with the procedure of Hazeltine and colleagues.

One potential explanation for the propagation of Task 1 RT manipulation effects onto these RTs in Task 2 in the context of the latent bottleneck model could be a moderate level of dual-task practice. This moderate practice level potentially could not have been sufficient to enable a complete elimination of a latent bottleneck and, therefore, might represent a non-optimal condition to test practiced dual-task processing. One option to provide more optimal conditions is, thus, to introduce a test of the effects of Task 1 prolongation after an increased practice amount. While the latent bottleneck model predicts a propagation of Task 1 prolongation into Task 2 after increased practice levels (i.e., this model continues to predict bottleneck processing) as well, a model predicting the practice-related elimination of a latent bottleneck would assume that an increase in the amount of practice increases the chance to observe no such propagation; thus, even when observing a propagation effect of Task 1 RTs into Task 2 RTs under conditions of moderate practice, the bottleneck elimination model would predict a lack of propagation with an increased amount of practice. Such a model might explain this result pattern by different levels of automaticity of translating component tasks’ stimulus-response information. While automaticity could be incomplete after a moderate practice amount, it might have been completed after an increased amount of practice.

In particular, these assumptions would be consistent with recent findings of the dual-task practice literature showing dual-task costs in only a low number of participants in a highly automatized Task 2 after an increased amount of practice (Maquestiaux et al., 2008, 2010), while the number of participants with dual-task costs was larger under conditions of a less automatized Task 2 and a moderate amount of practice (Ruthruff et al., 2006). To test the potential impact of the task automatization level and the potential consequences of this level for the propagation of Task 1 RT prolongation on Task 2 RTs, we realized the propagation test after a moderate (Experiment 1) and an increased practice amount (Experiment 2).

Prolongation of Task 2 Processes

According to the latent bottleneck model, not all manipulations of the duration of processing stages lead to an increase in processing duration in both component tasks of a dual task. In more detail, the prediction holds that a manipulation of the duration of the presumed bottleneck processes in Task 2 leads to a selective effect only on the RTs in that task and not on the RTs in Task 1. Figure 1C shows that this is so because there is no way for a carry-over of Task 2 RT effects into Task 1 RTs under the condition of a latent bottleneck-like scheduling of the tasks and of a lack of perceptual and motor interference between the two tasks.

A further related prediction holds that the size of the RT effect in Task 2 should be identical for Task 2 when it is processed as a single task and as a dual task. This is so because under the condition of a latent bottleneck, the manipulation of Task 2 bottleneck processes should not change the processing duration of other processes, but of the manipulated central stage in Task 2. Since the manipulation would affect the processing duration of processes at the bottleneck, the increase in the Task 2 processing time would completely add to the RT in Task 2. Importantly, the same amount of an increase in the RTs would be expected if that task were processed as a single task because the manipulation should affect the same processing stage in the task if processed alone. Therefore, the latent bottleneck model predicts that the size of prolonging the Task 2 response selection processes should be similar for the RTs in single and dual tasks. This latter outcome is a further key assumption of the latent bottleneck model and will be tested in Experiment 3.

Experiment 1

In Experiment 1, participants practiced a visual and an auditory task in single and mixed blocks (including dual tasks) for eight sessions, as in Schumacher et al. (2001). After the eighth practice session, we conducted a transfer session (Session 9) in which the duration of the presumed bottleneck stage in Task 1 was prolonged compared to the practice session. For that purpose, we changed from presenting circles at different screen locations and instructed location-related responses to triangles of different sizes presented in the centre of the screen in the visual task. Participants were then asked to respond to the centrally presented stimuli according to their size. The change of the perception and the response selection stages should lead to prolonged processing time in the visual task in the transfer compared to the practice sessions (Pashler & Baylis, 1991; Strobach et al., 2013). Unlike Task 1, Task 2 remained unchanged during transfer compared to practice. In that case, the latent bottleneck model assumes that the manipulation of the presumed bottleneck process in Task 1 results in similarly prolonged processing time in the manipulated Task 1 and the non-manipulated Task 2.

As in Schumacher et al. (2001), we used a bonus scheme to encourage the best performance of participants throughout the experiment. Monetary bonuses and penalties were calculated based on participants’ RTs and accuracy after each block of trials. However, unlike the procedure of Schumacher et al., we used performance values for the bonus calculation for single-task and dual-task trials, which stemmed from single-task and dual-task blocks separately (for more details, see section “Methods”). This procedure of bonus calculation should allow us to control for a possible difference between the relative effort that participants spend in trial types with different complexity, like single-task and dual-task trials (Tombu & Jolicœur, 2004).

Methods

Participants

We tested eight (seven female) students of Humboldt Universität zu Berlin who were paid for participation at a rate of 8 € per session plus performance-based bonuses. According to the experience from earlier practice studies (e.g., Strobach, Frensch, Soutschek, et al., 2012), a substantial reduction of dual-task costs requires a large number of practice sessions. On the other hand, a power analysis with G*Power (Faul et al., 2007), assuming a large effect size of Cohen’s f (Cohen, 1988) = 0.70 for ANOVA interactions (as in SPSS 27) of aggregated visual and auditory task RTs in single-task and dual-task trial types across practice sessions (Strobach & Schubert, 2017b), has shown that a group size of eight participants will provide sufficient power (0.90) with an alpha set at .05. The relatively large effect size could result from the rather low RT variance in the highly practiced sensorimotor tasks at the end of practice. This variance is already rather low at the beginning of practice because there is a full introduction session before the practice phase, including several hundred trials with each sensorimotor task (see design details below). Furthermore, previous dual-task practice studies applying the present design (Hartley et al., 2011; Hazeltine et al., 2002; Maquestiaux et al., 2004; Ruthruff et al., 2003, 2006; Ruthruff, Johnston, et al., 2001; Schumacher et al., 2001; Strobach, Frensch, Müller, et al., 2012a, 2012b; Strobach, Frensch, Soutschek, et al., 2012; Strobach et al., 2013, 2015; Strobach, Salminen, et al., 2014; Van Selst et al., 1999) used similar group sizes. Moreover, a group size of eight participants in this sample and eight practice sessions (plus one transfer session) thus allows bringing together the requirements for an increased number of practice sessions with the requirements of feasible experimental economics (Lakens, 2022; Schubert & Strobach, 2012). Nevertheless, the entire sample performed a total volume of 72 hr of individual (i.e., one experimenter and one participant) experimental sessions exclusively in this experiment (and likewise for Experiment 3), while the sample of Experiment 2 even performed 117 hr. Approval by the local ethics committee was obtained before commencement of the study, which was conducted in strict accordance with the local ethics policies of the Humboldt-Universität zu Berlin (Germany). Experiments were conducted with the understanding and written consent of each participant.

Component Tasks

Sessions 1 to 8 (Practice Sessions)

The experiment was carried out on a PC and controlled by ERTS software (Experimental Runtime System; Beringer, 2000). A visual and an auditory task were performed. In the visual task, participants responded manually to a white circle in a left, central, or right position that was horizontally arranged across the black background of a computer screen. The stimulus subtended approximately 2.38°, and the possible positions were separated by a visual angle of approximately 0.95° at a viewing distance of 60 cm. Three white dashes that served as placeholders for the possible positions were present approximately 0.5° below the stimuli on the screen. They appeared as a warning signal 500 ms before the imperative stimulus was presented. The stimulus remained visible until the participant responded or until a 2,000-ms response interval had expired. Participants responded manually by pressing a spatially compatible response button with the index, middle, and ring fingers of their right hand according to the location of the stimulus on the screen.

For the auditory task, participants responded verbally to one of three possible tones played on headphones by speaking out “1” to the low-frequency tone, “2” to the middle-frequency tone, or “3” to the high-frequency tone. The tones lasted in total for 40 ms, were low (350 Hz), medium (900 Hz), or high (1,650 Hz) in frequency, and were produced via a Sound Blaster Pro Sound Card. Verbal responses were recorded with a Sony microphone connected to an ERTS voice key (VK-1.3) and the EXKEY logic (Version 02/01; Beringer, 1994; Dutta, 1995). The experimenter typed the actual response on a computer keyboard so that accuracy could be assessed in the analysis.

Session 9 (Transfer Session)

The faster visual task was manipulated in Session 9, and the auditory task remained unchanged in Session 9 compared to the practice Sessions 1 to 8. In the visual task, the stimuli were changed from circles of one size to triangles of different sizes (large, medium, or small), compared to the visual stimuli in the practice sessions. Triangles were presented centrally on the computer screen, and participants responded according to their size with the index finger to the large, with the middle finger to the medium, and with the ring finger to the small triangle. From a viewing distance of 60 cm, the sizes of the large, medium, and small triangles corresponded to 2.48°, 1.52°, and 0.95°, respectively.

Procedure

Participants performed nine sessions during the experiment, which were scheduled on consecutive days when possible. The procedure of the practice sessions (Session 1 to Session 8) was basically identical to that of Schumacher et al. (2001). Participants conducted two types of trial blocks: single-task blocks and mixed blocks. During single-task blocks, they performed 45 trials of either the visual or the auditory task separately. The order of stimuli in a single-task block was randomized, and stimuli appeared equally frequently. During mixed blocks, participants performed a mixture of 30 single-task trials, called mixed single-task trials (15 trials with the visual task and 15 trials with the auditory task), and 18 dual-task trials. The single-task trials were identical to trials in the single-task blocks. In dual-task trials, we presented a visual and an auditory stimulus simultaneously. Participants were instructed to respond to both the visual and the auditory stimulus as fast and as accurately as possible. The order of the mixed single-task and dual-task trials was randomized, and stimuli appeared equally frequently within a mixed block.

During Session 1, participants conducted six single-task blocks of each task type in alternating order. The initial task block was counterbalanced across participants. Session 2 included six single-task blocks (three visual and three auditory) and eight mixed blocks. In Sessions 3 to 9, participants performed 6 single-task blocks (3 of each task type) and 10 mixed blocks. Except for the initial two single-task blocks, single-task blocks were alternating and separated by two mixed blocks.

To encourage the best task performance, we used the task instructions according to Schumacher et al. (2001). In dual tasks, participants were told not to respond in any particular order and to give equal priority to both tasks. The instructions were designed to encourage participants to perform the tasks as quickly and accurately as possible at all trials during all blocks. Feedback was given after each trial. After each trial, the actual RT was presented for 1,500 ms when a correct response was given. If both tasks were performed in one trial, the RT of the faster was presented. When participants performed an incorrect response or omitted one response, the word “Fehler” (German: error) appeared in the center of the screen.

Further, a bonus payment scheme (Schumacher et al., 2001) was introduced to motivate accurate and fast performance. However, we introduced some changes to this scheme (see also Tombu & Jolicœur, 2004). The present bonus payment scheme was based on an adaptive comparison between a participant’s performance in each trial (i.e., current RT) and a reference RT, the so-called target time. The experiment started with a target time of 2,000 ms, which was then adjusted after each block separately for each participant and task condition (single- vs. dual-task condition). Target times were calculated using the mean RT of single-task trials in single-task blocks and the mean RT of dual-task trials in mixed blocks (mixed single-task trials were excluded from the bonus scheme).

Depending on their individual performance improvement, participants could earn bonus money. When participants’ mean RT for a given block was slower than the target time but still in a range of 50 to 100 ms above the target time, they received 10 cents in addition for that block. When the mean RT was in a range of 0 to 50 ms above the target time, they received 25 cents. Importantly, when the RT of the ongoing block was faster than the target time, they received 50 cents, and the RT of the ongoing block served as the new target time for the upcoming blocks. The mean RT of the current block and the target time were presented at the end of each block.

Bonus payments were also made based on accuracy rates: one additional cent was given for each correct response, and 5 cents were deducted for each incorrect response. Participants earned separate bonuses for the two tasks (visual and auditory) as well as for single and mixed blocks. To increase motivation and task performance, a verbal instruction was given to respond as fast and accurately as possible.

Results

For the statistical analysis, we excluded all trials in which responses were incorrect, and we excluded trials from Session 1 since this session was considered an introduction session. Separate analyses of RTs and error rates were carried out for each task by using Session and Trial type as within-subject factors. As a specific criterion for dual-task costs, we used the difference of the RTs in dual-task trials minus RTs in single-task trials (Strobach & Schubert, 2017b; Tombu & Jolicœur, 2004). According to previous studies, this contrast provides the use of a strong and reliable criterion of the dual-task performance level (Hazeltine et al., 2002; Tombu & Jolicœur, 2004) because this combination of trials represents the trials with the most significant difference in the underlying cognitive processes, that is, single-task trials require an exclusive focus on one task only, whereas dual-task trials require the maintenance of task information of both tasks plus the performance of two tasks. Therefore, this contrast is the most informative one for investigating the relation between performance variability during dual-task practice and the benefit of this practice.

In contrast, we excluded mixed single-task trials from the analyses because the primary reason to include this trial type in the present protocol was to ensure equal preparation for both component tasks in dual-task trials (Schumacher et al., 2001; Strobach, Frensch, Müller, et al., 2012a). Further, processing associated with mixed single-task trials is less specified. For instance, in these trials, participants will also be partially prepared for the task that did not occur (e.g., the auditory task in single-task trials with the visual task). The omission of an expected stimulus and task to occur may have thrown off or surprised participants, causing them to perform more poorly in contrast to single-task block trials (de Jong, 1995; Tombu & Jolicœur, 2004). On the other hand, the occurrence of two tasks in the mixed single-task trial context increases the load on working memory capacity and, thus, the efficiency of stimulus-response transmission in mixed single-task trials. Some of the results of the practice sessions and the transfer session were published in Liepelt, Strobach et al. (2011).

