Appearance event ordination: a new biochronologic method

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Abstract
The fundamental goal of biochronology is ordering taxonomic first and last appearance events. The most useful biochronologic data are of the form “the first appearance event of one taxon predates the last appearance event of a second taxon” (FAE < LAE). FAE < LAE data sets are unusually reliable because they converge on a unique solution with greater sampling. The fact that the FAE of one taxoni< the LAE of another taxonjalways can be inferred either ifiis found lower thanjin a stratigraphic section, or ifiandjco-occur in at least one taxonomic list. Thus, FAE < LAE data accurately synthesize two disparate sources of information: routine biostratigraphic observations and taxonomic lists that may have no stratigraphic context. Appearance event ordination, the new method introduced here, is intended to summarize FAE < LAE data. The algorithm is founded on the following parsimony criterion: arrangements of FAEs and LAEs should always imply FAEi< LAEjwhen this is known, and otherwise imply LAEj< FAEiwhenever possible. The technique differs from others related to correspondence analysis in its use of FAE < LAE data and explicit definition as a parsimony method. The algorithm is even more unique in that it uses different subsets of FAEi< LAEjstatements at each iterative step, converging on separate sets of scores for the FAEs and LAEs. After arranging either the FAEs or the LAEs on the basis of their scores, the other set of scores can be discarded and the best arrangement of the remaining events can be inferred directly. An analysis of the Plio-Pleistocene mammalian record in the Lake Turkana region is used to illustrate the method. Biochronologic resolution on the order of 0.2-1.5 m.y. is achieved. The Turkana species lists by themselves demonstrate enough FAEi< LAEjrelationships to resolve the basic biochronologic pattern, but stratigraphic information is still of great use.