Explicit Timing Differently Predicts Implicit Timing Performance in Younger and Older Adults

Temporal processing can be divided into explicit timing and implicit timing. Explicit timing tasks require participants to attend to the temporal aspects of the task, whereas in implicit timing tasks, temporal information affects performance without explicit instruction to process time. Compared to younger adults, older adults have been shown to exhibit greater variability in explicit timing, while in implicit timing, they have been shown to rely more on temporal predictions formed by the hazard function. However, the relationship between explicit and implicit timing and its age-related changes have yet to be explored. To address this issue, we collected data in which younger and older adults performed a time bisection task (i.e., explicit timing task) and a foreperiod task (i.e., implicit timing task) in a within-subjects design. Based on a Bayesian optimization framework, we hypothesized that individuals with higher variability in explicit timing would show a stronger foreperiod effect, which is an index of the degree of reliance on temporal predictions. Results showed a different relation between explicit and implicit timing in younger and older adults. In older adults, results were consistent with the hypothesis that increased variability in explicit timing was associated with a stronger foreperiod effect. In contrast, bias in the temporal representation but not variability was associated with the foreperiod effect in younger adults. Implications for the age-related difference in the relation between explicit and implicit timing are discussed.


Introduction
The effects of aging on timing ability have been studied separately for explicit and implicit timing, depending on how temporal information is processed and used (Coull & Nobre, 2008).
In explicit timing tasks, subjects are required to pay attention to the temporal aspects of the task and thus explicitly process temporal information.Studies on the effects of aging on explicit timing have shown that older adults preserve as much accuracy as younger adults but exhibit greater variability (Capizzi et al., 2022;Droit-Volet et al., 2019;Hiroyasu & Yotsumoto, 2020).For example, Capizzi et al. (2022) investigated the effect of age on explicit timing in older adults using a time bisection task, in which subjects first memorized the durations of the short and long standard stimuli and then answered whether the duration of a test stimulus was similar to the short or long.Results showed that the increase in age did not affect the position of the psychometric function (i.e., the bisection point) but flattened the slope of the function, suggesting that aging increases the variability in the representation of time without changing the accuracy.Similar results have been obtained from the studies comparing younger and older adults using a temporal generalization task (Droit-Volet et al., 2019) and a rhythmic timing task (Hiroyasu & Yotsumoto, 2020).
In implicit timing tasks, on the other hand, subjects are not explicitly required to process temporal information, yet the performance is affected by the temporal structure of the stimuli.For example, in a warned reaction time (RT) task (also called 'foreperiod task'), subjects are instructed to respond to a target stimulus that follows a warning signal.In this task, temporal information is carried by the interval between the warning signal and the target stimulus, termed 'foreperiod' .When the foreperiods are uniformly distributed in a specific range, the probability that the target stimulus appears at a particular time point increases as the foreperiod becomes longer.This probability is mathematically described by the hazard function, i.e., the conditional probability that an event will occur given that it has not yet occurred.Consequently, RT decreases as the foreperiod increases, known as the 'variable foreperiod effect' (hereafter referred to as the foreperiod effect).The foreperiod effect demonstrates that subjects modulate their behavior by exploiting the temporal information of the stimuli to form predictions even if they are not instructed to pay attention to time (Coull, 2009;Niemi & Näätänen, 1981).Previous studies on implicit timing have shown that older adults rely more on the hazard function than younger adults (Bherer & Belleville, 2004a, b;Capizzi et al., 2022;Droit-Volet et al., 2019).For example, Capizzi et al. (2022) found that not only an overall slowing of RT but also an increase in the foreperiod effect was associated with increasing age.Moreover, the greater reliance on the hazard function was not associated with cognitive decline (Capizzi et al., 2022) or reduced cognitive abilities (Droit-Volet et al., 2019), which are typically accompanied by aging.
To date, the effects of aging on explicit and implicit timing have mostly been studied separately, and it is only recently that both types of timing have started to be investigated in a single study (Capizzi et al., 2022;Coull et al., 2013;Droit-Volet & Coull, 2016;Droit-Volet et al., 2019;Herbst et al., 2022;Hiroyasu & Yotsumoto, 2020;Piras & Coull, 2011).However, none of these studies have directly examined the age-related differences in the relationship between explicit and implicit timing performances.Therefore, to gain a more comprehensive understanding of the effects of aging on general timing behavior, it is imperative to examine the relationship between these two types of timing performances and how it changes with age.