Practice Sessions

For the practice sessions, separate analyses of RTs and error rates were carried out by using Session (Sessions 2–8) and Trial type (single-task trials, mixed single-task trials, and dual-task trials) as within-subject factors in repeated measures ANOVAs.

Visual Task

RTs in the visual task decreased with practice, F(6, 42) = 61.070, p < .001, $η_{p}^{2}$ = .92. As can be seen in Table 1, RTs differed across the different types of trials, F(2, 14) = 29.598, p < .001, $η_{p}^{2}$ = .74. In detail, RTs in single tasks were the smallest (M = 263 ms; SD = 45 ms), followed by those of the mixed single-task trials (M = 281 ms; SD = 51 ms) and of the dual-task trials (M = 307 ms; SD = 53 ms); all differences were significant, ps < .013. A significant interaction of the factors Session and Trial type, F(12, 84) = 15.296, p < .001, $η_{p}^{2}$ = .55, indicates that practice affected the RTs in different trial types to a different degree. Table 1 shows that practice led to a stronger reduction of the RTs in dual-task trials compared to single-task trials across practice. While the difference between RTs in dual-task trials and single-task trials, that is, the dual-task costs, amounts to M = 74 ms (SD = 12 ms) in Session 2, F(1, 7) = 48.174, p < .001, $η_{p}^{2}$ = .87, dual-task costs amount to only M = 22 ms (SD = 8 ms) in Session 8, F(1, 7) = 10.923, p = .029, $η_{p}^{2}$ = .48. Even though the difference between the RTs in dual-task trials and in single-task trials was still significant in Session 8, practice had extremely reduced the amount of dual-task costs.

Table 1.

Mean Reaction Times (in ms) and Mean Error Rates (in %, in Brackets) in Experiment 1 (Sessions 1–9).

Tasks	Sessions
Tasks	1	2	3	4	5	6	7	8	9
Visual-manual task
Single	319 (1.9)	289 (2.4)	277 (3.3)	266 (3.9)	260 (4.8)	253 (5.4)	250 (4.9)	246 (5.6)	372 (11.0)
Mixed		337 (0.7)	302 (0.4)	285 (0.9)	272 (0.9)	264 (1.9)	256 (1.5)	252 (2.6)	392 (12.0)
Dual		364 (4.8)	336 (2.6)	319 (2.4)	297 (2.2)	286 (1.7)	276 (3.1)	268 (2.9)	438 (9.9)
Auditory-verbal task
Single	649 (9.4)	567 (5.1)	520 (5.1)	476 (6.7)	453 (6.1)	418 (6.6)	409 (8.7)	391 (6.4)	382 (5.2)
Mixed		668 (5.0)	586 (6.3)	529 (5.1)	485 (6.9)	443 (5.6)	425 (5.0)	401 (6.1)	440 (5.2)
Dual		774 (9.5)	666 (7.3)	595 (8.6)	542 (8.7)	480 (7.5)	464 (8.6)	433 (7.7)	610 (12.4)

Note. Single = single-task trials in single-task blocks; Mixed = single-task trials in mixed blocks; Dual = dual-task trials in mixed blocks.

Error analyses revealed a significant effect for Session on error rates, F(6, 42) = 3.475, p = .010, $η_{p}^{2}$ = .33, showing that error rate increased from M = 2.7% (SD = 0.5%) in Session 2 to M = 3.7% (SD = 0.8%) in Session 8. The error rates in mixed single-task trials (M = 1.3%; SD = 0.3%) were significantly lower than in single-task trials (M = 4.3%; SD = 0.9%), p = .006, and in dual-task trials (M = 2.9%; SD = 0.7%), p = .010, which specifies the significant effect of Trial type, F(2, 14) = 7.327, p = .008, $η_{p}^{2}$ = .45, see Table 1. Although surprising, this result pattern was demonstrated in previous studies (Hazeltine et al., 2002; Strobach, Frensch, Müller, et al., 2012a, 2012b; Strobach, Frensch, Soutschek, et al., 2012), using the dual-task paradigm of Schumacher et al. (2001). This result pattern can be explained by a reduced degree of attentiveness in visual single-task trials due to lower processing demands in single-task trials than in mixed single-task trials and/or a more cautious performance in mixed single-task trials to avoid erroneous responses (Hazeltine et al., 2002; see also the error rates in the other experiments of the current study). We found a significant interaction of Session and Trial type, F(12, 84) = 3.148, p = .012, $η_{p}^{2}$ = .29, on error rates. As can be seen in Table 1, while error rates in single-task trials increased from Session 2 (M = 2.5%; SD = 0.5%) to Session 8 (M = 5.7%; SD = 1.0%), p = .018, error rates in dual tasks decreased from M = 4.8 % (SD = 1.0%) in Session 2 to M = 2.9% (SD = 0.7%) in Session 8, p = .022. Interestingly, we found no significant difference between error rates in dual-task trials and single-task trials either in Session 2 (p = .13) nor in Session 8 (p = .24). In Session 2, participants produced significantly more errors in single-task trials than in mixed single-task trials, F(1, 7) = 6.680, p = .032, $η_{p}^{2}$ = .42, and in dual-task trials compared to mixed single-task trials, F(1, 7) = 18.297, p = .017, $η_{p}^{2}$ = .71. While the difference between error rates in single-task trials and mixed single-task trials remained significant in Session 8, F(1, 7) = 8.205, p = .025, $η_{p}^{2}$ = .45, we found no difference between error rates in mixed single-task and dual-task trials anymore, p = .112; see Table 1 for details.

Auditory Task

Participants responded faster in Session 8 (M = 408 ms; SD = 75 ms) than in Session 2 (M = 669 ms; SD = 98 ms), leading to a main effect of practice, F(6, 42) = 108.133, p < .001, $η_{p}^{2}$ = .93. RTs were fastest in single-task trials (M = 462 ms; SD = 82 ms), followed by the RTs in mixed single-task trials (M = 505 ms; SD = 90 ms) and in dual-task trials (M = 565 ms; SD = 91 ms), all differences ps < .045. The corresponding effect of Trial type was significant, F(2, 14) = 60.591, p < .001, $η_{p}^{2}$ = .92. Practice affected the RTs in the different types of trials to a different degree, F(12, 84) = 19.698, p < .001, $η_{p}^{2}$ = .73. As can be seen in Table 1, the RTs in dual-task trials decreased more strongly across sessions than the RTs in the single-task trials; consequently, while the difference in RTs in dual-task trials minus RTs in single-task trials, i.e., the dual-task costs, amounts to M = 207 ms (SD = 37 ms) in Session 2, F(1, 7) = 46.576, p < .001, $η_{p}^{2}$ = .89, dual-task costs amount to only M = 42 ms (SD = 17 ms) in Session 8, F(1, 7) = 10.224, p = .028, $η_{p}^{2}$ = .55.

In the auditory task, error rate was not affected by practice, F(6, 42) < 1. A significant effect of Trial type, F(2, 14) = 4.714, p = .040, $η_{p}^{2}$ = .32, reflects the fact that the error rate in dual-task trials (M = 8.3%; SD = 1.5%) was larger than in mixed single-task trials (M = 5.8%; SD = 1.0%), F(1, 7) = 13.752, p = .022, $η_{p}^{2}$ = .65, while dual-task errors did not differ significantly from those in single-task trials (M = 6.4%; SD = 1.3%), p = .058.

Effects of Task 1 Manipulation

Group Level Analysis

First, we tested the predictions of the latent bottleneck model about the effects of the transfer manipulation in the visual task on dual-task performance in the two component tasks on the group level. For that purpose, we conducted separate ANOVAs with the within-subjects factors Session (Session 8 vs. Session 9) and Task (visual task vs. auditory task) on the mean RTs and error rates in the dual-task trials. In cases of a non-significant factor combination of Session × Task (consistent with the predictions of the latent bottleneck model), we additionally computed and report Bayesian Factors (BF₀₁) using JASP 0.18.1 with its default JASP Cauchy prior (JASP-Team, 2023). For this analysis, we selected only those trials in which participants responded on the visual task earlier than on the auditory task, which required elimination of 4.5% and 9.4% of the trials in Sessions 8 and 9, respectively. Note that the present predictions of the latent bottleneck model hold only for a manipulation of the faster of the two component tasks. If participants had scheduled the auditory task first and the manipulated visual task second, then a manipulation of the processing duration in the visual task cannot have affected the RTs in the auditory task via a hypothetically involved bottleneck.

As can be seen in Figure 2, the manipulation of the perception and response selection stages led to an increase of the dual-task RTs in Session 9 compared to Session 8 by 169 ms, F(1, 7) = 282.660, p < .001, $η_{p}^{2}$ = .96, in the changed visual task. The increase of the RTs from Session 8 to Session 9 in the unchanged auditory task amounted to 177 ms, F(1, 7) = 108.118, p < .001, $η_{p}^{2}$ = .93. The amount of the RT increase was not different between the two tasks, F(1, 7) < 1, BF₀₁ = 3.897. This result of the group-level analysis is consistent with the prediction of the latent bottleneck model. The prolongation of RTs in the faster task after extensive practice carries over to the RTs of the slower task via the involved bottleneck.

The findings of the error rate analysis paralleled those of the RT analysis. Error rates increased in the visual task by 7.0%, F(1, 7) = 28.317, p = .011, $η_{p}^{2}$ = .73, and numerically in the auditory task by 4.7%, F(1, 7) = 2.185, p = .182, in Session 9 compared to Session 8. The amount of the increase was fairly the same across both tasks, as is reflected by the non-significant interaction of Task and Session on the error rates, F(1, 7) < 1, BF₀₁ = 3.842. This shows that the findings of the RT analysis cannot be explained by a speed-accuracy trade-off.

Individual Subject Analysis

Subsequently, we tested whether the predictions of the latent bottleneck model hold for mean RT data only or for the individual RTs of each participant as well. For that purpose, we plotted the individual RT increases from Session 8 to Session 9 in the visual and the auditory tasks for every single subject in Figure 3; the x-axis of this figure depicts the amount of the RT increase from Session 8 to Session 9 in the visual task, while the y-axis depicts the corresponding RT increase in the auditory task. Participants who perform according to the predictions of the latent bottleneck model should be represented by data points that are distributed along a regression line of x = y; this is so because data points that are located on this line (or at least in the vicinity of it) are data points where each ms prolongation of the RTs in the visual task is completely carried over into the RTs in the auditory task. By contrast, data points near the horizontal axis and below the x = y line reflect participants who do not show a complete carry-over of the RT increase in Task 1 onto the RTs in Task 2. Data points near the vertical y-axis and above the x = y line reflect participants showing a larger increase in the RTs in the unchanged auditory task compared to the RT changes in the visual task. As can be seen in Figure 3, nearly all participants are distributed closely to the line x = y. Subsequent statistical testing qualified this statement. We calculated a linear regression of the distribution of the individual RT increases (Session 9 − Session 8) in the auditory task (Task 2) onto the corresponding RT increases in the visual task (Task 1). A regression coefficient amounting to 1 would indicate that the increase of the calculated linear regression line follows the theoretical regression of x = y. The analysis provided a function of the calculated regression of y = 1.29*x − 28.12. We tested whether the regression coefficient differs from 1 with a dependent t-test in which we set the alpha level to .25 for large effects of d = 0.8. This resulted in a test power of 87%. The result of this t-test showed that the increase of the regression line (b = 1.29) is not significantly different from 1, t(6) = 0.449, p = .669, and, thus, is similar to the increase of the x = y line (b = 1). A subsequent correlation analysis provided a correlation coefficient of r = .623, p = .09, and the resulting coefficient of determination resulted in R² = .39, which shows that the assumption of a linear relation between x and y describes the distribution of the individual data sufficiently well. Together, this shows that the predictions of the latent bottleneck model can be approved on an individual level of the analysis.

Test of Dual-Task Processing Bottleneck Characteristics

The aim of the following section was to elucidate the characteristics of a (latent) bottleneck processing and its potential location in the processing chain of the two component tasks at the end of practice (i.e., Session 8 without manipulations of the response selection stage) and during the transfer session (i.e., Session 9 with the manipulated response selection stage in the visual Task 1). The analyses should provide insights into the dual-task processing characteristics in both sessions and whether the characteristics of potential bottleneck processing would differ between Sessions 8 and 9. If we do not observe evidence for processing differences, then this is consistent with the assumption of constant bottleneck processing in the two sessions, that is, as predicted by a structural bottleneck model even after practice. A lack of difference between the bottleneck processing characteristics in Sessions 8 and 9 would, additionally, indicate that the difficulty manipulation has not (artificially) induced changes to participants’ dual-task processing strategies and, thus, validate the current analysis approach.

In the first analysis, we investigated the processing characteristics at the end of practice and in the transfer session by comparing the single-task performance in the manipulated visual task and the dual-task performance in the non-manipulated auditory task in Sessions 8 and 9. We tested the prediction of the latent bottleneck that the manipulation effect on the RTs in the visual single task should be identical to the effect on the RTs in the auditory dual Task 2. Please note that the latent bottleneck model predicts similar manipulation effects for the visual and the auditory tasks in the dual-task situation. However, we compared the increase in the visual single-task and the auditory dual Task 2 because this is an even more rigorous test for the prediction of equal RT increases after the visual task manipulation. If we did not find evidence for a difference between the RT increases, then this would support the assumption of a similar location of the manipulated response selection stage of the visual task in relation to the bottleneck in the final practice session and the transfer session. For the case of no difference, we additionally computed and report Bayesian Factors (BF₀₁) using JASP 0.18.1 with its default JASP Cauchy prior (JASP-Team, 2023). In contrast, a difference in the effects would represent evidence supporting the notion of changed processing characteristics.

