A mathematical/computer model was constructed to explore the effects of changes in rates of taphonomic loss, sediment reworking, and burial on time-averaging in fossil deposits. Using a Monte Carlo algorithm, the main controlling variables were thickness of the taphonomically active zone (TAZ; the interval where shells are likely to be destroyed), depth of final burial (DFB; below which shells can no longer be reworked into the TAZ), and burial rate. Output included both the decay trajectory of shells above the DFB as well as the frequency distribution of post-mortem shell ages at final burial (entry into the fossil record). Output was justified ergodically as equivalent to time-averaging in a deposit. The model helps to illuminate several important concepts for time-averaging. For example, it clarifies that DFB and TAZ need not be coincident. In fact, the mechanism of shell sequestering (allowing shells to remain in a safe zone between the TAZ and DFB) as a means of shell survival for 100s or 1000s of years after death requires that DFB be below TAZ. In addition, the model demonstrates the use of a shell's expected residence times above TAZ and DFB as a means of comparing time-averaging from different settings. Lastly, the model focuses attention on the potential variability in time-averaging among fossil deposits created under identical conditions due to stochastic variation. These results indicate the useful role of models in developing a process-based understanding of the nature and controls of time-averaging in fossil accumulations.

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