One of the prominent theoretical frameworks to explain general timing behavior is the Bayesian framework (Cicchini et al., 2012;Jazayeri & Shadlen, 2010;Maaß et al., 2021;Shi et al., 2013;Visalli et al., 2019Visalli et al., , 2021)).According to this framework, timing behavior is optimized by integrating current sensory information with the prior predictions formed by the stimulus distribution from which the current stimulus is drawn, weighted by their relative precisions.Therefore, the Bayesian hypothesis predicts that when the precision of sensory information decreases, individuals rely more on prior predictions.In aging research, studies have shown that older adults tend to overweight internal predictions as their sensory precision decreases, suggesting that the Bayesian framework can account for age-related changes in behavior (Moran et al., 2014;Wolpe et al., 2016).Consistent with these observations, it has been proposed that older adults rely more on prior predictions than on current sensory information when making temporal judgments, which serve as a compensatory mechanism for age-related declines in sensory timing abilities (Turgeon et al., 2016).
Here, the findings from previous research, which indicate that aging leads to increased variability in explicit timing and greater reliance on temporal predictions in implicit timing, seem to align conceptually with the Bayesian framework.In explicit timing, variability of the temporal representation is directly related to the degree of reliance on the prior distribution as formally described by the Bayesian models (e.g., Cicchini et al., 2012).On the other hand, the relationship between temporal variability and the degree of reliance on temporal predictions in implicit timing is not yet clearly established (Bueti et al., 2010;Janssen & Shadlen, 2005;Visalli et al., 2019Visalli et al., , 2021)).Although conceptual, if there is a common timing mechanism between explicit and implicit timing, it is conceivable that temporal variability is also related to the degree of reliance on prior predictions in implicit timing, as evaluated by the degree of reliance on the hazard function determined by the stimulus distribution (i.e., the foreperiod effect).Accordingly, we hypothesized that higher temporal variability in explicit timing would be associated with greater reliance on temporal predictions (i.e., stronger foreperiod effect) in implicit timing.
Note that in our study, we did not hypothesize about the specific mechanism by which the prior is established, but rather focused on the degree of reliance on an already established prior.In other words, we assumed that the prior (i.e. the hazard function) was already established, reflecting the exact stimulus distribution.While this assumption may be somewhat unrealistic, similar assumptions have been made in many studies that have examined Bayesian hypotheses in explicit timing (e.g., Jazayeri & Shadlen, 2010).
We collected data in which younger and older adults performed a time bisection task and a foreperiod task in a within-subjects design.In the analyses, we first obtained each participant's just noticeable difference (JND) and bisection point (BP) from the bisection task as an index of variability and bias of the temporal representation, respectively.Then, we examined whether these variables, along with age, predict RTs in the foreperiod task using linear mixed-effects models (LMMs).We expected that individuals with higher JND (i.e., higher temporal variability) would show a stronger foreperiod effect (i.e., a steeper decrease in RT with increasing foreperiod, or a greater reliance on temporal predictions).Although we did not make a specific hypothesis about the effect of bias on RTs, we included BP as a predictor because it is also an integral component of explicit timing.
In summary, the aim of this study was to examine the relationship between explicit timing and implicit timing and its age-related changes.Based on the hypothesis derived from the Bayesian framework, we expected that higher variability in the explicit timing task would be related to a stronger foreperiod effect in the implicit timing task.

Participants
The sample consisted of 123 participants: 70 younger adults (mean age = 24.01;SD = 2.34) and 53 older adults (mean age = 70.84;SD = 6.77) (Fig. 1).All data from younger adults were obtained for this study and have not been reported elsewhere.Among the data from 53 older adults, 42 were included in Capizzi et al. (2022), and 11 were additionally obtained for this study.The Mini-Mental State Examination (MMSE; Magni et al., 1996) was used to measure general cognitive ability; participants scoring between 30 and 28 were considered to have a normal cognitive function and were included in the present study.
All participants reported normal or corrected-to-normal vision and normal hearing.They provided written informed consent in accordance with the Declaration of Helsinki.The protocol was approved by the Ethics Committee of the Department of General Psychology of the University of Padova (No. 3387).

