The shape of time averaging: A meta-analysis of age-distribution moments derived from numerical dating of marine invertebrates

Time averaging (age mixing) is a fundamental attribute of the fossil record that determines the temporal resolution of paleontological samples. In the past three decades numerous case studies have used numerical dating of individual specimens (primarily relying on amino-acid racemization and radiocarbon methods) to quantify time averaging. The samples in those studies were derived either from surficial death assemblages (samples from modern seafloors) or from the recent geological record (samples from late Quaternary sediment cores). We integrated data from numerous dating projects to assess the shape of time averaging (skewness of age distributions) and test the hypothesis that age distributions of the subsurface-fossil and modern-subfossil samples differ in skewness. We used three skewness measures: parametric skewness [SP], median skewness [SM], and L-skewness [SL]. Results based on over 250 sample-level age distributions indicated that right-skewed age distributions are dominant regardless of the burial status. The right-skew tendency was demonstrable for core and seafloor samples (both means and medians of the three skewness estimates were significantly greater than 0; p < 0.001 in all cases; 10000-iteration ABC-Bootstrap). Fossil samples were significantly less skewed than subfossil samples for all mean/median skewness estimates (SP/SM/SL for subfossil samples > SP/SM/SL for fossil samples; p < 0.01 in all cases; 10,000 iteration ABC-Bootstrap). However, all three skewness estimates suggested substantial variation in shapes of age distributions and symmetrical and left-skewed distributions were also present, especially in the subsurface-fossil samples. The results confirm previous case studies and mathematical models postulating that the age structure of time-averaged assemblages predictably evolves during the burial process (surface-to-subsurface transition). However, the substantial variation in skewness indicates that the shape of time averaging is also influenced by other factors, which may include variability in intrinsic skeletal durability, rate of skeletal input, depth and intensity of bioturbation, severity of taphonomic processes, and historical contingency driven by sea-level history. Based on those results, it is expected that age distributions of fossil samples will be frequently, but not always, dominated by younger age cohorts. Consequently, paleontological samples are expected to show a statistical tendency toward overrepresenting populations and communities that lived in the last part of the time-averaged time intervals.