Accounting for the effects of biological variability and temporal autocorrelation in assessing the preservation of species abundance

Quantifying the effects of taphonomic processes on species abundances in time-averaged death assemblages (DAs) is pivotal for paleoecological inference. However, fidelity estimates based on conventional live-dead comparisons are fundamentally ambiguous: (1) data on living assemblages (LAs) are based on a very short period of sampling and thus do not account for biological variability in the LA, (2) LAs are sampled at the same time as the DA and thus do not necessarily reflect past LAs that contributed to the DA, (3) compositions of LAs and DAs can be autocorrelated owing to shared cohorts, and (4) fidelity estimates are cross-scale estimates because DAs are time-averaged and LAs are not. Some portion of raw (total) live-dead (LD) variation in species composition thus arises from incomplete sampling of LAs and from biological temporal variation among LAs (together = premortem component of LD variation), as contrasted with new variation created by interspecific variation in population turnover and preservation rates and by the time-averaging of skeletal input (together = postmortem component of LD variation). To tackle these problems, we introduce a modified test for homogeneity of multivariate dispersions (HMD) in order to (1) account for temporal autocorrelation in composition between LAs and DAs and (2) decompose total LD compositional variation into premortem and postmortem components, and we use simulations to evaluate the contribution of within-habitat time-averaging on the postmortem component. Applying this approach to 31 marine molluscan data sets, each consisting of spatial replicates of LAs and DAs in a single habitat, we find that total LD variation is driven largely by variation among LAs. However, genuinely postmortem processes have significant effects on composition in 25-65% of data sets (depending on the metric) when the effects of temporal autocorrelation are taken into account using HMD. Had we ignored the effects of autocorrelation, the effects of postmortem processes would have been negligible, inflating the similarity between LAs and DAs. Simulations show that within-habitat time-averaging does not increase total LD variation to a large degree it increases total LD variation mainly via increasing species richness, and decreases total LD variation by reducing dispersion among DAs. The postmortem component of LD variation thus arises from differential turnover and preservation and multi-habitat time-averaging. Moreover, postmortem processes have less effect on the compositions of DAs in habitats characterized by high variability among LAs than they have on DAs in temporally stable habitats, a previously unrecognized first-order factor in estimating postmortem sources of compositional variation in DAs.