Lecture © John Brzustowski
BIOL 606 Session, University of Alberta, April 12, 2000
There are several possible goals of integrating fossil stratigraphic information with reconstructed phylogenies:
The first quantitative method for assessing agreement between fossils and phylogeny (of those I surveyed, at least) is the Spearman Rank Correlation1 (SRC). This is the classical (Pearson) correlation coefficient applied to n pairs of ranks (Rf, Rp). Each pair corresponds to one taxon: Rf is the rank of that taxon in the fossil record (1 = earliest taxon to appear, n = most recent); and Rp is the rank of that taxon in the phylogeny (1 = most basal taxon, n = most derived taxon). SRC ranges from -1 to 1, representing complete disagreement (earliest clades branched most recently) to complete agreement (most recent clades are most derived). Unfortunately, the range of possible SRC values depends on tree topology, so comparisons of SRC between phylogenies is problematic. Moreover, ranking the fossil range data discards the magnitudes of age differences, thereby losing information.
The Stratigraphic Consistency Index2 (SCI) is similar to SRC, but is based on the n-1 clades in a tree, and is the fraction of these which are consistent with the fossil stratigraphic record. A clade is consistent if the earliest appearance of any taxon in that clade is later than the earliest appearance of any taxon in its sister clade. SCI suffers from the same problems as SRC.
Other proposed measures of fossil/phylogeny consensus use differences in dates of first appearance in the fossil record, rather than just their ranks. They all use a number called variously the Stratigraphic Debt (SD) or Minimum Implied Gap (MIG), which is the sum of all Ghost Ranges implied by the phylogeny. If two sister clades have different dates of earliest appearance in the fossil record, the associated ghost range is the magnitude of the difference between these dates. The implication is that the later appearing clade did not yield any fossils during a period when it must have existed, and our cladogram therefore makes a hypothesis of non-preservation. The SD is measured in units corresponding to a division of the fossil record into stratigraphic zones, so each time a lineage passes through a zone without leaving us a fossil, the SD increases by one.
The following consensus measures differ only in how they scale SD to allow comparison between different cladograms and datasets:
In all three cases, a significance test can be obtained by permuting first occurrence dates among taxa in all possible ways (or a random subset thereof) and asking how often one observes as large (or small) a consensus measure as was obtained with the non-permuted data.
One simulation study6 uses a simple model of evolution and preservation to ask whether the use of admittedly incomplete fossil information can at least in principal yield trees closer to the true phylogeny than can purely morphological cladistics. While the results are strongly affirmative, the evolutionary model is ad hoc, much of the model's parameter space was not explored, and the issue of whether ancestors are to be allowed in the phylogenetic reconstructions is not addressed.
A recent approach7 uses a Maximum Likelihood (ML) model, with preservation and extinction probabilities (per taxon per stratigraphic layer) as parameters, to assign probabilities to cladograms of various lengths. Effectively, SD has been added as a character, with one unit of SD given equal weight to one character state transition, and the method seeks a tree for which this hybrid length has maximum likelihood, given estimates of the preservation and extinction probabilities. Unfortunately, the method of computing ML is ad hoc due to the computational infeasibility of doing so correctly.