Modelling distributions of fossil sampling rates over time, space and taxa: assessment and implications for macroevolutionary studies

Abstract

Summary1. Observed patterns in the fossil record reflect not just macroevolutionary dynamics, but preservation patterns. Sampling rates themselves vary not simply over time or among major taxonomic groups, but within time intervals over geography and environment, and among species within clades. Large databases of presences of taxa in fossil-bearing collections allow us to quantify variation in per-collection sampling rates among species within a clade. We do this separately not just for different time/stratigraphic intervals, but also for different geographic or ecologic units within time/stratigraphic intervals. We then re-assess per-million-year sampling rates given the distributions of per-collection sampling rates 2. We use simple distribution models (geometric and lognormal) to assess general models of per-locality sampling rate distributions given occurrences among appropriate fossiliferous localities. We break these down not simply by time period, but by general biogeographic units in order to accommodate variation over space as well as among species. 3. We apply these methods to occurrence data for Meso-Cenozoic mammals drawn from the Paleobiology Database and the New and Old Worlds fossil mammal database. We find that all models of distributed rates do vastly better than the best uniform sampling rates and that the lognormal in particular does an excellent job of summarizing sampling rates. We also show that the lognormal distributions vary fairly substantially among biogeographic units of the same age. 4. As an example of the utility of these rates, we assess the most likely divergence times for basal (Eocene-Oligocene) carnivoramorphan mammals from North America and Eurasia using both stratigraphic and morphological data. The results allow for unsampled taxa or unsampled portions of sampled lineages to be in either continent and also allow for the variation in sampling rates among species. We contrast five models using stratigraphic likelihoods in different ways to summarize how they might affect macroevolutionary inferences.

A dynamic global equilibrium in carnivoran diversification over 20 million years

“…Another limitation is that we do not have many of the traits available to neontologists to delimit species; therefore, fossil species have the potential to be both over-and under-split. Ideally, molecular phylogenetic approaches and modelling observed fossil ocurrences need to be integrated to make best use of data from both extant and extinct organisms [32,45].…”

“…However, Wagner & Marcot [45] recently found that within-interval recovery rates for fossil mammals are best described by lognormal, not uniform, distributions, indicating this assumption is likely to be violated. One way to potentially include such details in this framework is to hypothesize factors that strongly contribute to species preservation/sampling and incorporate these factors as covariates in CMR models.…”

The non-uniformity of fossil preservation

“…Perhaps the most straightforward is to use databases to partition the data and develop per-locality sampling rate distributions that capture environmental, geographical and temporal variations in fossil recovery [5]. For example, Wagner & Marcot [5] calculated separate lognormal rates of recovery with the data binned by stage and continent, and using lepidosauromorphs (lizards, snakes, etc.) as a taphonomic/ecological control taxa for mammals, the subject of their study.…”

“…Likewise, partitioning the data by depositional environment may also yield improved results, but such an approach might be hindered by a lack of consistent environmental interpretations as well as problems of overpartitioning, leading to bins with insufficient data. Nonetheless, the approach of Wagner & Marcot [5] shows that considering environmental, geographic and temporal variations in sampling rate is superior to assuming uniform preservation.…”

“…Indirect proxies should be used with caution as they can give a misleading picture of potential fossil recovery where not all strata are 'sampling opportunities' [5], that is, collections from which a clade of interest could have been sampled had they been present. For example, Early Palaeozoic jawless vertebrates have a strong affinity for near-shore terrigenous sandy substrates [103,[105][106][107].…”