In a repeated measures ANOVA of Trial type (single tasks [visual task] vs. dual tasks [auditory task]) and Session (Session 8 vs. Session 9), RTs provided no evidence for a difference because there was no interaction of both factors, F(1, 7) = 1.315, p = .293, BF₀₁ = 2.897. Thus, we assume no differences in the characteristics and the location of bottleneck processes under practiced and manipulated dual-task conditions. This conclusion is consistent with the assumptions of a latent bottleneck.

In a second analysis of potential differences in bottleneck characteristics between performance at the end of practice (Session 8) and during transfer (Session 9), we analyzed the intervals between responses in the first and second tasks. In fact, we conducted distribution analyses of the inter-response intervals (IRIs) to analyze the degree of temporal overlap between the two tasks in a dual-task situation (Strobach, Frensch, Müller, et al., 2012a, 2012b). We reasoned that if these IRI distributions overlap in Sessions 8 and 9, then participants show identical scheduling characteristics to perform two tasks at the end of practice and during transfer. If there were differences between the distributions, however, then this would argue against the assumption of identical dual-task processing characteristics between the sessions.

To generate IRI distributions, we separately vincentized all correct dual-task trials for each participant in Sessions 8 and 9 into 10 bins. The resulting mean IRI distributions are illustrated in Figure 4. We analyzed these mean data with a repeated measures ANOVA, including the within-subjects factors Session (Session 8 vs. Session 9) and Bin (Bin 1–10); we were particularly interested in the main effect of and interaction with Session. The main effect of Session was non-significant, F(1, 7) = 1.583, p = .257, demonstrating no evidence for a difference of the IRIs between the end of practice and the transfer session. The interaction of Session and Bin was significant, F(9, 63) = 7.001, p < .001, $η_{p}^{2}$ = .42, and it suggests different effects of Session across the bins. However, when inspecting Figure 4, it becomes obvious that this interaction might stem from a few bins showing a numerical difference between Sessions 8 and 9 (in particular, Bins 9 and 10 are those candidates), while most other bins do not show such a difference. So, there seems to be evidence suggesting a session difference in some parts of the bin distribution. However, no individual t-test showed a significant session difference at the individual bin level when we applied a Bonferroni adjustment for multiple comparisons (since we are performing ten pairwise comparisons with an initial alpha level of p = .05, the Bonferroni-adjusted significance level is .05/10 = .005), ts(7) < 3.23, ps > .014, Cohen’s ds < 0.18. Thus, we conclude that there is no substantial statistical evidence for a difference in the bottleneck characteristics to process dual tasks at the end of practice (Session 8) and during transfer (Session 9) when the visual task was manipulated.

Discussion

Extensive practice decreased the amount of dual-task costs in a visual and an auditory component task of a dual-task situation tremendously. Compared to the study of Schumacher et al. (2001), who reported an elimination of the dual-task costs, we found small but still significant dual-task costs in the visual (22 ms) and the auditory tasks (42 ms). Interestingly, these particular amounts of the remaining dual-task costs are quite similar to those reported by Tombu and Jolicœur (2004) and in our studies (Strobach, Frensch, Soutschek, et al., 2012; Strobach, Salminen, et al., 2014), who capitalized on the role of the bonus schema for the degree of elimination of dual-task costs in task designs like that of Schumacher et al. In the current study, we used a bonus schema adapted from that of Tombu and Joliceour, which might explain the observation of small dual-task costs after practice in this study. However, we agree that the evaluation of the latent bottleneck model in this experiment might be restricted to a situation in which a reduction of dual-task costs was observed without showing a complete elimination of the dual-task costs. We will return to that issue in the section “General Discussion.”

The findings of the transfer manipulations in the present study are consistent with the predictions of the latent bottleneck model for the practice-related changes in the present task situation. In detail, the assumption of a latent bottleneck predicts that prolonging the duration of the pre-bottleneck and bottleneck stages in Task 1 after practice leads to a similar increase in the dual-task RTs in the two component tasks. This is precisely what we have found when analyzing the increase of the RTs in the visual and auditory tasks from Session 8 to Session 9 in the present experiment. Thus, this data is consistent with the prediction that a prolongation of the duration of the processes before or at the bottleneck stages in Task 1 of the Schumacher et al. (2001) paradigm carries over to the RTs of the second task via the bottleneck. Importantly, this prediction was proved based on the mean RTs on the group level and based on the individual participant data. Especially, the latter finding shows the robustness of the findings across the whole group of participants.

However, dual-task manipulation effects could also result from changes in bottleneck processing when performing two tasks. Three further findings are important, which suggest that such changes have probably not taken place in Experiment 1. First, dual-task costs were still evident in the auditory task at the end of practice. This finding of remaining dual-task costs in the slower task is inconsistent with the assumption of a complete parallel processing of two tasks in the current task situation, which might have resulted from the disappearance of bottleneck processing. The observation of remaining costs is, however, consistent with the predictions that latent bottleneck processing has occurred under the restriction that the presumed bottleneck processes are optimized but not perfectly latent at the end of practice. Second, the analysis of single-task RTs of Task 1 and dual-task RTs of Task 2 provides evidence for unchanged bottleneck processing before and after the introduced manipulation. In both conditions (i.e., before and after manipulation), the presumed bottleneck processing is unchanged and is presumably located at central response selection stages. Again, the findings are exactly what the latent bottleneck model predicts. This also demonstrates that there is no evidence for a change in the location of a potential bottleneck even when a particular processing stage was manipulated. Third, an analysis of the IRI distributions before and after manipulation also revealed no vital evidence for such changes in bottleneck location. Consequently, we conclude (a) there is no evidence for an account assuming that the experimental manipulation had induced a change in bottleneck processing characteristics (i.e., due to the manipulation of the response selection stage in Task 1), and (b) testing for a latent bottleneck by comparing data from the last practice Session 8 with that in a following transfer Session 9 is a valid procedure.

A potential explanation for the propagation of Task 1 RT manipulation effects onto RTs in Task 2 in the present experiment could be that the moderate amount of practice (eight practice sessions) was insufficient to achieve complete dual-task automatization and, thus, would represent a non-optimal condition for testing the dual-task performance after practice. To test the potential impact of the practice amount on the propagation effect of prolonging Task 1 RTs on Task 2 RTs, we conducted Experiment 2 and increased the amount of practice to 12 sessions.

Experiment 2

In Experiment 2, we increased the number of practice sessions from 8 in Experiment 1 to 12. This increase should allow assessing whether a more prolonged practice period would lead to a result pattern in which the increase in processing time in the visual task is not carried over into the RTs of the auditory task. Such an argument might be raised if, assuming that the amount of practice was not sufficient to achieve an elimination of a latent bottleneck in Experiment 1 (Maquestiaux et al., 2008, 2010), full automatization may be necessary for avoiding the carry-over of the RT increases from the shorter visual to the longer auditory component task. Opposed to that, the latent bottleneck model predicts bottleneck processing even after 12 practice sessions, so that an increase in practice should not change the observation of a carry-over of RT increases in Task 1 to Task 2 RTs.

Method

Participants

We tested nine (four female) students of the Humboldt Universität zu Berlin who were paid for participation at a rate of 8 € per session plus performance-based bonuses. The apparatus, component tasks, and procedure were the same as in Experiment 1, except for the fact that participants practiced 12 sessions before the visual task was changed in Session 13.

Results

The data handling for statistical analysis was similar to Experiment 1, except for the fact that we included 12 sessions in the practice analysis here.

Practice Sessions

Visual Task

RTs in the visual task decreased with practice, F(10, 80) = 22.414, p < .001, $η_{p}^{2}$ = .73. As can be seen in Table 2, RTs differed across the different types of trials, F(2, 16) = 12.148, p < .001, $η_{p}^{2}$ = .65. In detail, RTs in single tasks were the smallest (M = 261 ms; SD = 55 ms), followed by those of the mixed single-task trials (M = 272 ms; SD = 55 ms) and of the dual-task trials (M = 283 ms; SD = 74 ms); all differences were significant, ps < .039. A significant interaction of the factors Session and Trial type, F(20, 160) = 4.831, p < .001, $η_{p}^{2}$ = .34, indicates that practice affected RTs in different trial types to a different degree. Practice led to a stronger reduction of RTs in dual-task trials compared to single-task trials across practice. While the difference between RTs in dual-task trials and single-task trials, that is, the dual-task costs, amounts to M = 51 ms (SD = 18 ms) in Session 2, F(1, 8) = 14.002, p = .003, $η_{p}^{2}$ = .68, dual-task costs were eliminated in Session 12 (M = 2 ms; SD = .4 ms), F(1, 8) < 1.

Table 2.

Mean Reaction Times (in ms) and Mean Error Rates (in %, in Brackets) in Experiment 2 (Sessions 1–13).

Tasks	Sessions
Tasks	1	2	3	4	5	6	7	8	9	10	11	12	13
Visual-manual task
Single	315 (1.0)	286 (1.3)	274 (1.7)	264 (1.8)	260 (1.8)	255 (2.3)	251 (3.0)	250 (2.8)	239 (3.0)	260 (3.6)	261 (1.7)	255 (2.5)	361 (4.9)
Mixed		316 (0.9)	298 (0.5)	283 (0.6)	269 (0.5)	266 (1.3)	265 (1.0)	254 (1.1)	247 (1.9)	257 (1.6)	262 (1.9)	253 (1.9)	390 (7.3)
Dual		338 (1.4)	310 (0.5)	295 (0.8)	276 (0.8)	275 (1.0)	277 (0.7)	266 (1.2)	254 (0.6)	261 (1.8)	273 (0.9)	257 (0.2)	420 (4.6)
Auditory-verbal task
Single	545 (5.3)	504 (3.0)	479 (4.1)	434 (2.0)	410 (2.7)	388 (2.6)	379 (3.6)	370 (3.2)	363 (3.7)	356 (2.8)	384 (2.1)	369 (2.9)	363 (1.9)
Mixed		586 (5.6)	541 (4.6)	502 (4.8)	461 (4.3)	431 (5.7)	411 (5.6)	409 (5.8)	392 (7.1)	395 (6.2)	408 (4.2)	385 (6.1)	431 (2.6)
Dual		673 (6.6)	618 (4.4)	551 (3.8)	501 (3.6)	465 (4.0)	443 (5.5)	434 (3.3)	416 (4.0)	414 (4.4)	434 (3.4)	405 (3.2)	540 (7.5)

Note. Single = single-task trials in single-task blocks; Mixed = single-task trials in mixed blocks; Dual = dual-task trials in mixed blocks.

Error analyses revealed a significant effect for Session, F(10, 80) = 4.555, p < .001, $η_{p}^{2}$ = .33, showing that error rates varied during practice, as presented in Table 2. The error rates in single-task trials (M = 2.3%; SD = 0.7%) were significantly higher than in dual-task trials (M = 0.8%; SD = 0.3%) and in mixed single-task trials (M = 1.2%; SD = 0.4%), ps < .010, which specifies the significant effect of Trial type, F(2, 16) = 20.893, p < .001, $η_{p}^{2}$ = .69. We found no interaction of Session and Trial type, F(20, 160) = 1.486, p = .089.

Auditory Task

Participants responded faster in Session 12 (M = 384 ms; SD = 78 ms) than in Session 2 (M = 593 ms; SD = 142 ms), leading to a main effect of Session, F(10, 80) = 33.126, p < .001, $η_{p}^{2}$ = .88 (Table 2). RTs were fastest in single-task trials (M = 403 ms; SD = 88 ms), followed by RTs in mixed single-task trials (M = 445 ms; SD = 110 ms) and in dual-task trials (M = 481 ms; SD = 137 ms), all differences ps < .009. The corresponding effect of Trial type was significant, F(2, 16) = 16.859, p < .001, $η_{p}^{2}$ = .70. Practice affected the RTs in the different types of trials to a different degree, F(20, 160) = 14.211, p < .001, $η_{p}^{2}$ = .68. As can be seen in Table 2, RTs in dual-task trials decreased more strongly across sessions than RTs in single-task trials; consequently, the amount of dual-task costs (M = 172 ms; SD = 43 ms) in Session 2, F(1, 8) = 43.553, p < .001, $η_{p}^{2}$ = .89, was reduced to M = 36 ms (SD = 10 ms) in Session 12, F(1, 8) = 5.365, p = .040, $η_{p}^{2}$ = .39.

The error rates of the auditory task are presented in Table 2. The analysis revealed that error rates were not affected by practice, F(10, 80) = 1.397, p = .092. A significant effect of Trial type, F(2, 16) = 5.857, p = .041, $η_{p}^{2}$ = .41, reflects the fact that the error rates in single-task trials (M = 2.9%; SD = 0.8%) were smaller than in mixed single-task trials (M = 5.2%; SD = 1.4%), p = .029; error rates in dual-task trials (M = 4.1%; SD = 1.1%) did not differ significantly from the error rates in the other trial types, ps > .17. The interaction of Session and Trial type, F(20, 160) = 1.859, p = .036, $η_{p}^{2}$ = .11, indicates a reduction of error rates from Session 2 to Session 12 under dual-task conditions, F(1, 8) = 5.652, p = .024, $η_{p}^{2}$ = .40, but no such reduction under conditions of mixed single-task and single-task trials, both Fs < 1.

