Relative Number of Transitional Sequences in the Fossil Record

by Wesley R. Elsberry
Last updated: 980413

There is no support that I have seen to indicate that Darwin thought the incompleteness of the fossil record would be remedied by application of more effort. Darwin's argument concerning the incompleteness of the fossil record incorporated both geological and biological factors, including some key principles that are now associated with punctuated equilibria.

The fact is that we do have many examples of transitional sequences available. The idea that all transitional sequences could be found is not one that Darwin would have supported.

Let's derive an expectation of ratio of transitional to non-transitional fossils from what Darwin actually said, shall we? Darwin stated that natural selection would work intermittently, and often only at long intervals.

Darwin addressed geographical distribution of fossils as a factor. In his famous section on the imperfection of the geological record, Darwin gave several further reasons to doubt that we would ever have a complete record of past life. Given these views of Darwin, we can derive an expectation of the ratio of transitional to non-transitional fossils found. I include in the following only those factors which yield a differential expectation of discovery of transitional fossils displaying the action of natural selection.

        EFR = (NSTP * NSPP * AP * SEVR * FSDP)
        ETF = EFR * OFS

        where EFR is the "expected fossil ratio",
        NSTP is the "natural selection time proportion",
        NSPP is the "natural selection population proportion",
        AP is the "area proportion",
        SEVR is the "subsidence vs. elevation variation ratio",
        FSDP is the "formation to species duration proportion",
        ETF is the "expected number of transitional fossils",
        and OFS is the number of "observed fossil species".

Now, we can assign some estimated numbers to the variables listed above. Because Darwin said "often only at long intervals", NSTP should be small. Let's assign a relatively large "small" value of 0.1. Since  Darwin said that natural selection operates on only a very few inhabitants at a time, NSPP should be smaller still than NSTP. Let's assign a value of 0.01. For AP, the area proportion between the geographic extent of a widely ranging species and its local variety, a value of 0.1 is probably an overestimate, but let's leave it at that for the moment. For SEVR, Darwin's text would indicate a value of 0.25 or less would be reasonable. FSDP is something best estimated by a geologist, but Darwin probably felt it to be under 0.5.

Replacing values, we find that

        EFR = 0.1 * 0.01 * 0.1 * 0.25 * 0.5
        EFR = 0.0000125 = 1/80,000

David Raup has estimated the number of catalogued fossil species at 250,000. This allows us to generate an estimate for number of transitional sequences expected under Darwin's own views as:

        ETF = EFR * OFS = 0.0000125 * 250,000 = 3.125

Roger Cuffey's 1974 paper on paleontologic evidence listed references for at least 139 fine-grained species to species transitional sequences. According to an expectation derived from Darwin's own words and values from the real world, it can be seen that the fossils have been rather more forthcoming than one would expect, not less.


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