Procedure and Task
The experimental procedure was the same as in Capizzi et al. (2022).Participants were individually tested during one experimental session.The time bisection and foreperiod tasks consisted of the same stimulus material and general procedure but differed in the specific task instructions given to participants.Stimuli were a gray circle and a gray cross that appeared at the center of the computer screen.In the time bisection task, the experimental session started with a training phase, in which participants were instructed to memorize two standard durations: 480 (short standard) and 1920 ms (long standard), each presented 10 times.During a subsequent testing phase, participants were instructed to judge in a temporal interval between the appearance of the circle and the cross at its center and decide if it was closer to the 'short standard' or to the 'long standard' previously learned.In the foreperiod task, participants were instructed to press the spacebar as fast as possible when the cross appeared.The interval durations were 480, 720, 960, 1200, 1440, 1680, and 1920 ms and were identical for both tasks.The experiment comprised a total of six blocks (three blocks for each timing task) of 42 trials each (six repetitions for each temporal interval).The order of the task was randomized across participants (see Capizzi et al., 2022 for more details).

Statistical Analysis
From the time bisection task, for each participant, the BP and the JND were obtained by fitting the cumulative normal distribution to the proportion of 'long' responses.Goodness-of-fit of the psychometric function was evaluated using McFadden's pseudo R 2 for each participant.The BP corresponded to the duration at which the probability of 'long' responses reached 50%.Therefore, the BP indicates bias in the participant's temporal representation; a higher (lower) BP indicates an underestimation (overestimation) of the actual duration.The JND was defined as the standard deviation of the fitted normal distribution.Therefore, a higher JND indicates greater variability in the participant's temporal representation.Using a box-and-whisker plot, participants with BP (or JND) lower than the first quartile minus 1.5 times the interquartile range (Q1-1.5 × IQR)or higher than the third quartile plus 1.5 times the interquartile range (Q3 + 1.5 × IQR)were considered outliers and excluded from the subsequent analysis.To examine the effect of age group and task order, three separate two-way analyses of variance (ANOVAs) were conducted on R 2 , BP, and JND, with age group (young or old) and task order (explicit-implicit or implicit-explicit) as between-subject factors.Each participant's BP and JND were then used as predictors in a LMM.
For the foreperiod task, trials with anticipated (RT < 100 ms) or missing responses to the target were discarded.Then, log-transformed RTs from single trials were linearly regressed to the interval duration for each participant.The slopes of the linear regressions were used as indices of the foreperiod effect, with more negative slopes indicating stronger foreperiod effects.To examine how interval duration, age group, and task order affect implicit timing performance, a threeway mixed ANOVA was conducted on mean log-transformed RTs.Interval duration was included as a within-subject factor, and age group (young or old) and task order (explicit-implicit or implicit-explicit) were included as between-subject factors.The Greenhouse-Geisser correction for the degree of freedom was used when the sphericity of the data was violated.In addition, a two-way ANOVA was performed on the foreperiod-effect index (i.e., the slope of the linear regression) with age group and task order as between-subject factors.
In the main analysis, log-transformed RTs from single trials in the foreperiod task were modeled with LMMs using R and the lme4 package (Bates et al., 2015).The full LMM included 'Interval duration' , 'BP' , 'JND' , and 'Age' and their interaction terms as fixed-effect factors.These continuous variables were mean-centered and scaled to improve the fit of the model.Participants were included as a random-effect factor.As mentioned earlier, the foreperiod effect is characterized by a decrease in RT with an increasing foreperiod.This would be captured by a negative slope of the regression line (i.e., a significant main effect of Interval duration).In addition, a significant interaction between BP, JND, or Age and Interval duration is interpreted as changes in the size of the foreperiod effect by BP, JND, or Age.Specifically, a significant negative interaction indicates an increase in the foreperiod effect associated with an increase in the variable.In contrast, a significant positive interaction indicates a decrease in the foreperiod effect with an increase in the variable.To evaluate the significance of the fixed-effect factors, backward model selection was conducted using the 'step' function provided by the lmerTest package (Kuznetsova et al., 2017).The statistical significance of the fixed-effect factors was evaluated from the selected model.The Degrees-of-freedom was calculated by Satterthwaite's method.It should be noted that we attempted to include random slopes for the significant fixed-effect factors, but none of the models converged.Therefore, we report the results of the random-intercept models.
We first analyzed the data for both younger and older adults to identify the general trends in the sample.Next, we repeated the same analysis separately for younger and older adults to see if each group had distinct trends.
For the fixed-effect factors that were significant for the younger or older age groups, we examined the correlation between the variable and the foreperiodeffect index to assess the robustness of the results to interindividual variability.

