Taking advantage of time-averaging

Abstract One of the major obstacles in dealing with any form of data derived from fossils is the effects of time-averaging, which are the result of mixing the remains of organisms that did not live contemporaneously. Although this process results in loss of temporal resolution, it also serves to filter out short-term variations. Temporal resolution of a collection depends not only on the range of fossil ages, but also on their frequency distribution. Previous studies of marine molluscs indicate that most shells in an accumulation are relatively young. Such a distribution of shell ages can be fit by an exponential curve (assuming both a constant probability of shell loss and a constant rate of shell addition), which implies that 90% of the shells were added during the last 50% of the time interval represented by the collection. That is to say, differences between two collections can be discerned even if they overlap 50% in time, because the proportion of shells with shared ages is only 10%. Applying the exponential model to previously published data suggests that long-term rates of destruction are controlled by how frequently shells from the taphonomically active zone are re-exposed to rapid destruction. To take advantage of the “noise-filtering” property of time-averaging, samples need to be large enough to catch the full range of environmental variation recorded by an accumulation. A simple probability formula indicates that samples of easily achievable size can give satisfactory time-averaged results depending on the level of confidence and sampling density defined by the researcher.