Relative Number of Transitional Sequences in the Fossil Record

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.

On the other hand, I do believe that natural selection will always act very slowly, often only at long intervals of time, and generally on only a very few of the inhabitants of the same region at the same time. (CR Darwin, Origin of Species, 1st ed., p.153)

One other consideration is worth notice: with animals and plants that can propagate rapidly and are not highly locomotive, there is reason to suspect, as we have formerly seen, that their varieties are generally at first local; and that such local varieties do not spread widely and supplant their parent-forms until they have been modified and perfected in some considerable degree. According to this view, the chance of discovering in a formation in any one country all the early stages of transition between any two forms, is small, for the successive changes are supposed to have been local or confined to some one spot. Most marine animals have a wide range; and we have seen that with plants it is those which have the widest range, that oftenest present varieties; so that with shells and other marine animals, it is probably those which have had the widest range, far exceeding the limits of the known geological formations of Europe, which have oftenest given rise, first to local varieties and ultimately to new species; and this again would greatly lessen the chance of our being able to trace the stages of transition in any one geological formation. (CR Darwin, Origin of Species, 1st ed., p.306)

I have attempted to show that the geological record is extremely imperfect; that only a small portion of the globe has been geologically explored with care; that only certain classes of organic beings have been largely preserved in a fossil state; that the number both of specimens and of species, preserved in our museums, is absolutely as nothing compared with the incalculable number of generations which must have passed away even during a single formation; that, owing to subsidence being necessary for the accumulation of fossiliferous deposits thick enough to resist future degradation, enormous intervals of time have elapsed between the successive formations; that there has probably been more extinction during the periods of subsidence, and more variation during the periods of elevation, and during the latter the record will have been least perfectly kept; that each single formation has not been continuously deposited; that the duration of each formation is, perhaps, short compared with the average duration of specific forms; that migration has played an important part in the first appearance of new forms in any one area and formation; that widely ranging species are those which have varied most, and have oftenest given rise to new species; and that varieties have at first often been local. All these causes taken conjointly, must have tended to make the geological record extremely imperfect, and will to a large extent explain why we do not find interminable varieties, connecting together all the extinct and existing forms of life by the finest graduated steps. (CR Darwin, Origin of Species, 1st ed., pp.340-341)

        EFR = (NSTP * NSPP * AP * SEVR * FSDP)
        and
        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.