Charles Darwin understood that evolution was a slow and gradual process. By gradual, Darwin did not mean "perfectly smooth," but rather, "stepwise," with a species evolving and accumulating small variations over long periods of time until a new species was born. He did not assume that the pace of change was constant, however, and recognized that many species retained the same form for long periods. Still, if evolution is gradual, there should be a fossilized record of small, incremental changes on the way to a new species.
Although the sudden appearance of species and its relationship to speciation was proposed and identified by Mayr in historians of science generally recognize the Eldredge and Gould paper as the basis of the new paleobiological research program.
I coined the term punctuated equilibrium and wrote most of our paper, but Niles is the proper first author in our pairing of Eldredge and Gould. Other parts are harder to reconstruct.
Gould edited the entire manuscript for better consistency. We sent it in, and Schopf reacted strongly against it—thus signaling the tenor of the reaction it has engendered, though for shifting reasons, down to the present day.
Rate of evolution The fossil record includes well documented examples of both phyletic gradualism  and punctuational evolution. Based on paleontological evidence it has remained unchanged, even at the level of fossilized nuclei and chromosomes, for at least million years.
Smaller populations on the other hand, which are isolated from the parental stock, are decoupled from the homogenizing effects of gene flow.
In addition, pressure from natural selection is especially intense, as peripheral isolated populations exist at the outer edges of ecological tolerance. If most evolution happens in these rare instances of allopatric speciation then evidence of gradual evolution in the fossil record should be rare.
This hypothesis was alluded to by Mayr in the closing paragraph of his paper: Rapidly evolving peripherally isolated populations may be the place of origin of many evolutionary novelties. Their isolation and comparatively small size may explain phenomena of rapid evolution and lack of documentation in the fossil record, hitherto puzzling to the palaeontologist.
As time went on biologists like Gould moved away from wedding punctuated equilibrium to allopatric speciation, particularly as evidence accumulated in support of other modes of speciation.
Gould was initially attracted to I. However this hypothesis was rejected over time,  as evidence accumulated against it. But the change between generations does not accumulate. Instead, over time, the species wobbles about its phenotypic mean.
Both macromutation and relatively rapid episodes of gradual evolution could give the appearance of instantaneous change, since 10, years seldom registers in the geological record.
Transitional forms are generally lacking at the species level, but they are abundant between larger groups. First, punctuated equilibrium was more modest in scope, in that it was addressing evolution specifically at the species level. Lastly, and perhaps most significantly, quantum evolution took no position on the issue of stasis.
Although Simpson acknowledged the existence of stasis in what he called the bradytelic mode, he considered it along with rapid evolution to be unimportant in the larger scope of evolution. The state of rest, as in bradytely, is the exception and it seems that some restraint or force must be required to maintain it.
To this end, Gould later commented that "Most of our paleontological colleagues missed this insight because they had not studied evolutionary theory and either did not know about allopatric speciation or had not considered its translation to geological time.
Our evolutionary colleagues also failed to grasp the implication sprimarily because they did not think at geological scales". His first point is to argue that phyletic gradualism — understood in the sense that evolution proceeds at a single uniform rate of speed, called "constant speedism" by Dawkins — is a "caricature of Darwinism"  and "does not really exist".
Variable speedism may also be distinguished one of two ways:Punctuated gradualism is a microevolutionary hypothesis that refers to a species that has "relative stasis over a considerable part of its total duration [and] underwent periodic, relatively rapid, morphologic change that did not lead to lineage branching".
Introduction Has the evolution of life proceeded as a gradual stepwise process, or through relativelylong periods of stasis punctuated by short periods of rapid evolution? To date, what is clear isthat both evolutionary patterns – phyletic gradualism and punctuated equilibrium have playedat least some role in the evolution of life.
In modern biology, stasis refers primarily to a relative lack of evolutionary change over a long period during the history of a species. It is one of the key facets of macroevolution, or evolution that takes place at or above the level of the species.
The relative importance of punctuated and gradual patterns of evolution is a subject of debate and research. Punctuated Equilibrium: are the processes that produce rapid evolution.
Abstract The fossil record displays remarkable stasis in many species over long time periods, yet studies of extant populations often reveal rapid phenotypic evolution and genetic differentiation among populations. Recent advances in our understanding of the fossil record and in population genetics and evolutionary ecology point to the complex .
Although Simpson acknowledged the existence of stasis in what he called the bradytelic mode, he considered it (along with rapid evolution) to be unimportant in the larger scope of evolution.
In his Major Features of Evolution Simpson stated, "Evolutionary change is so nearly the universal rule that a state of motion is, figuratively, normal in.