A downcore increase in time averaging is the null expectation from the transit of death assemblages through a mixed layer

Understanding how time averaging changes during burial is essential for using Holocene and Anthropocene cores to analyze ecosystem change, given the many ways in which time averaging affects biodiversity measures. Here, we use transition-rate matrices to explore how the extent of time averaging changes downcore as shells transit through a taphonomically complex mixed layer into permanently buried historical layers: this is a null model, without any temporal changes in rates of sedimentation or bioturbation, to contrast with downcore patterns that might be produced by human activity. Assuming stochastic burial and exhumation movements of shells between increments within the mixed layer and stochastic disintegration within increments, we find that almost all combinations of net sedimentation, mixing, and disintegration produce a downcore increase in time averaging (interquartile range [IQR] of shell ages), this trend is typically associated with a decrease in kurtosis and skewness and by a shift from right-skewed to symmetrical age distributions. A downcore increase in time averaging is thus the null expectation wherever bioturbation generates an internally structured mixed layer (i.e., a surface, well-mixed layer is underlain by an incompletely mixed layer): under these conditions, shells are mixed throughout the entire mixed layer at a slower rate than they are buried below it by sedimentation. This downcore trend created by mixing is further amplified by the downcore decline in disintegration rate. We find that transition-rate matrices accurately reproduce the downcore changes in IQR, skewness, and kurtosis observed in bivalve assemblages from the southern California shelf. The right-skewed shell age-frequency distributions typical of surface death assemblages - the focus of most actualistic research - might be fossilized under exceptional conditions of episodic anoxia or sudden burial. However, such right-skewed assemblages will typically not survive transit through the surface mixed layer into subsurface historical layers: they are geologically transient. The deep-time fossil record will be dominated instead by the more time-averaged assemblages with weakly skewed age distributions that form in the lower parts of the mixed layer.