A quantitative model describes the relationship between the average size of biostratigraphic gaps and the size, shape, and number of fossils in a volume of rock: where fossil distribution is random, the mean vertical distance between neighboring fossils exposed in cross-sections (V) should be approximated by the relationship 1/Na(w) where Na is the number of fossils exposed per unit area and w is the width of section observed. Because the number exposed (Na) is itself a function of volumetric fossil abundance (Nv), fossil shape (k), and fossil size (x), we can go further and relate gaps to these factors as well. Thus, V = 1/(Nv)(k)(x)(w). Testing and analysis of this model reveal that: (1) Gap size decreases (and so biostratigraphic resolution increases) as abundance, sphericity, and size of fossils increase; this is because each of these proportionately increases the probability of fossil exposure by a random cross-sectional "slice". (2) The "hollow curve" nature of the function means that where volumetric abundance is slow, small increases in abundance can greatly reduce gap size, but as overall abundance increases, gap size is proportionately less and less affected so that after a point even large increases in abundance have almost no effect on biostratigraphic resolution. For smaller fossils, this stabilization occurs at much larger gap sizes than for larger fossils. However, this can be offset by increasing section width observed. (3) Biostratigraphy essentially "collapses" fossils onto a vertical reference axis, eliminating the horizontal component of their position in two-dimensional space. This is a cumulative process so that all fossils in a section are quickly crowded on the axis, creating a very low mean gap size. The combination of random positioning and very low mean causes the gaps to follow the Poisson distribution often noted in field data. A number of practical uses derive from these observations.