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This fish does not appear to have undergone modifications for a hundred million years
a coelacanth fossil
A pillar of Darwin's theory of evolution is the claim that evolution proceeds by the continuous accumulation of very small changes each of which confers a reproductive advantage to individuals possessing that change. Gould and Eldredge with their theory of punctuated equilibrium challenged the notion that evolution is a "continuous accumulation".
A longish title for Darwin's theory might be "Evolution is descent with modification from a common ancestor." Darwin's great success, in his lifetime, was to persuade scientists that all life on Earth descended from a single common ancestor. Where Darwin and his followers have always had trouble is explaining the source of modifications and the mechanism through which modifications spread through populations.
Darwin proposed natural selection as the mechanism of evolution. His claim was that modifications are associated with greater or lesser reproductive success. Those modifications whose bearers have more than the average number of offspring that live to themselves have offspring will increase in incidence in a population. Those modifications associated with relative reproductive failure will decline in incidence. Today, the claim that natural selection is THE mechanism of evolution is controversial.
Darwin had no idea as to how these modifications might arise. He was certain that evolution required numerous, successive, small modifications. That is Darwin was a gradualist. He also believed that these small changes occurred continuously, so there would be individuals in each generation with small modifications on which natural selection would act.
Richard Dawkins explains the concepts of continuous gradual change and common descent well in the chapter "Dogs, Cows, and Cabbages" of The Greatest Show on Earth. He imagines following a rabbit lineage backwards in time. Each generation of parents is imperceptibly different from their children, but as one goes further and further back in time, while the difference between successive generations is tiny, if present at all, the 'ancestor' rabbits begin to look quite different from modern rabbits
Eventually, in this thought experiment, one arrives at an ancestor animal, the common ancestor of rabbits and, say, leopards. Dawkins calls this the 'hairpin' animal. If one follows the other limb of the hairpin forward, once again the differences between successive generations are tiny but after a large number of generations the animals are 'leopard like' and finally we arrive at modern leopards.
Gould and Eldredge did not deny that continuous gradual change could happen. Their point was that the fossil record showed that some species persisted in a state of stasis for many millions of years. On the flip side, genuine evolutionary change, the appearance of modifications, took place relatively quickly over millions or a few tens of millions of years- time intervals that were short compared to the periods of stasis.
The problem stasis presents to standard evolutionary theory is that from time to time in at least some species evolution gets 'stuck' and external events that might be expected to change selection pressures (such as dramatic environmental change) have no effect in the sense that they do not generate modifications.
It does seem, with the few "living fossil" species such as coelacanths and tuatara, alive today that genetic mutations or change continue to occur, and this is the central issue. It is with the mechanism by which modifications develop rather than with the idea of evolution as descent with modification from a common ancestor. It seems that natural selection acting on accumulated minute changes is not always enough to produce modifications.