Time Bisection Task (Explicit Timing Task)
Figure 2 shows the distribution of R 2 , BP, and JND for each age group.Based on the BP and JND, 13 participants (nine older and four younger) were excluded from the subsequent analysis.
In summary, the results indicate that older adults maintain as much temporal accuracy as younger adults, but exhibit higher temporal variability.No significant effect of task order on explicit timing performance was observed.

Foreperiod Task (Implicit Timing Task)
Figure 3 shows the mean log-RTs and the foreperiod-effect index (the slope of the linear regression) for each age group.
In summary, the results suggest that while older adults generally exhibit slower RTs compared to younger adults, the size of the foreperiod effect is similar between the two groups.No significant effect of task order on implicit timing performance was observed.

LMM Results for Both Younger and Older Adults
When combining the data of younger and older adults, the model selection showed that the best-fitting model was the full model, which included Interval duration, BP, JND, Age, and their respective interaction terms.The LMM output is summarized in Table 1.Results showed an overall increase in RT with increasing Age (significant main effect of Age; Fig. 4B).Notably, the foreperiod effect increased with higher JND (significant negative interaction between Interval duration and JND: Fig. 4A), and it increased with increasing Age (significant negative interaction between Interval duration and Age; Fig. 4B).However, there was also a significant threeway interaction between Interval duration, BP and Age (Supplementary Fig. S1),   a significant three-way interaction between Interval duration, JND and Age (Supplementary Fig. S2), and a significant four-way interaction between Interval duration, BP, JND and Age.

Predictors
These results suggest that both variability in the temporal representation (i.e., JND) and age are associated with a stronger foreperiod effect.However, the results also suggest that BP and JND are differently related to the foreperiod effect depending on age.Specifically, in younger individuals, a stronger foreperiod effect is associated with higher BP.Conversely, in older individuals, a stronger foreperiod effect is associated with higher JND.

LMM Results for Older Adults
When analyzing older adults' data, the best-fitting model included Interval duration, BP, JND, and Age (Table 2).Figure 5 shows that the foreperiod effect increased with higher JND (significant negative interaction between Interval duration and JND; Fig. 5A).Moreover, an across-participants correlation between JND and the foreperiod-effect index was significant: r = −0.316,p = 0.036 (Fig. 5B).In contrast, the foreperiod effect was not significantly modulated by Age, although Age increased overall RT (significant main effect of Age; Fig. 5C).A correlation between the Age and the foreperiod-effect index was not significant: r = −0.13,p = 0.401 (Fig. 5D).There was also a significant three-way interaction between Interval duration, BP, and Age (Supplementary Fig. S3), indicating that the lower the Age, the higher BP is associated with a stronger foreperiod effect.
These results suggest that temporal variability is a better predictor of the size of the foreperiod effect than age itself in older adults.While increasing age is associated with slower overall RTs, it may not modulate the foreperiod effect.

LMM Results for Younger Adults
When analyzing younger adults' data, the best-fitting model included Interval duration, BP, and JND, but not Age (Table 3).Figure 6 shows an overall increase in RT with higher JND (significant main effect of JND; Fig. 6A).However, there was neither a significant interaction between Interval duration and JND, nor a significant correlation between JND and the foreperiod-effect index: r = 0.029, p = 0.815 (Fig. 6B).Instead, a negative interaction between Interval duration and BP was significant (Fig. 6C), suggesting a stronger foreperiod effect with higher BP.However, an across-participants correlation between BP and the foreperiod-effect index failed to reach significance: r = −0.213,p = 0.086 (Fig. 6D).
These results suggest that, unlike in older adults, temporal variability is not a significant predictor of the foreperiod effect in younger adults.Instead, the results partially suggest that bias in the temporal representation (i.e., BP) may be related to the size of the foreperiod effect.

