**Spatial Mechanics of Biostratigraphic Gap Formation**

**Michael L. McKinney**

A quantitative model describes how biostratigraphic gaps form. Specifically,
I show that three aspects of fossils determine the average biostratigraphic gap
size (i.e., average vertical distance between adjacent fossils). These aspects
are the size, shape, and number of fossils in the rock volume. The larger, more
spherical, and more numerous the fossils are, the less the average gap is
between them. Stereological principles show that larger, spherically shaped, and
more numerous particles in a given volume have a greater chance of being
intersected by a random plane (i.e., cross section) and, hence, of being
exposed, which reduces the average gap size. Based on theory and rigorous
mathematical modeling, I show that this relationship may be expressed as G =
0.354/^radical(Nkx), where: G is average gap size; N is number of fossils/unit
volume; k is a fossil shape factor; and x is mean fossil length. Thus, the
inverse relationship between gap size and these factors is * nonlinear*. An
important implication is that small, irregularly shaped fossils must occur in
much greater abundance than large, spherical forms to achieve the same level of
biostratigraphic resolution. For instance, the model indicates that it takes
about 20 times as many 1-cm long rod-shaped fossils to achieve the same average
gap size as 10-cm long spherical forms. Therefore, where the two forms occur in
similar abundances, the smaller, irregular forms ould have an average
biostratigraphic gap about 450% greater than the larger, spherical forms.

AAPG Search and Discovery Article #91043©1986 AAPG Annual Convention, Atlanta, Georgia, June 15-18, 1986.