The perturbation model, developed by William K. Estes (1972, 1997), provides a mathematical account of serial order memory in which items are associated with positional codes that undergo random perturbation over time. This stochastic drift produces the characteristic pattern of transposition errors (items recalled in the wrong position), which tend to involve nearby positions rather than distant ones.
The Perturbation Process
Each item in a sequence is tagged with a positional code at the time of encoding. Over time, each item's position code has a probability θ of being perturbed at each time step. When perturbation occurs, the item's code is randomly reassigned to one of the other positions. This creates a Markov process where positional uncertainty grows with time:
After multiple time steps, the probability distribution over positions for each item spreads out, creating a positional uncertainty gradient. Items are most likely to remain in their correct position but have decreasing probability of occupying positions further away.
Transposition Gradients
The model predicts that errors in serial recall should show a characteristic transposition gradient: items are most often displaced to adjacent positions, with displacement probability declining monotonically with distance. This prediction has been confirmed across diverse tasks including immediate serial recall, order reconstruction, and probed recall. The locality of transposition errors is one of the strongest empirical constraints on models of serial order memory.
Temporal Dynamics of Forgetting
Because perturbation accumulates over time, the model predicts that order information degrades gradually while item information may be relatively preserved. This accounts for the finding that delayed serial recall often produces more order errors relative to item errors. The model also predicts that the shape of the transposition gradient should flatten with longer retention intervals, which has been confirmed experimentally.
Extensions and Legacy
Estes' perturbation model was a precursor to modern positional coding models such as the Start-End Model (Henson, 1998) and the SIMPLE model. Lee and Estes (1977) extended the model to account for temporal grouping effects. Nairne (1991) developed a feature-based version where perturbation operates on individual features of positional codes, providing a more graded account of positional uncertainty. The perturbation framework remains influential as a core mechanism in several contemporary models of serial order memory.
A key insight of the perturbation model is that forgetting of serial order need not involve trace decay or loss. Instead, order information is progressively blurred as positional codes drift. The information is degraded but not destroyed, which explains why partial order information is often preserved even when exact recall fails.