Quantifying the Uncertainty in Times of Appearance and Disappearance in the Fossil Record: A Bayesian Approach

对局部化石记录的不完备性进行量化最有效的方法是基于施特劳斯和萨德勒()的可信区间方法。这一系列方法(包括马歇尔[1994,1997]的无分布和泛化方法)假定该剖面已连续取样，并且化石基本上可以在该剖面的任何地方找到。然而，在大多数剖面中，这些假设被违反，要么是因为只对剖面的一部分进行了采样(例如，对于岩心数据)，要么是因为化石被限制在特定的层面上，或者是因为地层间隔较窄。作为另一种选择，Weiss和马歇尔(1999)发展了一种贝叶斯方法，用于估计离散采样的局部剖面中分类群的地层终点的不确定性。然而，该方法基于一些过于简单的假设：采集强度在所有采样层位都是相等的；物种在任何时候都保持相同的相对丰度；以及采样的床层没有垂直厚度。此外，我们的方法(和所有其他方法一样)没有利用化石记录中的丰度数据。在这里，我们建议将Weiss和Matt(1999)中提出的方法发展成一系列更复杂的方法，这些方法可以适应化石记录中典型的不均一性，并在记录时利用丰富的数据。我们的最终目标是提供一个可广泛应用于各种问题的统计“工具包”。

0000385MarshallThe most powerful methods for quantifying the incompleteness of the fossil record in local sections are based on Strauss and Sadler's (1989) confidence interval approach. This family of methods (including the distribution-free and generalized methods of Marshall [1994, 1997]) assume that the section has been continuously sampled, and that fossils may be found essentially anywhere in the section. However, in most sections these assumptions are violated, either because only parts of the section have been (e.g., for core data), or can be, sampled, or because fossils are restricted to specific bedding planes, or narrow stratigraphic intervals. As an alternative, Weiss and Marshall (1999) developed a Bayesian approach for estimating the uncertainty in stratigraphic end points of taxa in local sections that have been sampled discretely. However, the method is based on some overly simple assumptions: that collecting intensity is equal at all sampled horizons; that species remain at the same relative abundance at all times; and, that the beds sampled have no vertical thickness. Further, our approach (like all others) does not make use of abundance data in the fossil record.Here we propose to develop the method presented in Weiss and Marshall (1999) into a series of more sophisticated methods that can accommodate the inhomogeneities typically seen in the fossil record, as well as take advantage of abundance data when it is recorded. Our ultimate goal is to provide a statistical "tool-kit" that can be broadly applied to a wide range of problems.