Effects of Task 1 Prolongation

Group Level Analysis

Next, we tested the predictions of the latent bottleneck model about the effects of the transfer manipulation in the visual task on dual-task performance in the two component tasks. We conducted separate repeated measures ANOVAs with the factors Session (Session 12 vs. Session 13) and Task (visual task vs. auditory task) on group mean RTs and error rates in dual-task trials. We considered only trials with a response order of visual then auditory task, which led to a removal of 3.4% and 23.1% of trials in Sessions 12 and 13, respectively. Note that more participants in Experiment 2 responded to the auditory task first, particularly during the transfer session, compared to 9.4% in Experiment 1. This may be because the auditory task was more automatized than the changed visual task in Experiment 2 than in Experiment 1 due to the larger amount of practice.

The difficulty manipulation of the perception and the response selection stage led to an increase of the dual-task RTs in Session 13 compared to Session 12 by 145 ms, F(1, 8) = 76.282, p < .001, $η_{p}^{2}$ = .92, in the changed visual task (Figure 5). The increase of the RTs from Session 12 to Session 13 in the unchanged auditory task amounted to 152 ms, F(1, 8) = 25.126, p < .001, $η_{p}^{2}$ = .72. The amount of the RT increase was not different between the two tasks, F < 1, BF₀₁ = 4.918. This result of the group-level analysis is consistent with the prediction of the latent bottleneck model. A prolongation of the RTs in the faster task after extensive practice should carry-over to the RTs of the slower task via the involved bottleneck.

The findings of the error rate analysis paralleled those of the RT analysis. Error rates increased in the visual task by 4.5%, F(1, 8) = 19.136, p = .006, $η_{p}^{2}$ = .67, and in the auditory task by 3.8%, F (1, 8) = 5.988, p = .042, $η_{p}^{2}$ = .40, in Session 13 compared to Session 12. The amount of the increase was fairly the same across both tasks, as is reflected by the non-significant interaction of Session and Task on the error rates, F < 1, BF₀₁ = 4.112.

Individual Subject Analysis

Subsequently, we tested whether the predictions of the latent bottleneck model hold for mean RT data only or for the RTs of the individual participants as well. For that purpose, we plotted the individual values of the dual-task RT increases from Session 12 to Session 13 in the visual and the auditory tasks for every single participant in Figure 6. Participants who perform according to the predictions of the latent bottleneck model should be represented by data points that are distributed along a regression line of x = y; this is so because data points that are located on this line (or at least in the vicinity of it) are data points where each ms prolongation of the visual task RTs is completely carried over into the RTs of the auditory task. By contrast, data points near the horizontal axis and below the x = y line reflect participants who do not show a complete carry-over of the RT increase in Task 1 into the RTs in Task 2. Data points near the vertical y-axis and above the x = y line reflect participants showing a larger increase in the RTs in the unchanged auditory task compared to the RT changes in the visual task. As can be seen in Figure 6, participants are mostly distributed around a line of x = y. Similar to Experiment 1, we conducted statistical testing to support this qualitative statement. The regression line of the distribution of the data points has the function of y = 1.26*x − 31.20. Again, we tested whether the increase of the regression line (b = 1.26) is similar to the increase of the x = y line (b = 1) and performed a dependent t-test in which we set the alpha level to .25 for large effects of d = .8 (resulting in a test power of 87%). The result of this t-test showed that the increase of the regression line is not significantly different from 1, t(7) = .519, p = .620. A subsequent correlation analysis showed a correlation coefficient of r = .692, p = .039, which shows that the assumption of a linear relation describes the current distribution of the data with sufficient strength (R² = .48). Together, this shows that the predictions of the latent bottleneck model also hold on an individual level for all participants.

Test of Dual-Task Processing Bottleneck Characteristics

Similar to Experiment 1, the aim of the present section was an investigation of the characteristics of a (latent) bottleneck and its location within the component tasks when performing two tasks at the end of practice (i.e., Session 12, without manipulations of the response selection stage) and during the transfer session (i.e., Session 13, with the manipulated response selection stage). To investigate these bottleneck characteristics at the end of practice and after task manipulation, we investigated single-task performance in the manipulated visual task and dual-task performance in the non-manipulated auditory task in Sessions 12 and 13. In fact, we investigated whether the manipulation effect in the visual single-task is identical to that effect in the auditory dual tasks, which is a rigorous test of the latent bottleneck assumptions. If so, then in the current data set there is no support for a change in the characteristics of bottleneck processing at the end of practice and during the transfer session. In contrast, if we were to find evidence for a difference in the effects, then this would represent support for the assumption of changed processing characteristics before and during transfer. In other words, an interaction of Trial type (single tasks [visual task] vs. dual tasks [auditory task]) and Session (Session 12 vs. Session 13) in a repeated measures ANOVA is consistent with the assumption of a change in characteristics, while a lacking interaction is not. An analysis of the RTs provided no evidence for such a change because we did not observe a significant interaction of both factors, F(1, 8) = 1.958, p = .230, BF₀₁ = 2.729 (Table 2). This shows that the current data set does not provide evidence in favor of a change in bottleneck characteristics at the end of practice and in the transfer session, and the results are consistent with the predictions of a latent bottleneck model.

We also analyzed mean IRI distributions at the end of practice and during transfer. We reasoned that if these distributions largely overlap in Sessions 12 and 13, then participants demonstrate comparable bottleneck processing characteristics when performing the two tasks, while differences between these distributions would contradict the assumption of comparable characteristics. To generate IRI distributions, we separately vincentized all correct dual-task trials for each participant in Sessions 12 and 13 in 10 bins. The resulting mean IRI distributions are illustrated in Figure 7. We analyzed the mean of the IRIs in a repeated measures ANOVA including the within-subjects factors Session (Session 12 vs. Session 13) and Bin (Bin 1–10); we were particularly interested in the main effect of and interaction with Session. The main effect of Session was non-significant, F(1, 8) < 1, demonstrating no evidence for a general IRI difference between the end of practice and the transfer session. The interaction of Session and Bin was significant, F(9, 72) = 7.351, p < .001, $η_{p}^{2}$ = .45, suggesting different effects of Session depending on the individual bins. As in Experiment 1, when inspecting Figure 7, this interaction seems to stem from a few bins providing signs of a numerical difference between Sessions 8 and 9 (in particular, Bins 9 and 10 might be those candidate bins), while other bins do not show such a difference. So, there may be selective differences, but only in two distribution bins. In fact, however, none of the pairwise t-tests showed a significant session difference in the individual bins when we applied a Bonferroni adjustment for multiple comparisons, ts(8) < 3.18, ps > .013, Cohen’s ds < 0.17 (since we are performing 10 pairwise comparisons with an initial alpha level of p = .05, the Bonferroni-adjusted significance level is .05/10 = .005). Thus, there is no substantial statistical evidence for a difference in the bottleneck processing when performing dual tasks at the end of practice (Session 12) and during transfer (Session 13) when the visual task was manipulated.

Discussion

In Experiment 2, we replicated the observation of a strong decrease in the dual-task costs after extensive practice, as shown in Schumacher et al. (2001, Experiment 1) and others. Noteworthy is that the error rates in Experiment 2 were lower than in Experiment 1, which might be due to a different sample of participants and longer practice in the present experiment. Participants performed 12 instead of only 8 practice sessions, and we tested if this increased amount of practice has eliminated the observation of findings pointing to a latent bottleneck in the current dual-task situation.

The assumption of a latent bottleneck predicts that prolonging the duration of the bottleneck stage in Task 1 after practice leads to a similar increase of the dual-task RTs in the two component tasks. This is precisely what we have found when analyzing the increase of the dual-task RTs in the visual and the auditory tasks from Session 12 to Session 13 in the present experiment. Thus, this observation is consistent with the prediction that a prolongation of the processing duration of processes at the bottleneck stage in Task 1 carries over to the RTs of the second task via the bottleneck. Importantly, this prediction was proved on the basis of the mean RTs and on the basis of the data of the individual participants. Especially, the latter finding shows the robustness of the findings across the whole group of participants.

Similarly to the results in Experiment 1, we again obtained data that are inconsistent with the assumption that the experimental manipulation located at the presumed bottleneck stage (i.e., the stimulus-response translation) has influenced the characteristics of the bottleneck processing in the current dual-task situation. First, dual-task costs were still evident in the auditory task at the end of practice. Second, RT changes in the visual single tasks were similar to these changes in auditory dual tasks. Third, investigating the amount of task processing overlap at the end of practice and under the condition of the Task 1 manipulation in the transfer session revealed no substantial statistical differences for the assumption across all vincentized IRI bins. Consequently, we conclude (a) there is no evidence justifying the assumption that the difficulty manipulation in Task 1 in the transfer Session 13 has changed the bottleneck processing characteristics of participants after extensive practice of 12 sessions; (b) testing the occurrence of a latent bottleneck by comparing data from the last practice Session 12 in a following transfer Session 13 is a valid procedure; and (c) Experiment 2’s results are largely equivalent to the data of Experiment 1, encompassing only eight practice sessions. Thus, both experiments, encompassing either 8 or 12 practice sessions, produced data that are consistent with the predictions of the latent bottleneck model in the current task situation.

Experiment 3

In Experiment 3, we conducted a manipulation of the presumed bottleneck stage in Task 2 and tested its effects on the RTs in this manipulated task and the non-manipulated Task 1. We administered a transfer session (Session 9) in which the duration of the presumed bottleneck stage in Task 2 was prolonged compared to the task situation in the eighth practice session. To that end, we instructed participants on an incompatible mapping between the tone stimuli and verbal responses of the auditory Task 1 in the transfer Session 9. Unlike Task 2, Task 1 remained unchanged during practice and transfer. For such a situation, the latent bottleneck model predicts an increase of the RTs from Session 8 to Session 9 only in Task 2 but not in Task 1; this increase in Task 2 should be identical for the auditory task performed either in single-task or in dual-task situations.

Methods

We tested 8 students (4 female; 18–35 years) of the Humboldt Universität zu Berlin. Apparatus, component tasks, and procedure were identical to Experiment 1, with the exception that the auditory task but not the visual task was manipulated during transfer Session 9 after eight practice sessions. In this transfer session, the mapping of the auditory stimuli to the vocal responses was changed, which corresponds to a manipulation of the difficulty of the response selection stage of the auditory task. Now, participants responded to the low-frequency tone by saying “2,” to the medium-frequency tone by saying “3,” and by saying “1” to the high-frequency tone.

Results

Data handling of the practice and transfer sessions in the present experiment was similar to that handling in Experiment 1.

Practice Sessions

Visual Task

Practice substantially reduced the RTs from Session 2 to Session 8, F(6, 42) = 46.131, p < .001, $η_{p}^{2}$ = .87; see Table 3. The main effect of Trial type, F(2, 14) = 10.923, p = .013, $η_{p}^{2}$ = .61, indicates a difference between RTs in dual-task, mixed single-task, and single-task trials; in detail, RTs were slower in dual-task trials (M = 278 ms; SD = 56 ms) when compared to mixed single-task trials (M = 258; SD = 59 ms), p = .044, and compared to single-task trials (M = 252 ms; SD = 55 ms), p = .037. A significant interaction of the factors Session and Trial type indicates that RTs in the different trial types decreased to a different degree across the practice sessions, F(12, 84) = 13.323, p < .001, $η_{p}^{2}$ = .66. RTs in dual-task trials decreased more strongly across sessions than single-task RTs; consequently, while the difference in RTs in dual-task trials minus RTs in single-task trials amounts to M = 79 ms (SD = 22 ms) in Session 2, F(1, 7) = 17.560, p = .007, $η_{p}^{2}$ = .72, the difference amounts to a non-significant M = 9 ms (SD = 2 ms) in Session 8, F(1, 7) = 3.564, p = .101. This indicates the disappearance of the dual-task RT costs after practice.

Table 3.

Mean Reaction Times and Mean Error Rates (in %, in Brackets) in Experiment 3 (Sessions 1–9).

Tasks	Sessions
Tasks	1	2	3	4	5	6	7	8	9
Visual-manual task
Single	293 (1.2)	272 (2.4)	260 (3.6)	256 (3.6)	252 (4.0)	247 (3.4)	244 (4.7)	240 (5.1)	238 (4.7)
Mixed		306 (1.1)	273 (0.9)	256 (1.5)	250 (1.9)	245 (3.0)	240 (3.1)	238 (2.7)	245 (0.8)
Dual		351 (5.0)	299 (2.5)	272 (4.0)	267 (2.5)	260 (2.8)	253 (3.6)	249 (3.7)	271 (2.9)
Auditory-verbal task
Single	623 (11.5)	517 (5.2)	467 (6.8)	420 (5.2)	407 (6.4)	372 (6.1)	344 (5.6)	332 (6.7)	452 (10.9)
Mixed		622 (8.1)	520 (6.9)	477 (6.4)	446 (6.1)	400 (6.3)	374 (6.1)	359 (8.4)	481 (13.6)
Dual		703 (10.7)	586 (9.3)	528 (8.3)	482 (9.4)	431 (8.3)	400 (7.7)	380 (7.0)	525 (13.7)

Note. Single = single-task trials in single-task blocks; Mixed = single-task trials in mixed blocks; Dual = dual-task trials in mixed blocks.

