Directionality in distribution and temporal structure of variability in skill acquisition

Masaki O. Abe, Dagmar Sternad

Observable structure of variability presents a window into the underlying processes of skill acquisition, especially when the task affords a manifold of solutions to the desired task result. This study examined skill acquisition by analyzing variability in both its distributional and temporal structure. Using a virtual throwing task, data distributions were analyzed by the Tolerance, Noise, Covariation-method (TNC); the temporal structure was quantified by autocorrelation and detrended fluctuation analysis (DFA). We tested four hypotheses: (1) Tolerance and Covariation, not Noise, are major factors underlying long-term performance improvement. (2) Trial-to-trial dynamics in execution space exhibits preferred directions. (3) The direction-dependent organization of variability becomes more pronounced with practice. (4) The anisotropy is in directions orthogonal and parallel to the solution manifold. Results from 13 subjects practicing for 6 days revealed that performance improvement correlated with increasing Tolerance and Covariation; Noise remained relatively constant. Temporal fluctuations and their directional modulation were identified by a novel rotation method that was a priori ignorant about orthogonality. Results showed a modulation of time-dependent characteristics that became enhanced with practice. However, this directionality was not coincident with orthogonal and parallel directions of the solution manifold. A state-space model with two sources of noise replicated not only the observed temporal structure but also its deviations from orthogonality. Simulations suggested that practice-induced changes were associated with an increase in the feedback gain and a subtle weighting of the two noise sources. The directionality in the structure of variability depended on the scaling of the coordinates, a result that highlights that analysis of variability sensitively depends on the chosen coordinates.