The incompleteness of the fossil record hinders the inference of evolutionary rates and patterns. Here, we derive relationships among true taxonomic durations, preservation probability, and observed taxonomic ranges. We use these relationships to estimate original distributions of taxonomic durations, preservation probability, and completeness (proportion of taxa preserved), given only the observed ranges. No data on occurrences within the ranges of taxa are required. When preservation is random and the original distribution of durations is exponential, the inference of durations, preservability, and completeness is exact. However, reasonable approximations are possible given non-exponential duration distributions and temporal and taxonomic variation in preservability. Thus, the approaches we describe have great potential in studies of taphonomy, evolutionary rates and patterns, and genealogy.Analyses of Upper Cambrian-Lower Ordovician trilobite species, Paleozoic crinoid genera, Jurassic bivalve species, and Cenozoic mammal species yield the following results: (1) The preservation probability inferred from stratigraphic ranges alone agrees with that inferred from the analysis of stratigraphic gaps when data on the latter are available. (2) Whereas median durations based on simple tabulations of observed ranges are biased by stratigraphic resolution, our estimates of median duration, extinction rate, and completeness are not biased. (3) The shorter geologic ranges of mammalian species relative to those of bivalves cannot be attributed to a difference in preservation potential. However, we cannot rule out the contribution of taxonomic practice to this difference. (4) In the groups studied, completeness (proportion of species [trilobites, bivalves, mammals] or genera [crinoids] preserved) ranges from 60% to 90%. The higher estimates of completeness at smaller geographic scales support previous suggestions that the incompleteness of the fossil record reflects loss of fossiliferous rock more than failure of species to enter the fossil record in the first place.

中文翻译：

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化石保存和分类群的地层范围

化石记录的不完整性阻碍了进化速率和模式的推断。在这里，我们推导出真实分类持续时间、保存概率和观察到的分类范围之间的关系。我们使用这些关系来估计分类持续时间、保存概率和完整性（保存的分类群的比例）的原始分布，只给定观察到的范围。不需要有关分类群范围内发生的数据。当保存是随机的并且持续时间的原始分布是指数时，持续时间、可保存性和完整性的推断是准确的。然而，考虑到非指数持续时间分布以及可保存性的时间和分类变化，合理的近似值是可能的。因此，我们描述的方法在埋藏学研究中具有巨大潜力，对上寒武统-下奥陶统三叶虫种、古生代海百合属、侏罗纪双壳类和新生代哺乳动物物种的分析得出以下结果：（1）仅从地层范围推断的保存概率与推断的一致当有后者的数据时，对地层差距的分析。(2) 虽然基于观测范围的简单表格的中位持续时间受到地层分辨率的影响，但我们对中位持续时间、灭绝率和完整性的估计没有偏差。(3) 哺乳动物物种相对于双壳类的较短地质范围不能归因于保存潜力的差异。但是，我们不能排除分类实践对这种差异的贡献。(4) 在研究的组中，完整性（物种[三叶虫、双壳类、哺乳动物]或属[海百合]保存的比例）范围从60%到90%。在较小的地理尺度上对完整性的更高估计支持先前的建议，即化石记录的不完整性反映了化石岩石的损失，而不是物种未能首先进入化石记录。