Practice affected the error rates, as indicated by the main effect of Session, F(6, 42) = 2.538, p = .040, $η_{p}^{2}$ = .27. Mean error rates, as presented in Table 3, increased from Session 2 (M = 2.9%; SD = 0.8%) to Session 8 (M = 3.9%; SD = 0.9%; see also Hazeltine et al., 2002; Schumacher et al., 2001; Strobach, Liepelt, et al., 2012). Error rates differed between the trial types, F(2, 14) = 6.731, p = .014, $η_{p}^{2}$ = .49. Participants made more errors during the processing of dual-task trials (M = 3.9%; SD = 1.0%) compared to mixed single-task trials (M = 2.1%; SD = 0.5%), p = .023, but differences in error rates between dual-task trials and single-task trials (M = 3.5%; SD = 0.8%) as well as between mixed single-task trials and single-task trials were not significant, smallest p = .063. Further, we found a significant interaction of Session and Trial type, F(12, 84) = 2.644, p < .01, $η_{p}^{2}$ = .27: while there was no significant difference between these rates in dual-task and single-task trials in Session 2, F(1, 7) = 3.118, p = .122, and Session 8, F(1, 7) = 3.330, p = .112, the increased error rates in dual-task compared with mixed single-task trials in Session 2, F(1, 7) = 7.252, p = .026, $η_{p}^{2}$ = .51, were reduced in Session 8, F(1, 7) = 2.930, p = .133.

Auditory Task

Participants responded generally faster with increasing amounts of practice, F(6, 42) = 58.504, p < .001, $η_{p}^{2}$ = .89 (Table 3). The RTs were slower in dual-task trials (M = 501 ms; SD = 124 ms) than in mixed single-task trials (M = 457 ms; SD = 114 ms) and in single-task trials (M = 409 ms; SD = 99 ms), all ps < .001, which is reflected by the main effect of Trial type, F(2, 14) = 58.288, p < .001, $η_{p}^{2}$ = .89. Again, there was a significant interaction of Session and Trial type, F(12, 84) = 16.183, p < .001, $η_{p}^{2}$ = .70. This indicates that practice reduced RTs more strongly in dual-task than in single-task trials; in detail, the difference between RTs in dual-task and single-task trials (i.e., dual-task costs) decreased from M = 186 ms (SD = 44 ms) in Session 2 to M = 47 ms (SD = 9 ms) in Session 8; in both cases, however, RTs were significantly larger in dual-task compared to single-task trials, F(1, 7) = 113.963, p < .001, $η_{p}^{2}$ = .94, and, F(1, 7) = 18.281, p = .012, $η_{p}^{2}$ = .72, for Sessions 2 and 8, respectively. Thus, practice reduced the large amount of dual-task costs at the beginning to a small, though significant, amount at the end of the practice sessions.

For error rates, we found a significant effect of Trial type, F(2, 14) = 11.412, p = .008, $η_{p}^{2}$ = .62, reflecting an increased error rate in dual-task (M = 8.7%; SD = 2.1%) compared to mixed single-task (M = 7.0%; SD = 1.7%) and single-task trials (M = 6.1%; SD = 1.5%), all ps < .009 (Table 3). However, the difference between the error rates tends to disappear with an increasing amount of practice, F(12, 84) = 1.785, p = .069, $η_{p}^{2}$ = .20. This tendency is due to a reduction of the error rates in the dual-task condition from Session 2 to Session 8, F(1, 7) = 5.476, p = .051, $η_{p}^{2}$ = .44, while the error rates remain rather constant for single-task and mixed single-task trials across these sessions, F(1, 7) = 1.106, p = .338, and F < 1, respectively. The general effect of Session was non-significant, F(1, 7) = 1.529, p = .197.

Effects of Task 2 Prolongation

Group-Level Analyses

First, we tested the predictions of the latent bottleneck model about the effects of the transfer manipulation in the auditory task on dual-task performance on the group level. We conducted separate repeated measures ANOVAs with the within-subjects factors Session (Session 8 vs. Session 9) and Task (visual task vs. auditory task) on mean RTs and error rates in the dual-task trials. Again, we selected only those trials in which participants responded on the visual task earlier than on the auditory task, which required elimination of 4.5% and 2.8% of the trials in Sessions 8 and 9, respectively.

The increased difficulty of the response selection stage in the auditory task in Session 9 compared to Session 8 led to different effects on the RTs in the unchanged visual and the changed auditory tasks, as is illustrated in Figure 8. While the manipulation led to a significant increase of the dual-task RTs in the auditory task by 145 ms, F(1,7) = 41.376, p < .001, $η_{p}^{2}$ = .86, it did not cause a significant increase of the RTs in the unchanged visual task (23 ms), F(1, 7) = 4.509, p = .072. The interaction of Session and Task was significant, F(1, 7) = 46.357, p < .001, $η_{p}^{2}$ = .87. Although the effect of Task 2 manipulation on Task 1 was non-significant, there was a minimal RT increase. This increase may be explained by increased demands of stimulus-response mapping rules on working memory when new rules were included after practice of old rules (Hartley & Little, 1999; Schubert & Strobach, 2018; Schubert et al., 2024). Such demands affect processes located at the beginning of dual-task trials and thus before the start of Task 1. So, Task 1 is probably influenced by processing task instantiation in working memory when Task 2 mapping rules are manipulated.

The analysis of the error rates paralleled those of the RT data, as can be seen in Table 3. We found a selective increase of the error rates from Session 8 of 7.0% to Session 9 of 13.8% in the changed auditory task, F(1, 7) = 8.547, p = .029, $η_{p}^{2}$ = .55, but not in the unchanged visual task (from 3.7% to 2.9%), F(1, 7) = 2.930, p = .128. The resulting interaction of Session and Task is also significant, F(1, 7) = 8.551, p = .029, $η_{p}^{2}$ = .55, which clearly demonstrates different change patterns and is again consistent with the prediction of the latent bottleneck model.

Individual Subject Analysis

Subsequently, we tested whether the predictions of the latent bottleneck model hold for mean RT data only or for the RTs of the individual participants as well. For that purpose, we plotted the individual values of RT increases from Session 8 to Session 9 in the visual and the auditory tasks for every single participant in Figure 9; the x-axis of this figure depicts the amount of the RT increase in the visual task, while the y-axis depicts the RT increase in the auditory task. Data points that are distributed near the vertical y-axis and above the x = y line reflect participants who show a considerable increase in the RTs in the changed auditory task and only a small RT increase in the unchanged visual task. Figure 9 shows that this is the case for the individual data points of the participants in Experiment 3, which is supported by corresponding statistical testing. Thus, the regression line of the distribution of the data points had the function y = 4.30*x + 72.36. A subsequent dependent t-test with an alpha level set to .25 for large effects of d = 0.8 (power of 87%) showed that the increase of the regression line was significantly different from 1, t(6) = 3.574, p = .048. This is consistent with the prediction of the latent bottleneck model that the manipulation of the response selection in Task 2 primarily leads to an RT increase in the auditory task (Task 2) but not in the visual task (Task 1), which causes the empirical data points to not follow the x = y line but to be closely distributed in the direction of the vertical y-axis. The subsequent correlation analysis between the individual x and y values showed that the relation between both variables can be described sufficiently well (R² = .54) with the assumption of a linear relation, r = .732, p = .058 (note that the correlation might be only marginally significant because of the low number of participants). This shows, on an individual level, that this data basically confirms the prediction of the latent bottleneck model.

Test of Dual-Task Processing Bottleneck Characteristics

To investigate bottleneck characteristics and a potential bottleneck location at the end of practice and after difficulty manipulation, we investigated the RT increases in the single- and dual-task performance of the auditory task in Sessions 8 and 9. We focused on the auditory task because it is the longer task (Task 2), and its data are most diagnostic for bottleneck identification. The latent bottleneck model predicts that the increase in the response selection difficulty in Session 9 compared to Session 8 should lead to an increase in the RTs of Task 2, and the amount of that increase should be similar to the RT increase if that task was performed as a single-task. If we found evidence for this pattern, then the current data set would be consistent with the assumption of a similar location of the manipulated response selection stage related to the location of a processing bottleneck in the two sessions. Consequently, the findings of a significant interaction of Trial type (single tasks vs. dual tasks) and Session (Session 8 vs. Session 9) in a repeated measures ANOVA would be evidence against the assumption of similar and unchanged bottleneck processing, while a lack of interaction would not. The analysis of RTs provided no evidence for a change in bottleneck processing between the practice and transfer sessions because we did not find a significant interaction of both factors, F(1, 7) = 3.218, p = .119. Furthermore, the lack of interaction in the error data supports the assumption of a lack of a location change, F(1, 7) < 1. Thus, the current data set does not justify an assumption according to which the bottleneck processing characteristics differed between dual-task processing in the final practice session and the transfer session. This conclusion is consistent with assumptions of a latent bottleneck model, emphasizing the validity of our method to investigate dual-task processing architectures in the present study.

Similar to the previous experiments, we analyzed the mean of vincentized IRI distributions at the end of practice and during transfer. In contrast to Experiments 1 and 2, however, we expected a clear difference between these conditions: IRIs in Session 9 (transfer) should clearly increase those of Session 8 (end of practice) since processes in the longer, in contrast to the shorter, of the two tasks are prolonged (which is evidenced by mean RT analyses). In Figure 10, this increase is illustrated in the form of a shift of the IRI distribution from Session 8 (left distribution) to Session 9 (right distribution). The analysis of the IRI data in a repeated measures ANOVA included the within-subjects factors Session (Session 8 vs. Session 9) and Bin (Bins 1–10); we were particularly interested in the main effect of and interaction with Session. The main effect of Session was significant, F(1, 7) = 44.249, p < .001, $η_{p}^{2}$ = .86, reflecting evidence for a general IRI effect between the end of practice and the transfer session. The interaction of Session and Bin was also significant, F(9, 63) = 34.606, p < .001, $η_{p}^{2}$ = .83 and reflects different effects of Session at the individual bins. Importantly, however, IRIs in Session 9 were significantly increased at all bins in contrast to the Session 8 IRIs when we applied a Bonferroni adjustment for multiple comparisons (since we are performing ten pairwise comparisons with an initial alpha level of p = .05, the Bonferroni-adjusted significance level is .05/10 = .005), ts(7) > 4.27, ps < .004, Cohen’s ds > 0.35, but increased with increasing bin number (Figure 10). This IRI data is basically consistent with the predictions of the latent bottleneck model when we prolong processes in the longer Task 2.

Discussion

Similar to the previous experiments, extensive practice decreased but did not eliminate the amount of dual-task RT costs in a visual and an auditory component task of a dual-task situation (see also section “General Discussion”). Most importantly, we found a selective increase of dual-task RTs in the two component tasks after introducing a manipulation affecting the duration of the response selection stage in Task 2. This particular manipulation led to a strong increase in RTs in Task 2 and to a non-significant prolongation of Task 1 RTs. This finding is consistent with the predictions of the latent bottleneck model. According to this model’s assumption, a selective prolongation of a bottleneck stage in Task 2 after practice should lead to a prolongation of the RTs in Task 2 but not of the RTs in Task 1 in the transfer phase. A detailed analysis of the data of the individual participants showed that the predictions of the latent bottleneck model hold for the individual participants and not only for the mean performance values.

There are two additional observations in this experiment’s data pattern that render it unlikely that the dual-task manipulation effects result from performing two tasks without bottleneck processing. First, similar to the previous experiments, dual-task costs were still evident in the auditory task at the end of practice. Second, the analysis of single-task and dual-task RTs of Task 2 provides evidence for a similar bottleneck processing before and after the introduced manipulation in Task 2. In both situations (i.e., before and after manipulation), the presumed bottleneck processing is presumably located at central response selection stages. These findings are exactly what the latent bottleneck model predicts. That is, (a) there is no evidence for an induced manipulation-based change in bottleneck processing (i.e., induced by the manipulation of the response selection stage in Task 2), and (b) testing a latent bottleneck of a last practice Session 8 in a following transfer Session 9 is a valid procedure. This procedure produces data that are consistent with predictions of the latent bottleneck model of practice dual-task performance.

General Discussion

In three experiments, we found a tremendous reduction of the dual-task costs when participants practiced a visual and an auditory choice RT task for several sessions in dual-task and single-task trials. This observation replicates the well-known findings of Schumacher et al. (2001, Experiment 1; for similar findings with this paradigm, see also Anderson et al., 2005; Göthe et al., 2016; Hartley et al., 2011; Hazeltine et al., 2002; Israel & Cohen, 2011; Liepelt, Strobach, et al., 2011; Schubert et al., 2017; Strobach & Huestegge, 2021; Strobach & Schubert, 2017b; Strobach, Frensch, Müller, et al., 2012a, 2012b; Strobach, Frensch, Soutschek, et al., 2012; Strobach et al., 2015; Strobach, Salminen, et al., 2014). To explain this tremendous reduction of dual-task costs after practice, we test predictions of the latent bottleneck model.

Selective Prolongations of Processing Times: Evidence for a Latent Bottleneck!

To test the assumptions of a latent bottleneck model, we separately manipulated the duration of central response selection stages of the two component tasks and analyzed the resulting effects on the RTs in subsequent transfer sessions after practice. The effects of these manipulations show selective prolongations of the processing times in the two-component tasks. Moreover, the specific pattern of these prolongations depends on the location of the manipulated processing stage relative to a presumed latent bottleneck. In detail, the findings of Experiments 1 and 2 indicate that when prolonging the processing time of processing stages that are located at or before the assumed latent bottleneck in the shorter of the two component tasks (Task 1), then this leads to an increase in the RT in that task and to an equal increase in the RT in Task 2. Further, the findings of Experiment 3 showed that when increasing the processing time of a Task 2 stage that is located at the presumed bottleneck, this leads to a significant increase of the RT in that changed task, that is, Task 2, but not in the unchanged Task 1.

