Lecture © Jonathan M. G. Perry
BIOL 606 Session, University of Alberta, March 29, 2000
By all accounts, the fossil record is incomplete, and there are several different ways in which it is incomplete. However, the fossil record &endash; though incomplete &endash; is perfectly adequate for many purposes (e.g., for proving dinosaurs did not coexist with humans) (Paul, 1998). The fossil record is inadequate for other purposes (e.g., for reconstructing the soft tissues of many organisms). Therefore, statistical tests are used to assess the degree to which the fossil record is incomplete.
Some statistical methods test completeness by comparing the known ranges of taxa to their inferred ranges based on phylogenetic tree topologies. Some claim to do the former without referring to a tree, by rather base estimates of true taxon duration on models of constant extinction over time. Others look at the ratio of taxa with a fossil record: taxa without a fossil record (within some higher-level taxon).
Foote and Sepkoski (1999) compare two statistical methods for testing the completeness of the fossil record. Their first method (Foote and Raup, 1996) estimates the probability of preservation (per time interval) of a single genus within a class of organisms. Assuming a constant rate of extinction and assuming all members of a class preserve equally well, long-lived taxa will be fewer than short-lived ones. This gives a uniformly curved (with a negative slope) frequency distribution for the original durations of all genera within the class, where the x-axis is the arbitrary intervals of time during which genera lived.
Given a low probability of preservation (per interval) for all genera, the resulting frequency distribution of fossil ranges for genera (within the class studied) will strongly-favour short ranges. However, with a high probability of preservation per interval, the frequency distribution will be more evenly curved - closely resembling the frequency distribution for original durations. Given known fossil ranges for genera within a particular class, the true value of R (=probability of preservation per interval) for that class can be estimates from the proportions of taxa with a fossil range of one, two and three intervals of time. The formula is: R = f(2)2 / f(1)f(3).
Assuming intervals of 5.5 million years and 5.3 million years, Foote and Sepkoski (1999) plot values of R on the y-axis for a number of classes of animals against a measure of the proportion of the living families (within a given class) that have a fossil record. The data from the two methods correlate positively, suggesting that both methods are measuring a common phenomenon: preservability. Most classes fall just below the line of unit slope because a family is more 'preservable' than a genus (more species = more individuals = more opportunity for preservation) and because the x-axis method looks at a greater slice of time (most families are longer-lived than 5.4 million years).
Outliers that score high using the y-axis method (e.g., cephalopods) contain many soft-bodied families, with some very preservable, hard-bodied families. Sharks are an outlier that scores high on the x-axis method because the high frequency of early sharks known from only one stratigraphic horizon lowers the R-value for that class. Classes that are common biostratigraphic indicators score high on the y-axis method as they are highly preservable. Because of the positive correlation between two very different methods, using different data sets, both methods are inferred to be useful measures of completeness.
The unrealistic model assumed by Foote and Raup's (1996) method (i.e., uniform preservation and constant rate of extinction) gives us reason to wonder, "how realistic are the results it gives?". If preservation is uniform within a class (which it is not) and if extinction proceeds at a constant rate (which seems unlikely) then the Foote and Raup method stands on solid ground. Both methods fail to test some types of completeness; such as, completeness of the population of the genus, completeness of the rock record, etc.. Therefore neither of these methods is the answer to all our questions about the completeness of the fossil record.
Foote, M. and Raup, D. M. 1996. Fossil preservation and the stratigraphic ranges of taxa. Paleobiology 22(2): 121-140
Foote, M. and Sepkoski, J. Jr. 1999. Absolute measure of the completeness of the fossil record. Nature 398: 415-417
Paul, C. R. C. 1998. Adequacy, completeness and the fossil record. In The Adequacy of the Fossil Record. Edited by S. K. Donovan and C. R. C. Paul. John Wiley and Sons. New York, pp. 1-22.
Rapporteur: Curt Strobeck