Darwin wrote:
Given the remarkably slow changes in the evolution of species over time, as required by Darwin's hypothesis, what is the probability that millions of fossils collected randomly from a fossil record spanning 650 million years would show a pattern of abrupt appearances and equally abrupt extinction events for most fossil species and that these highly visible fossil species would span an intervening time of many millions of years without any evidence of evolution?Why should not Nature take a sudden leap from structure to structure? On the theory of natural selection, we can clearly understand why she should not; for natural selection acts only by taking advantage of slight successive variations; she can never take a great and sudden leap, but must advance by the short and sure, though slow steps. — Charles Darwin, "On the Origin of Species by Means of Natural Selection, or the Preservation of Favoured Races in the Struggle for Life."
The evolution hypothesis should not be called true science without passing obvious mathematical tests. Suppose that the millions of fossils already collected randomly from the entire fossil record can be sorted and cataloged as belonging to n distinct species S1, S2, S3, … Sn. Let Mi (i=1,2,3, …,n) be the number of fossils discovered for species Si. Assuming that each fossil was taken randomly from a virtually smooth continuum of fossils, how do we measure the likelihood that the fossil record supports the idea that Darwinian evolution took place?
To imagine a 650 million-year timeline is easy. To reasonably estimate the mathematical distribution of catastrophes over time that caused the ancient animals to be fossilized seems doable. What is preventing us from being able to create a mathematical model of the fossil record's creation?
http://www.everythingimportant.org/devolution