These findings were confirmed when analyzing mean RTs and also when analyzing the data of the individual participants. Thus, in Experiments 1 and 2, the individual data points relating to RT1 and RT2 (and the amount of increase in the corresponding RTs from practice to transfer) are located near a line in Figures 3 and 6, at which every millisecond of prolongation in Task 1 is propagated into RT2. Furthermore, in Experiment 3, all RT1-RT2 data points of the individuals are located along the vertical y-axis and near the zero point at the x-axis.

The observed selective changes of the processing times after practice are precisely predicted by a latent bottleneck model and its assumptions of a processing architecture in the dual-task paradigm in Schumacher et al. (2001, Experiment 1). According to that model, after extensive practice, the bottleneck stages in the two-component tasks are scheduled in a non-overlapping fashion, with the perception and response selection processes of the visual task processed before the response selection of the auditory task. Because of that architecture, an increase in Task 1 (visual task) processing time at pre- and bottleneck stages should carry over into the processing time of Task 2 (auditory task), which explains the equal RT effects after the transfer manipulations in Experiments 1 and 2. Furthermore, the model predicts that an increase in the processing time at the bottleneck stage in Task 2 should not affect the processing time of the other task in the transfer session, as was observed in Experiment 3. Thus, these findings show that the latent bottleneck model represents a valid explanation of the current practice effects.

The specific effect pattern of the selective RT prolongations in Experiments 1 to 3 allows excluding an alternative assumption about the source of the observed RT increases in the transfer session, namely that an unspecific difficulty increase has caused the particular transfer effects in the current dual-task situation (Duncan, 1979; Kahneman, 1973). While an unspecific difficulty assumption might, in theory, explain the findings of Experiments 1 and 2, in which the increase of the difficulty in one task led to an increase of the processing time in the other task, it cannot explain the findings of Experiment 3. In this experiment, the RT increase of the difficulty manipulation in one task did not lead to a significant increase in the processing time in the other task. Whereas the observed effect pattern in the transfer sessions is not consistent with the unspecific difficulty assumption, it is precisely predicted by the assumption of a latent bottleneck in the current dual-task practice situation.

One could argue that the pure response selection manipulation in the auditory task of Experiment 3 was somewhat different from the difficulty manipulation of the visual task in Experiments 1 and 2, including a change of the perceptual and the response selection stages of the visual task. The more substantial change of the task in Experiments 1 and 2 could have, in theory, induced a larger difficulty of the manipulation than that in Experiment 3, which might explain the different effects of the transfer manipulation between experiments. However, we especially aimed to selectively manipulate only the response selection stage in Experiment 3 in order to specifically test the relevant latent-bottleneck hypothesis that a change of the bottleneck stage in Task 2 should not affect the RTs in Task 1 but the RTs in Task 2. In addition, an important further aspect of the empirical data renders the alternative argumentation of a confound by the manipulation type rather unlikely. Namely, the current findings show that the difficulty manipulation of the visual task in Experiment 2 (after prolonged practice) and of the auditory task in Experiment 3 have led to roughly similar increases of the RTs in the manipulated tasks of the transfer sessions, that is, to about 135 and 132 ms collapsed for the dual-task and single-task trials, respectively. These very similar increases in the empirical data are consistent with the assumption that the difficulty manipulation in the visual task after prolonged practice is comparable with the manipulation in the auditory task; please note that the increase in Experiment 1 amounts to 148 ms. Therefore, we do not believe that differences in the type of manipulation across Experiments 1/2 versus 3 would explain the current effect pattern, but the specific location of the manipulated processing stage and the presumed task scheduling according to a latent bottleneck.

The present findings are consistent with the ACT-R model of Anderson et al. (2005), which allows for a simulation of perfect time-sharing effects similar to those reported by Schumacher et al. (2001) and Hazeltine et al. (2002). As core assumptions, this model proposes perceptual-motor modules, including the cognitive parts of the response selection stage, which are simulated with a production-based model approach. While some perceptual-motor modules may run in parallel, cognitive modules may run only serially in a dual-task situation. According to the model, long processing times are assumed for the operations of the auditory module (equivalent to the P stage in Task 2 in Figure 1A) because of the arbitrary assignment of the different tone frequencies to their corresponding perceptual categories. The time for preparing the visual module, encompassing the encoding of the visual stimulus, selecting, and initiating the manual key response (equivalent to the P and RS stages in Task 1 in Figure 1A), fits well in the time duration of the auditory module. As a result, this prevents any delay for the start of the cognitive module in the auditory task. However, while the work of Anderson et al. (2005) provides a formalized (production-based) model for a latent-bottleneck scheduling of the response selection processes in two tasks, the current data set provides the corresponding empirical evidence for that assumption for the case of a dual-task situation similar to that of Schumacher et al. (2001).

Selective Prolongations of Processing Time: Evidence for Parallel Processing Models?

Schumacher et al. (2001) proposed that their finding of a practice-related elimination of dual-task costs is suggestive of an alternative to the RSB assumption, according to which no capacity limitation exists at the response selection stage; such an interpretation was also presented by other practice studies (Maquestiaux et al., 2008, 2010; Oberauer & Bialkova, 2011; Oberauer & Kliegl, 2004) and non-practice studies (Lyphout-Spitz et al., 2022, 2024; Maquestiaux et al., 2020). According to that alternative, processing delays in dual-task situations may be caused by a strategic postponement of central processes (i.e., not caused by capacity limitation) or by interference between overlapping peripheral input (i.e., perceptual) and output (i.e., motor) systems (Meyer & Kieras, 1997). Because interference at peripheral systems was prevented in the task situation of Schumacher et al., the authors concluded that the two task streams, including the response selection stages, were processed completely in parallel at the end of practice; this basic parallel model of dual-task processing allows the participants to perform the two tasks in a dual-task situation without costs. Thus, presumed bottleneck stages in dual tasks are not structural and unavoidable phenomena, but they are strategic. In this case, two tasks can be processed sequentially or in parallel; this latter assumption is not consistent with the RSB assumption, suggesting strict sequential processing of bottleneck stages. In summary, Schumacher et al. and others interpreted their findings as evidence for a strategic bottleneck model including strategic inclusions of (central) processing postponement. An important issue concerns the question of to which the selective changes of the processing times during the transfer sessions of Experiments 1 to 3 challenge views assuming parallel processing of the two tasks during dual-task processing. Different versions of parallel models have to be discussed here.

According to a basic parallel model, practice has caused the two tasks to be processed completely in parallel after practice because there is no capacity limitation at the response selection stage anymore. One mechanism for realizing that parallel processing might be automatization, which, according to several authors, reflects the transformation of a process from a controlled to an automatic mode (Schneider & Shiffrin, 1977). Many authors consider a process or a task as automatic if it can be performed simultaneously with another process without any processing detriments; this is the capacity criterion (Hasher & Zacks, 1979; Neumann, 1984, 2016; Schneider & Shiffrin, 1977).¹ For the present experiments, such a criterion of automaticity would require that the manipulation of the processing time in one of the component tasks after practice should not affect the processing times of the other task during the transfer session. According to that criterion, the findings of Experiment 3 would be largely consistent with a basic parallel model because in this experiment, the prolongation of one task did not affect the processing times in the other task. However, the results of Experiments 1 and 2 cannot be reconciled with the basic parallel model. In particular, the findings of these experiments showed an equal increase in the RTs in Task 2 after we prolonged the processing time in Task 1, which is not consistent with the assumption that the processes can operate in parallel. Thus, a basic model of parallel processing assuming automatization of the two component tasks does not provide a plausible explanation for the whole data pattern found in the present study. We will come back to a further elaborated automatization model version proposing selective automatization of only one of the two task streams in a later section.

Another way to reconcile the present data with the assumption of parallel response selection processes after practice may be to assume that the transfer manipulations have induced a serial task scheduling strategy only after practice. This would be in accord with the assumptions of the executive-process interactive control architecture of Meyer and Kieras (1997), who attribute a serial ordering of the response selection processes in dual tasks more to a strategic than to a structural RSB. According to these authors, serial processing strategies are promoted, especially in task situations in which the stimuli for the two tasks are presented with short intervals between them and participants are instructed to respond to the stimuli in order of their occurrence. In addition, the authors assume that a serial strategy is promoted under conditions of low practice, under conditions of a lack of incentives to perform the tasks at their performance limits, or in situations involving peripheral interference (Meyer & Kieras, 1999). Although the present task situation avoided such task characteristics, one might assume that a change in the response selection difficulty as applied in the transfer session of Experiments 1 and 2 led participants to reinterpret the task situation as a new dual-task situation. As a consequence, participants may, in theory, have (re)instated a serial processing strategy (Meyer & Kieras, 1997).

Although we agree that a strategy view can explain part of the present findings, we do not believe that this view can explain the present data as a sole account. If the change in difficulty of one component task, especially by manipulating the response selection difficulty, would be identical to a change of the task representation and of the strategy, then we would expect the same pattern of a strategy change across all experiments with comparable difficulty manipulations. For example, consider the particular case of Experiment 3; in this experiment, we manipulated the difficulty of the response selection stage of Task 2 only. However, we obtained specific prolongations of the RTs only for that task. While the latent bottleneck model precisely predicts the findings in Experiments 1 and 2, we do not see any opportunity a priori to predict the current pattern of selective RT changes based solely on a strategy view (Meyer & Kieras, 1997).

Furthermore, tests on changes in bottleneck processing characteristics could be considered as changes in dual-task processing strategies after practice. That is, if there were changes in these characteristics, then this would be consistent with the assumption that changes in the strategies to schedule the two tasks had occurred. However, the current tests on changes of bottleneck processing characteristics and thus processing strategies provided no evidence for such a strategy change, even after long-lasting practice (12 sessions) in Experiment 2 or shorter practice in Experiment 1. That is, we investigated the location of sources for remaining dual-task costs in Task 2 at the end of practice and during transfer. This investigation produced data consistent with the assumption of similar characteristics of processing bottlenecks (presumably at the central response selection stage) in both conditions, i.e., end of practice and transfer. Furthermore, analyses of the overlap of both tasks demonstrated similar vincentized distributions. In summary, these data reveal no evidence for a key assumption for the strategy (change) view.

In a different dual-task practice context, Strobach, Schubert, et al. (2014) (see also Heidemann et al., 2020, 2024; Orscheschek et al., 2019) also provided data ruling out the assumption of changing dual-task processing strategies after practice. In that study, at the outset of dual-task practice with two memory retrieval tasks, participants performed the memory retrievals in both tasks sequentially. While some selected results were tempting to assume differences in the dual-memory organization strategies of participants before and after practice, a closer look at the participants’ individual data showed unchanged dual-task strategies with practice. Thus, this study, as well as the current study, provide data that is inconsistent with assumptions of changed dual-task strategies between final practice and transfer sessions in dual-task situations (Strobach, 2020).

In summary, the latent bottleneck model provides the most parsimonious account for explaining the observed pattern of selective processing changes after practice across the present Experiments 1 to 3. Other models assuming parallel task processing as a basic architecture alone or in combination with assumptions about changing task strategies do not allow explaining the whole data pattern as a sole account.

Relation to Other Studies on Dual-Task Practice

In the present study, the reduction of the dual-task RT costs in the visual task was complete after 12 practice sessions (Experiment 2) but was still evident after 8 sessions (Experiments 1 and 3). In the auditory task, this reduction, although tremendous, was not complete, although we applied between 8 and 12 practice sessions. Thus, in all experiments, the differences between this task’s RTs in dual-task and single-task trials reached the level of statistical significance, which differs from the findings in Schumacher et al. (2001, Experiment 1). Therefore, researchers might be concerned about generalizing the evaluation of the latent bottleneck model, as in the present experiments, to situations in which dual-task costs appeared to be eliminated. However, the finding of remaining dual-task costs after practice sessions fits well with findings of several other dual-task practice studies using a design similar to Schumacher et al. (Israel & Cohen, 2011; Liepelt, Strobach, et al., 2011; Strobach, Frensch, Müller, et al., 2012a; Strobach, Frensch, Soutschek, et al., 2012; Strobach, Salminen, et al., 2014). Therefore, the results of the present experiments are suitable to reflect practice-related improvements of dual-task performance in this design.

To explain the still remaining dual-task costs, we take a closer look at earlier findings of other authors, for example, Tombu and Jolicœur (2004). These authors could also not replicate the observation of statistically non-significant dual-task costs. While these authors reported dual-task costs of 26 and 40 ms after eight practice sessions (Experiment 1a), we found dual-task costs of 16 and 45 ms (averaged for both experiments with eight sessions, Experiments 1 and 3) for the visual and the auditory tasks, respectively (see also Liepelt, Fischer, et al., 2011, for similar values). Importantly, Tombu and Jolicoeur argue for a decisive role of the bonus schema applied for encouraging participants’ best performance in the dual-task situation of Schumacher et al. (2001). While Schumacher et al. used RTs from the heterogeneous single-task trials (we call them mixed single-task trials) for calculating the bonus for both the single-task and the dual-task trials, Tombu and Jolicoeur used different values for these two different types of trials. According to Tombu and Jolicoeur, the specific procedure for determining bonus values in Schumacher et al. may have led to an increased mobilization of effort in dual-task trials and to an artificially decreased mobilization of effort in single-task trials in Schumacher et al.; consequently, this may have led to a confounding of effort in different types of trials and dual-task costs in Schumacher et al. The fact that we, using a similar deadline procedure as Tombu and Jolicoeur, found similar dual-task costs as these authors supports the assumption of a role of mobilized effort for the complete disappearance of dual-task costs in the present paradigm.

