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

1. 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.

1. 化石记录（fossil record）中观测到的模式，不仅反映宏观演化动力学（macroevolutionary dynamics），同时也体现化石保存模式（preservation patterns）。采样率（sampling rates）的变化并非仅随时间推移或在主要分类群（major taxonomic groups）间产生差异，还存在于同一时间间隔内的地理与环境梯度中，以及演化支（clade）内部的不同物种之间。基于收录含化石标本馆藏的大型物种出现数据库，我们可量化某一演化支内不同物种的单馆藏采样率（per-collection sampling rates）差异。本研究不仅针对不同时间/地层间隔（stratigraphic intervals）分别开展此类分析，还会在同一时间/地层间隔内，针对不同地理或生态单元展开独立分析。随后，我们将基于单馆藏采样率的分布特征，重新评估每百万年采样率（per-million-year sampling rates）。
2. 我们采用简单的分布模型——几何分布（geometric）与对数正态分布（lognormal），基于适宜含化石产地（fossiliferous localities）的物种出现数据，评估单产地采样率分布（per-locality sampling rate distributions）的通用模型。此类分析不仅按地质时代划分，还结合通用生物地理单元（biogeographic units）进行拆解，以兼顾空间与物种间的采样率差异。
3. 我们将上述方法应用于取自古生物学数据库（Paleobiology Database）及新旧世界化石哺乳动物数据库（New and Old Worlds fossil mammal database）的中新生代哺乳动物（Meso-Cenozoic mammals）出现数据。研究发现，所有分布式采样率模型的表现均远优于最优均匀采样率模型，其中对数正态分布模型在总结采样率特征方面表现尤为出色。此外我们还证实，同一时代的不同生物地理单元间，对数正态分布的差异较为显著。
4. 为展示此类采样率的应用价值，我们结合地层学与形态学数据，评估了北美与欧亚大陆基干始新世-渐新世食肉形类哺乳动物（carnivoramorphan mammals）的最可能分化时间（divergence times）。该分析结果允许未被采样的分类群或已采样谱系的未采样部分存在于任一大陆，同时兼顾了物种间的采样率差异。我们通过不同方式利用地层似然值对比五种模型，以阐明其对宏观演化推论（macroevolutionary inferences）的潜在影响。