In our dynamic world, decisions about noisy stimuli can require temporal accumulation of evidence to identify steady signals, differentiation to detect unpredictable changes in those signals, or both. Normative models can account for learning in these environments but have not yet been applied to faster decision processes. We present a novel, normative formulation of adaptive learning models that forms decisions by acting as a leaky accumulator with non-absorbing bounds. These dynamics, derived for both discrete and continuous cases, depend on the expected rate of change of the statistics of the evidence and balance signal identification and change detection. We found that, for two different tasks, human subjects learned these expectations, albeit imperfectly, then used them to make decisions in accordance with the normative model. The results represent a unified, empirically supported account of decision-making in unpredictable environments that provides new insights into the expectation-driven dynamics of the underlying neural signals.DOI: http://dx.doi.org/10.7554/eLife.08825.001

Adult zebra finch songs consist of stereotyped sequences of syllables. Although some behavioral and physiological data suggest that songs are structured hierarchically, there is also evidence that they are driven by nonhierarchical, clock-like bursting in the premotor nucleus HVC (used as a proper name). In this study, we developed a semiautomated template-matching algorithm to identify repeated sequences of syllables and a modified dynamic time-warping algorithm to make fine-grained measurements of the temporal structure of song. We find that changes in song length are expressed across the song as a whole rather than resulting from an accumulation of independent variance during singing. Song length changes systematically over the course of a day and is related to the general level of bird activity as well as the presence of a female. The data also show patterns of variability that suggest distinct mechanisms underlying syllable and gap lengths: as tempo varies, syllables stretch and compress proportionally less than gaps, whereas syllable-syllable and gap-gap correlations are significantly stronger than syllable-gap correlations. There is also increased temporal variability at motif boundaries and especially strong positive correlations between the same syllables sung in different motifs. Finally, we find evidence that syllable onsets may have a special role in aligning syllables with global song structure. Generally, the timing data support a hierarchical view in which song is composed of smaller syllable-based units and provide a rich set of constraints for interpreting the results of physiological recordings.

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Pupils tend to dilate in response to surprising events, but it is not known whether these responses are primarily stimulus driven or instead reflect a more nuanced relationship between pupil-linked arousal systems and cognitive expectations. Using an auditory adaptive decision-making task, we show that evoked pupil diameter is more parsimoniously described as signaling violations of learned, top-down expectations than changes in low-level stimulus properties. We further show that both baseline and evoked pupil diameter is modulated by the degree to which individual subjects use these violations to update their subsequent expectations, as reflected in the complexity of their updating strategy. Together these results demonstrate a central role for idiosyncratic cognitive processing in how arousal systems respond to new inputs and, via our complexity-based analyses, offer a potential framework for understanding these effects in terms of both inference processes aimed to reduce belief uncertainty and more traditional notions of mental effort.

Motor variability often reflects a mixture of different neural and peripheral sources operating over a range of timescales. We present a statistical model of sequence timing that can be used to measure three distinct components of timing variability: global tempo changes that are spread across the sequence, such as might stem from neuromodulatory sources with widespread influence; fast, uncorrelated timing noise, stemming from noisy components within the neural system; and timing jitter that does not alter the timing of subsequent elements, such as might be caused by variation in the motor periphery or by measurement error. In addition to quantifying the variability contributed by each of these latent factors in the data, the approach assigns maximum likelihood estimates of each factor on a trial-to-trial basis. We applied the model to adult zebra finch song, a temporally complex behavior with rich structure on multiple timescales. We find that individual song vocalizations (syllables) contain roughly equal amounts of variability in each of the three components while overall song length is dominated by global tempo changes. Across our sample of syllables, both global and independent variability scale with average length while timing jitter does not, a pattern consistent with the Wing and Kristofferson (1973) model of sequence timing. We also find significant day-to-day drift in all three timing sources, but a circadian pattern in tempo only. In tests using artificially generated data, the model successfully separates out the different components with small error. The approach provides a general framework for extracting distinct sources of timing variability within action sequences, and can be applied to neural and behavioral data from a wide array of systems.