The Latent Bottleneck: A General Processing Architecture for Dual-Task Processing After Practice?

Several studies have already provided evidence for the occurrence of a latent bottleneck in situations in which participants practiced PRP tasks without any overlap between the processing modalities of input and output processes for many sessions. For such a situation, Van Selst et al. (1999) as well as Ruthruff and colleagues (Ruthruff, Johnston, et al., 2001; Ruthruff et al., 2003) showed with careful analyses that the predictions of a latent bottleneck are fulfilled after selective participants had performed the PRP task in many sessions (e.g., 6 participants with 36 sessions in Van Selst et al., 1999; specific analysis of one of those 6 participants in Ruthruff et al., 2003). A latent-bottleneck-like structure was also proposed by Lien et al. (2005) for a PRP situation in which participants performed two highly compatible component tasks for moderate amounts of practice. In detail, participants pronounced the name of an auditory letter in the auditory task and performed a spatially compatible key press reaction on the presentation of a left- or right-pointing arrow. Although the RTs in both tasks were relatively low and the PRP effect (RT2 long interval minus RT2 short interval) was nearly negligible, Lien et al. showed that a bottleneck between tasks had not been bypassed but was preserved and shifted to later processing components (but see Greenwald, 2005).

The findings of the present study extend those earlier results because they indicate that the latent bottleneck represents a reasonable interpretation for the practice effects in the paradigm of Schumacher et al. (2001, Experiment 1), which had earlier been interpreted as evidence for parallel response selection processes. While the former studies provided evidence for a latent bottleneck architecture, preferably for task situations with a variable interval between the component tasks, which is prone to induce serial processing (Meyer & Kieras, 1997), the present study used a task situation in which the tasks were presented with a zero interval. The fact that we provided evidence for a latent bottleneck even for the latter situation lends support for the assumption that the latent bottleneck model represents a general theoretical perspective for practice effects in dual-task situations with a (near) elimination of dual-task costs.

The present view of latent bottleneck processing is consistent with reports highlighting the role of a practice-related reduction of the processing time of the response selection stage for the reduction of the dual-task costs. As had been shown by Strobach et al. (2013) for the Schumacher et al. (2001) situation, practice leads to a particular speedup of the processing time for the response selection processes in the combined visual and auditory choice RT tasks (see also Thomson et al., 2015). If, in a dual-task situation, practice leads to a reduction in the duration of the response selection stage in Task 1, then this reduces the time for Task 2 waiting for the end of the bottleneck processes in Task 1 as well, and this, consequently, leads to a reduction of Task 2 dual-task costs. Consistent with that prediction, Ruthruff et al. (2006) have shown that the time reduction of the processing time in Task 1 of a PRP situation is strongly correlated to the amount of the PRP effect in the Task 2 processing stream. This is also consistent with the findings of a neuroimaging study by Dux et al. (2009), who investigated practice-related changes in the brain when participants trained a visual and an auditory choice RT task in single- and dual-task trials. The authors showed a specific pattern of neural activity in the prefrontal cortex, which indicates serial processing of the response selection for those brain regions that are commonly involved in the response selection processes of the two-component tasks. Most importantly, practice led to a tremendous reduction in the time duration of that activation for both the visual and the auditory tasks, suggesting an increase in the information processing speed associated with the response selection in the two tasks.

Both mechanisms, the practice-related reduction of the response selection time and the non-overlapping scheduling of critical processes in dual-task situations, represent two main components for a practice-related optimization of dual-task processing. An interesting question for future research will concern which specific task characteristics are supportive for the development of a latent bottleneck and which prevent its development even under conditions of extensive practice.

It is important to note that despite considerable evidence in favor of the latent bottleneck model, there are particular findings pointing to the possibility of bottleneck elimination due to practice in certain dual-task situations. For example, Ruthruff et al. (2006) reported practice effects, which they interpreted as evidence that some of the participants processed the second task of a PRP task situation not serially with the processes of Task 1 but in parallel (for other practice studies, see also Maquestiaux et al., 2008, 2010, and for other non-practice studies, see Lyphout-Spitz et al., 2022, 2024; Maquestiaux et al., 2020). In particular, this was reported for task situations in which a visual-manual Task 1 was combined with an auditory-verbal Task 2. The fact that the reversed task combination did not provide any evidence for a practice-related bottleneck elimination led Ruthruff et al. to conclude that an auditory-verbal task may be selectively automatized in the dual-task context with a visual-manual task. Subsequently, this may lead to practice-related bottleneck elimination in these particular task situations, which may be expressed by a lacking (or minimal) PRP effect on the auditory-verbal RT2 (Maquestiaux et al., 2008). On the basis of their findings, Ruthruff et al. highlighted the specific character of auditory-verbal tasks for automatization because this task had less need of central bottleneck resources to begin with, because the stimulus-response mapping in the auditory-verbal task was highly compatible (e.g., say “high” to a high tone), or because auditory stimuli are better than visual stimuli in alerting motor responses because auditory stimuli more readily attract attention to themselves. This, subsequently, may cause a greater probability of bottleneck elimination due to practice compared with other task combinations.

However, for the present task situation, the concept of a selective automatization of the auditory-verbal task does not provide either a valid or a consistent interpretation for the current findings. As an explanation, consider the case of the already mentioned capacity criterion for defining a process or a task as being automatized, namely that the process in question can operate without any processing detriments simultaneously with another process/task (Hasher & Zacks, 1979; Schneider & Shiffrin, 1977). According to that criterion, the particular findings of Experiment 2 would be inconsistent with the assumption that the particular processes of the auditory-verbal Task 2 had been automatized because the transfer manipulation of the visual task led to a change in the RTs in the auditory task. On the basis of this inconsistent finding, it becomes obvious that the prescription of automatization in the context of the present study does not allow for an equivocal and consistent interpretation of the findings (see also Neumann, 1984). Contrary to that, the latent bottleneck model allows for precisely predicting the reported findings and the related data pattern. It represents a more powerful model than the assumption of a selective automaticity of the auditory task for the present task situation.

A study by Oberauer and Kliegl (2004) provided evidence for parallel processing of two central operations in working memory. In that study, the authors showed by comparing empirical data with simulation data that a serial schedule of mental operations after practice cannot explain the observed data pattern, contrary to the assumption of parallel scheduling. It is important to note that the two central operations in the Oberauer and Kliegl study did not require two independent motor actions but only one response, which should be given depending on the outcome of the two mental operations. Future studies may assess whether the need to select and execute two overt instead of one overt motor response on two information processing streams limits the possibility for simultaneous central processing after practice.

In conclusion, the latent bottleneck model seems to be a reasonable candidate for explaining practice phenomena in dual-task processing. This assumption holds for the specific dual-task situation used by Schumacher et al. (2001, Experiment 1) and other situations of extensive dual-task practice.

Footnotes

Acknowledgements

The present research was supported by a grant of the German Research Foundation to T.S. (first author; Schu 1397/5-1). It was conducted while the authors worked at the Humboldt-Universität zu Berlin, Berlin, Germany. We thank Peter Frensch for his helpful comments on earlier drafts of this manuscript.

ORCID iDs

Torsten Schubert

Roman Liepelt

Tilo Strobach

Ethical Considerations

All procedures performed in this study involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki Declaration and its later amendments or comparable ethical standards. The study was approved by the ethical committee of the Humboldt-Universität zu Berlin.

Consent to Participate

Informed consent was obtained from all participants before the commencement of the study.

Consent for Publication

The manuscript has been approved by the responsible institutions.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was funded by Deutsche Forschungsgemeinschaft (DFG, Schu 1397/5-1).

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data Availability Statement

The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request. This procedure allows providing detailed information about the data structure.

Notes

References

Anderson

J. R.

Taatgen

N. A.

Byrne

M. D.

(2005). Learning to achieve perfect timesharing: architectural implications of Hazeltine, Teague, and Ivry (2002). Journal of Experimental Psychology: Human Perception and Performance, 31(4), 749–761. https://doi.org/10.1037/0096-1523.31.4.749

Beringer

(1994). ERTS: A flexible software tool for developing and running psychological reaction time experiments on IBM PCs. Behavior Research Methods, 26(3), 368–369. https://doi.org/10.3758/BF03204646

Beringer

(2000). Experimental runtime system. BeriSoft Cooperation.

Cohen

(1988). Statistical power analysis for the behavioral sciences (2nd ed.). Erlbaum. https://doi.org/10.4324/9780203771587

de Jong

. (1995). The role of preparation in overlapping-task performance. The Quarterly Journal of Experimental Psychology A: Human Experimental Psychology, 48A(1), 2–25. https://doi.org/10.1080/14640749508401372

Duncan

(1979). Divided attention: The whole is more than the sum of its parts. Journal of Experimental Psychology: Human Perception and Performance, 5(2), 216–228. https://doi.org/10.1037/0096-1523.5.2.216

Dutta

(1995). Experimental RunTime System: Software for developing and running reaction time experiments on IBM-compatible PCs. Behavior Research Methods, Instruments, & Computers, 27, 516–519. https://doi.org/10.3758/BF03200453

Dux

P. E.

Tombu

M. N.

Harrison

Rogers

B. P.

Tong

Marois

(2009). Training improves multitasking performance by increasing the speed of information processing in human prefrontal cortex. Neuron, 63, 127–138. https://doi.org/10.1016/j.neuron.2009.06.005

Faul

Erdfelder

Lang

A.-G.

Buchner

(2007). G*Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences. Behavior Research Methods, 39(2), 175–191. https://doi.org/10.3758/BF03193146

10.

Fischer

Plessow

(2015). Efficient multitasking: Parallel versus serial processing of multiple tasks. Frontiers in Psychology, 6, 1366. https://doi.org/10.3389/fpsyg.2015.01366

11.

Göthe

Oberauer

Kliegl

(2016). Eliminating dual-task costs by minimizing crosstalk between tasks: The role of modality and feature pairings. Cognition, 150, 92–108. https://doi.org/10.1016/j.cognition.2016.02.003

12.

Greenwald

A. G.

(2005). A reminder about procedures needed to reliably produce perfect timesharing: comment on Lien, McCann, Ruthruff, and Proctor (2005). Journal of Experimental Psychology: Human Perception and Performance, 31(1), 221–225. https://doi.org/10.1037/0096-1523.31.1.221

13.

Hartley

A. A.

Little

D. M.

(1999). Age-related differences and similarities in dual-task interference. Journal of Experimental Psychology: General, 128(4), 416–449. https://doi.org/10.1037/0096-3445.128.4.416

14.

Hartley

A. A.

Maquestiaux

Butts

N. S.

(2011). A demonstration of dual-task performance without interference in some older adults. Psychology and Aging, 26(1), 181–187. https://doi.org/10.1037/a0021497

15.

Hasher

Zacks

R. T.

(1979). Automatic and effortful processes in memory. Journal of Experimental Psychology: General, 108(3), 356. https://doi.org/10.1037/0096-3445.108.3.356

16.

Hazeltine

Ruthruff

Remington

R. W.

(2006). The role of input and output modality pairings in dual-task performance: Evidence for content-dependent central interference. Cognitive Psychology, 52(4), 291–345. https://doi.org/10.1016/j.cogpsych.2005.11.001

17.

Hazeltine

Teague

Ivry

R. B.

(2002). Simultaneous dual-task performance reveals parallel response selection after practice. Journal of Experimental Psychology: Human Perception and Performance, 28(3), 527. https://doi.org/10.1037/0096-1523.28.3.527

18.

Heidemann

Rickard

T. C.

Schubert

Strobach

(2020). Dual-memory retrieval efficiency after practice: Effects of strategy manipulations. Psychological Research, 84(8), 2210–2236. https://doi.org/10.1007/s00426-019-01217-y

19.

Heidemann

Rickard

T. C.

Schubert

Strobach

(2024). Age does not modify the processing architecture of dual memory retrieval: An investigation of age-related effects on dual-retrieval practice in younger and older adults. Aging, Neuropsychology, and Cognition, 31(1), 114–144. https://doi.org/10.1080/13825585.2022.2128029

20.

Israel

Cohen

(2011). Involuntary strategy-dependent dual task performance. Psychological Research, 75, 513–524. https://doi.org/10.1007/s00426-011-0359-y

21.

JASP-Team. (2023). JASP (Version 0.18.1).

22.

Kahneman

(1973). Attention and effort. Prentice-Hall.

23.

Koch

Poljac

Müller

Kiesel

(2018). Cognitive structure, flexibility, and plasticity in human multitasking—An integrative review of dual-task and task-switching research. Psychological Bulletin, 144(6), 557–583. https://doi.org/10.1037/bul0000144

24.

Lakens

(2022). Sample size justification. Collabra: Psychology, 8(1), 33267. https://doi.org/10.1525/collabra.33267

25.

Levy

Pashler

(2001). Is dual-task slowing instruction dependent? Journal of Experimental Psychology: Human Perception and Performance, 27(4), 862. https://doi.org/10.1037/0096-1523.27.4.862

26.

Lien

M.-C.

