WHERE DOES THE TIME GO: MIXING AND THE DEPTH-DEPENDENT DISTRIBUTION OF FOSSIL AGES

Knowing how time is distributed within the fossil record is fundamental to paleobiological inference. This has prompted increasing efforts to quantify rates of specimen loss from modern age frequency distributions and thereby bracket the temporal resolution of sub-fossil and fossil assemblages. Here we present and test a model for the formation of bounded fossil sequences that provides a mechanistic understanding of how time becomes distributed across strata. By adding to the dimension of time the dimensions of specimen age and depth, our model predicts that age-frequency distributions will exhibit a secular trend from right- to left skew and decreasing kurtosis with increasing stratigraphic depth. We confirm these predictions using empirical age-frequency distributions of 80 kangaroo rat (Dipodomys sp.) femora, dated by AMS ¹⁴C, from the modern to early Holocene record of Homestead Cave, Utah. Our results provide the first quantitative evaluation of age-frequency distributions in a terrestrial system and offer several new insights into the relationship between stratum depth and time-averaging, the implications of which are broad-reaching across marine and terrestrial systems. In particular, we show: (i) how survivorship-only models fit to surficial strata overestimate specimen decay rates because age-frequency distribution shape is dependent on both decay and vertical mixing, (ii) how the temporal resolution of near-surface assemblages is finer than has been previously assumed, and (iii) how mixing imposes a null expectation for the dynamics of biodiversity over time. More specifically, biodiversity dynamics observed across a faunal sequence may be a consequence of time-averaging rather than true biological signal. Accounting for the influence of time-averaging is thus important for using subfossil and fossil assemblages to interpret the structure of modern ecological systems in the context of the past.