Best-Fit Intervals and Consensus Sequences

Biostratigraphers subdivide geologic time using the sequence of first and last appearances of only a small fraction of the available fossil taxa. Thus, there appears to be considerable scope for improving biostratigraphic resolution simply by incorporating more first and last appearance events. The problem, of course, is that the correct sequence becomes more difficult to determine as the number of events rises. Figure 1 illustrates how a mild example of the problem can be visualized in the form of a tangled fence diagram. It is constructed from the observed ranges of trilobites collected by Palmer (1954) from the Cambrian Riley Formation of Texas. The seven fence posts represent seven different stratigraphic sections. Each wire line connects the horizons of the lowest or highest find of a taxon that has been recovered from adjacent sections. The wire lines cross wherever a pair of events have been preserved in contradictory order in adjacent sections. These Riley data are a classic example of a relatively internally consistent set of range charts. They have become a benchmark for testing and illustrating new quantitative methods: graphic correlation (Shaw, 1964); unitary associations (Guex, 1991); and constrained optimization (Kemple et al., 1995). Nevertheless, 253 of all the possible pairs of first and last appearance events in this data set have been observed in contradictory order. for another 543 pairs, at least one section is equivocal, in the sense that the events are preserved at the same stratigraphic level — a condition that is consistent with either order. Traditionally, the Riley ranges are used to separate only six or seven zones.