Discussion
The aim of this study was to examine the relationship between explicit and implicit timing and how it changes with age.Based on the Bayesian framework, we hypothesized that individuals with higher variability in explicit timing would exhibit a stronger foreperiod effect in implicit timing.Previous studies suggest that older adults tend to rely more on the hazard function than younger adults in implicit timing (Bherer & Belleville, 2004a, b;Capizzi et al., 2022;Droit-Volet et al., 2019).However, the effect of age on the foreperiod effect was only partially supported in the current study.Specifically, while it was confirmed that overall RTs increased with age, there was no significant difference in the foreperiod effect between the younger and older age groups.Meanwhile, we found that temporal variability (i.e., JND) obtained from the time bisection task correlated with the size of the foreperiod effect in older adults, where individuals with higher temporal variability showed a stronger foreperiod effect.This finding seems consistent with our hypothesis.However, this trend was observed only in older adults and not in younger adults.
In younger adults, higher temporal variability was associated with an overall slowing of RT.Increased temporal variability is observed in aging (Turgeon et al., 2016) and in clinical populations (Mioni et al., 2018) and is often discussed as a  (Tales et 2012).While cognitive decline can be excluded as a cause of higher temporal variability in our younger participants, we can still assume interindividual variability in the level of engagement among participants during the task.It is possible that participants who were less engaged in cognitive processing during the task showed higher temporal variability as well as higher RTs.Considering that no measures of cognitive abilities were included for younger participants, future studies should further investigate this aspect.Contrary to our prediction, no evidence supported a link between temporal variability and the foreperiod effect.Unexpectedly, the LMM analysis suggested a foreperiod effect in younger adults with higher BP.In the time bisection task, a shift in the BP is interpreted as bias in temporal representation, where a higher BP suggests an underestimation of physical duration.One possible explanation for the association between the stronger foreperiod effect and the higher BP may be inadequate temporal preparation, particularly for shorter intervals.It is conceivable that participants who underestimate time in the bisection task also underestimate the interval in the foreperiod task.Since temporal preparation for subjectively shorter foreperiods is likely inadequate, participants who underestimated time might show a delay in responses.Moreover, as different neural mechanisms are suggested for the temporal processing of subsecond (i.e., shorter than 1 s) and suprasecond (i.e., longer than 1 s) intervals (Coull et al., 2000;Lewis & Miall, 2003;Miniussi et al., 1999), the underestimation could lead to inadequate temporal preparation only for the subsecond intervals, resulting in delayed responses to those targets and leading to a steeper decrease in RTs as the interval increases.However, since the current study did not have a specific hypothesis regarding the relationship between bias in time perception and temporal preparation, this explanation remains speculative.Future research should systematically address how bias in explicit timing affects implicit timing performance.
In older adults, temporal variability was found to be a better predictor of the size of the foreperiod effect than age itself.This finding is consistent with our hypothesis that increased temporal variability is related to the age-related changes of increased reliance on the hazard function.Previous studies have shown that variability in explicit timing is associated with attentional capacity and cognitive decline (Capizzi et al., 2022;Droit-Volet & Coull, 2016;Droit-Volet et al., 2019), whereas the degree of reliance on the hazard function is not accounted for by either of these factors (Capizzi et 2022;Droit-Volet & Coull, 2016;Droit-Volet et al., 2019).Therefore, it is possible that temporal variability itself is causally related to the degree of reliance on temporal prediction guided by the hazard function.On the other hand, the general increase in RTs with increasing age is likely related to general motor slowing associated with aging (Falkenstein et al., 2006).Unlike younger adults, the effect of the BP on the foreperiod effect interacted with age.Although it is difficult to provide a plausible explanation for this interaction, the overall direction of the effect was consistent with that observed in younger adults; a stronger foreperiod effect associated with a higher BP (i.e., underestimation of time) in younger individuals.Therefore, a similar mechanism may partly be involved in younger and older adults.
Overall, our data show that the different components of explicit timing predict the performance of implicit timing in younger and older adults.This dissociation suggests that they may employ different cognitive strategies in simple RT tasks like the foreperiod task (Bherer & Belleville, 2004a, b).For example, younger adults may afford sensory information more weight, while older adults may overweight prior predictions (Moran et al., 2014;Wolpe et al., 2016;Zanto et al., 2011).According to this explanation, the reason why temporal variability did not predict the foreperiod effect in younger adults could be that they did not adopt a strategy of adjusting the weight on predictions in such a simple RT task with little cognitive demand (Droit-Volet et al., 2019).In contrast, the association between temporal variability and the foreperiod effect in older adults might reflect a cognitive strategy of relying on predictions to compensate for reduced sensory precision, regardless of the task (Turgeon et al., 2016;Wolpe et al., 2016).Future studies should examine at what stage in aging such dissociation emerges, using samples that include a wider range of age groups.
A major limitation of our study is that we did not formulate a hypothesis that connects explicit and implicit timing from which detailed quantitative predictions are derived.Nevertheless, our study is the first to examine the relation between explicit and implicit timing using a within-subject design in younger and older adults.Future research needs to connect computational models that have been proposed separately in explicit (e.g., Cicchini et al., 2012;Jazayeri & Shadlen, 2010;Maaß et al., 2021;Shi et al., 2013) and implicit timing (e.g., Visalli et al., 2019Visalli et al., , 2021) ) and develop a formal model that predicts timing behavior in general.Furthermore, the current study did not measure general cognitive or sensorimotor abilities.As the potential influence of mediating variables between high temporal variability and strong foreperiod effects cannot be completely ruled out, future studies should investigate the presence of such hidden factors by simultaneously measuring cognitive and sensorimotor abilities, along with explicit and implicit timing performances.
In conclusion, our study extends the understanding of the relationship between explicit and implicit timing by showing that different components of explicit timing are associated with implicit timing performance in younger and older adults.In younger adults, bias in temporal representations rather than variability was related to implicit timing.In older adults, increased variability in temporal representations was associated with increased reliance on temporal prediction, which could be explained by the Bayesian optimization framework.