McCann

R. S.

Ruthruff

Proctor

R. W.

(2005). Dual-task performance with ideomotor-compatible tasks: Is the central processing bottleneck intact, bypassed, or shifted in locus? Journal of Experimental Psychology: Human Perception and Performance, 31(1), 122–144. https://doi.org/10.1037/0096-1523.31.1.122

27.

Liepelt

Fischer

Frensch

P. A.

Schubert

(2011). Practice-related reduction of dual-task costs under conditions of a manual-pedal response combination. Journal of Cognitive Psychology, 23(1), 29–44. https://doi.org/10.1080/20445911.2011.448025

28.

Liepelt

Strobach

Frensch

Schubert

(2011). Improved intertask coordination after extensive dual-task practice. The Quarterly Journal of Experimental Psychology, 64(7), 1251–1272. https://doi.org/10.1080/17470218.2010.543284

29.

Logan

G. D.

Gordon

R. D.

(2001). Executive control of visual attention in dual-task situations. Psychological Review, 108(2), 393–434. https://doi.org/10.1037/0033-295X.108.2.393

30.

Lyphout-Spitz

Maquestiaux

Ruthruff

(2022). Bypassing the central bottleneck with easy tasks: Beyond ideomotor compatibility. Psychonomic Bulletin & Review, 29, 501–511. https://doi.org/10.3758/s13423-021-01974-1

31.

Lyphout-Spitz

Maquestiaux

Ruthruff

Chaloyard

(2024). Uncorking the central bottleneck: Even novel tasks can be performed automatically. Journal of Experimental Psychology: Human Perception and Performance, 50(1), 74. https://doi.org/10.1037/xhp0001169

32.

Maquestiaux

Hartley

A. A.

Bertsch

(2004). Can practice overcome age-related differences in the psychological refractory period effect? Psychology and Aging, 19(4), 649–667. https://doi.org/10.1037/0882-7974.19.4.649

33.

Maquestiaux

Laguë-Beauvais

Bherer

Ruthruff

(2008). Bypassing the central bottleneck after single-task practice in the psychological refractory period paradigm: Evidence for task automatization and greedy resource recruitment. Memory & Cognition, 36(7), 1262–1282. https://doi.org/10.3758/MC.36.7.1262

34.

Maquestiaux

Laguë-Beauvais

Ruthruff

Hartley

Bherer

(2010). Learning to bypass the central bottleneck: Declining automaticity with advancing age. Psychology and Aging, 25(1), 177–192. https://doi.org/10.1037/a0017122

35.

Maquestiaux

Lyphout-Spitz

Ruthruff

Arexis

(2020). Ideomotor compatibility enables automatic response selection. Psychonomic Bulletin & Review, 27, 742–750. https://doi.org/10.3758/s13423-020-01735-6

36.

McCann

R. S.

Johnston

J. C.

(1992). Locus of the single-channel bottleneck in dual-task interference. Journal of Experimental Psychology: Human Perception and Performance, 18(2), 471–484. https://doi.org/10.1037/0096-1523.18.2.471

37.

Meyer

D. E.

Kieras

D. E.

(1997). A computational theory of executive cognitive processes and multiple-task performance: Part 2. Accounts of psychological refractory-period phenomena. Psychological Review, 104(4), 749–791. https://doi.org/10.1037/0033-295X.104.4.749

38.

Meyer

D. E.

Kieras

D. E.

(1999). Précis to a practical unified theory of cognition and action: Some lessons from EPIC computational models of human multiple-task performance. In Gopher

Koriat

(Eds.), Attention and performance XVII: Cognitive regulation of performance: Interaction of theory and application (pp. 17–88). The MIT Press. https://doi.org/10.7551/mitpress/1480.001.0001

39.

Miller

Ulrich

Rolke

(2009). On the optimality of serial and parallel processing in the psychological refractory period paradigm: Effects of the distribution of stimulus onset asynchronies. Cognitive Psychology, 58(3), 273–310. https://doi.org/10.1016/j.cogpsych.2006.08.003

40.

Neumann

(1984). Automatic processing: A review of recent findings and a plea for an old theory. In Prinz

Sanders

A. F.

(Eds.), Cognition and motor processes (pp. 255–293). Springer. https://doi.org/10.1007/978-3-642-69382-3_17

41.

Neumann

(2016). Beyond capacity: A functional view of attention. In H. Heuer & A. Sanders (Eds.), Perspectives on perception and action (pp. 361–394). Routledge.

42.

Oberauer

Bialkova

(2011). Serial and parallel processes in working memory after practice. Journal of Experimental Psychology: Human Perception and Performance, 37(2), 606–614. https://doi.org/10.1037/a0020986

43.

Oberauer

Kliegl

(2004). Simultaneous cognitive operations in working memory after dual-task practice. Journal of Experimental Psychology: Human Perception and Performance, 30(4), 689–707. https://doi.org/10.1037/0096-1523.30.4.689

44.

Orscheschek

Strobach

Schubert

Rickard

(2019). Two retrievals from a single cue: A bottleneck persists across episodic and semantic memory. Quarterly Journal of Experimental Psychology, 72(5), 1005–1028.

45.

Pashler

(1994). Dual-task interference in simple tasks: Data and theory. Psychological Bulletin, 116(2), 220–244. https://doi.org/10.1037/0033-2909.116.2.220

46.

Pashler

(1998). The psychology of attention. MIT Press.

47.

Pashler

Baylis

G. C.

(1991). Procedural learning: I. Locus of practice effects in speeded choice tasks. Journal of Experimental Psychology: Learning, Memory, and Cognition, 17(1), 20. https://doi.org/10.1037/0278-7393.17.1.20

48.

Pashler

Johnston

J. C.

(1989). Chronometric evidence for central postponement in temporally overlapping tasks. The Quarterly Journal of Experimental Psychology A: Human Experimental Psychology, 41(1-A), 19–45. https://doi.org/10.1080/14640748908402351

49.

Pashler

Johnston

J. C.

(1998). Attentional limitations in dual-task performance. In Pashler

(Ed.), Attention (pp. 155–189). Taylor & Francis Press.

50.

Ruthruff

Johnston

J. C.

Van Selst

(2001). Why practice reduces dual-task interference. Journal of Experimental Psychology: Human Perception and Performance, 27(1), 3–21. https://doi.org/1O.1O37//0O96-1523.27.1.3

51.

Ruthruff

Johnston

J. C.

Van Selst

Whitsell

Remington

(2003). Vanishing dual-task interference after practice: Has the bottleneck been eliminated or is it merely latent? Journal of Experimental Psychology: Human Perception and Performance, 29(2), 280–289. https://doi.org/10.1037/0096-1523.29.2.280

52.

Ruthruff

Pashler

H. E.

Klaassen

(2001). Processing bottlenecks in dual-task performance: Structural limitation or strategic postponement? Psychonomic Bulletin & Review, 8(1), 73–80. https://doi.org/10.3758/BF03196141

53.

Ruthruff

Van Selst

Johnston

J. C.

Remington

(2006). How does practice reduce dual-task interference: Integration, automatization, or just stage-shortening? Psychological Research, 70(2), 125–142. https://doi.org/10.1007/s00426-004-0192-7

54.

Schneider

Shiffrin

R. M.

(1977). Controlled and automatic human information processing: I. Detection, search, and attention. Psychological Review, 84(1), 1–66. https://doi.org/10.1037/0033-295X.84.1.1

55.

Schubert

(1999). Processing differences between simple and choice reactions affect bottleneck localization in overlapping tasks. Journal of Experimental Psychology: Human Perception and Performance, 25(2), 408–425. https://doi.org/10.1037/0096-1523.25.2.408

56.

Schubert

Strobach

(2012). Video game experience and optimized executive control skills—On false positives and false negatives: Reply to Boot and Simons (2012). Acta Psychologica, 141(2), 278–280. https://doi.org/10.1016/j.actpsy.2012.06.010

57.

Schubert

Strobach

(2018). Practice-related optimization of dual-task performance: Efficient task instantiation during overlapping task processing. Journal of Experimental Psychology: Human Perception and Performance, 44(12), 1884–1904. https://doi.org/10.1037/xhp0000576

58.

Schubert

Kübler

Strobach

(2024). A mechanism underlying improved dual-task performance after practice: Reviewing evidence for the memory hypothesis. Psychonomic Bulletin & Review, 8, 73–80. https://doi.org/10.3758/s13423-024-02498-0

59.

Schubert

Liepelt

Kübler

Strobach

(2017). Transferability of dual-task coordination skills after practice with changing component tasks. Frontiers in Psychology, 8, 956. https://doi.org/10.3389/fpsyg.2017.00956

60.

Schumacher

E. H.

Seymour

T. L.

Glass

J. M.

Fencsik

D. E.

Lauber

E. J.

Kieras

D. E.

Meyer

D. E.

(2001). Virtually perfect time sharing in dual-task performance: Uncorking the central cognitive bottleneck. Psychological Science, 12(2), 101–108. https://doi.org/10.1111/1467-9280.00318

61.

Schweickert

(1983). Latency network theory: Scheduling of processes in sentence verification and the Stroop effect. Journal of Experimental Psychology: Learning, Memory, and Cognition, 9(3), 353. https://doi.org/10.1037/0278-7393.9.3.353

62.

Strobach

(2020). The dual-task practice advantage: Empirical evidence and cognitive mechanisms. Psychonomic Bulletin & Review, 27(1), 3–14. https://doi.org/10.3758/s13423-019-01619-4

63.

Strobach

Huestegge

(2021). Structuralist mental representation of dual-action demands: Mechanisms of improved dual-task performance after practice in older adults. Experimental Aging Research, 47(2), 109–130. https://doi.org/10.1080/0361073X.2021.1873053

64.

Strobach

Schubert

(2017a). Mechanisms of practice-related reductions of dual-task interference with simple tasks: Data and theory. Advances in Cognitive Psychology, 13(1), 28. https://doi.org/10.5709/acp-0204-7

65.

Strobach

Schubert

(2017b). No evidence for task automatization after dual-task training in younger and older adults. Psychology and Aging, 32(1), 28. https://doi.org/10.1037/pag0000144

66.

Strobach

Frensch

P. A.

Müller

H. J.

Schubert

(2012a). Age- and practice-related influences on dual-task costs and compensation mechanisms under optimal conditions of dual-task performance. Aging, Neuropsychology, and Cognition, 19(1–2), 222–247. https://doi.org/10.1080/13825585.2011.630973

67.

Strobach

Frensch

P. A.

Müller

H. J.

Schubert

(2012b). Testing the limits of optimizing dual-task performance in younger and older adults. Frontiers in Human Neuroscience, 6, 39. https://doi.org/10.3389/fnhum.2012.00039

68.

Strobach

Frensch

P. A.

Soutschek

Schubert

(2012). Investigation on the improvement and transfer of dual-task coordination skills. Psychological Research, 76, 794–811. https://doi.org/10.1007/s00426-011-0381-0

69.

Strobach

Frensch

Müller

Schubert

(2015). Evidence for the acquisition of dual-task coordination skills in older adults. Acta Psychologica, 160, 104–116. https://doi.org/10.1016/j.actpsy.2015.07.006

70.

Strobach

Liepelt

Pashler

Frensch

P. A.

Schubert

(2013). Effects of extensive dual-task practice on processing stages in simultaneous choice tasks. Attention, Perception, & Psychophysics, 75, 900–920. https://doi.org/10.3758/s13414-013-0451-z

71.

Strobach

Liepelt

Schubert

Kiesel

(2012). Task switching: Effects of practice on switch and mixing costs. Psychological Research, 76(1), 74–83. https://doi.org/10.1007/s00426-011-0323-x

72.

Strobach

Salminen

Karbach

Schubert

(2014). Practice-related optimization and transfer of executive functions: a general review and a specific realization of their mechanisms in dual tasks. Psychological Research, 78(6), 836–851. https://doi.org/10.1007/s00426-014-0563-7

73.

Strobach

Schubert

Pashler

Rickard

(2014). The specificity of learned parallelism in dual-memory retrieval. Memory & Cognition, 42, 552–569. https://doi.org/10.3758/s13421-013-0382-x

74.

Thomson

S. J.

Danis

L. K.

Watter

(2015). PRP training shows Task1 response selection is the locus of the backward response compatibility effect. Psychonomic Bulletin & Review, 22, 212–218. https://doi.org/10.3758/s13423-014-0660-z

75.

Tombu

Jolicœur

(2003). A central capacity sharing model of dual-task performance. Journal of Experimental Psychology: Human Perception and Performance, 29(1), 3–18. https://doi.org/10.1037/0096-1523.29.1.3

76.

Tombu

Jolicœur

(2004). Virtually no evidence for virtually perfect time-sharing. Journal of Experimental Psychology: Human Perception and Performance, 30(5), 795–810. https://doi.org/10.1037/0096-1523.30.5.795

77.

Van Selst

Ruthruff

Johnston

J. C

. (1999). Can practice eliminate the Psychological Refractory Period effect? Journal of Experimental Psychology: Human Perception and Performance, 25(5), 1268–1283. https://doi.org/10.1037/0096-1523.25.5.1268

78.

Welford

A. T.

(1952). The Psychological refractory period and the timing of high-speed performance—A review and a theory. British Journal of Psychology. General Section, 43(1), 2–19. https://doi.org/10.1111/j.2044-8295.1952.tb00322.x

79.

Wickens

C. D.

(2014). The structure of attentional resources. In R. S. Nickerson (Ed.), Attention and performance VIII (pp. 239–257). Psychology Press. https://doi.org/10.1007/978-1-4419-1428-6_25