Figure 2 .
Figure 2. Results of the time bisection task.Distribution of R 2 (A), BP (B), and JND (C) for younger and older age groups.The left panel shows data from all participants with outlier participants highlighted with triangles.The right panel shows data after excluding the outlier participants.Note that the outlier participants were excluded based on BP and JND.

Figure 3 .
Figure 3. Results of the foreperiod task.(A) The mean log-RTs for younger and older age groups.Black connected circles indicate the across-participants mean of the log-RTs.Each small circle indicates the mean log-RT for each individual.(B) Distribution of the foreperiod-effect index (i.e., the slope of the linear regression) for younger and older age groups.

Figure 4 .
Figure 4. Results of the LMM analysis for both younger and older adults.The log-RT as a function of Interval duration derived from the best-fitting LMM is plotted.(A) The interaction between Interval duration and JND was significant.(B) The interaction between Interval duration and Age as well as the main effect of Age was significant.The plots show the marginal mean and the 95% confidence interval of the first predictor (i.e., Interval duration) at one standard deviation above (+1SD) and below (−1SD) the mean and at the mean itself of the second predictor (i.e., JND and Age).

Figure 5 .
Figure 5. Results of the LMM analysis and the correlation analysis for older adults.(A) The interaction between Interval duration and JND was significant.(B) Across-participants correlation between JND and the foreperiod-effect index.(C) The main effect of Age was significant, but the interaction between Interval duration and Age was not significant.(D) Across-participants correlation between Age and the foreperiod-effect index.In (B) and (D), each small circle represents an individual's data.The solid line indicates a best-fitting regression line.

Figure 6 .
Figure 6.Results of the LMM analysis and the correlation analysis for younger adults.(A) The main effect of JND was significant, but the interaction between Interval duration and JND was not significant.(B) Across-participants correlation between JND and the foreperiod effect index.(C) The interaction between Interval duration and BP was significant.(D) Across-participants correlation between BP and the foreperiod effect index.In (B) and (D), each small circle represents an individual's data.The solid line indicates a best-fitting regression line.

Table 1 .
Summary of the LMM results for both younger and older adults (N = 110).

Table 2 .
Summary of the LMM results for older adults (N = 44).Downloaded from Brill.com 05/05/2024 12:38:43PM via Open Access.This is an open access article distributed under the terms of the CC BY 4.0 license.https://creativecommons.org/licenses/by/4.0/marker of cognitive changes

Table 3 .
Summary of the LMM results for younger adults (N = 66).