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Punctuated equilibrium is a hypothesis in evolutionary biology which proposes that speciation generally alternates between long periods of stability, and geologically rapid events of evolutionary change. This is in contrast with the classic view of evolution which is seen as smooth and continuous.
It has been argued by some scientists that the Scottish horticulturalist Patrick Matthew had described something very similar to punctuated equilibrium in 1831. The term punctuated equilibrium (PE) was first used by Niles Eldredge and Stephen Jay Gould in their 1972 paper, "Punctuated Equilibria: An Alternative to Phyletic Gradualism," Their model attempted to explain the observation of abrupt appearance and subsequent stability of species in the fossil record. The authors believed that evolutionary biologist Ernst Mayr's allopatric model (see following) explains the rapid speciation that accounts for the patterns observed in the fossil record.
Summary of features
PE predicts that most adaptive change in evolutionary lines occurs via speciation through the mechanism of species selection. Most speciation is accomplished by branching from ancestral species rather than one species gradually changing into another. The hypothesis maintains that most mutations, even beneficial ones, get lost in the broader population and where change does happen it is rare and rapid.
Most speciation occurs via allopatric speciation, that is in a location remote from the ancestral population. Daughter species usually evolve in a small geographic area and during a relatively brief period of time compared to the total lifespan of the species.
Observation of the fossil record reveals that new species overtake an area suddenly, having taken advantage of changes in the environment. Large and successful species usually change very slowly during their total lifespan.
Gould and Eldredge argued that punctuated equilibrium is in contrast to Darwin's version of evolution. They stated, "To Darwin, therefore, speciation entailed the same expectation as phyletic evolution: a long and insensibly graded chain of intermediate forms." Some scholars have argued that Darwin was not a phyletic gradualist.
It is commonly believed that punctuated equilibrium is the opposite of gradualism. However, this is due to a misunderstanding of the definition of gradualism. Although PE is in contrast to phyletic gradualism, that evolution happens slowly and by transformation of species, it is nonetheless a form of gradualism in the sense that it predicts evolution by minor genetic changes between generations.
Some misconceptions of punctuated equilibrium are due to misunderstanding its tenets. PE's tenet of long periods of stasis in a fossil species does not mean that it does not change at all but rather that change varies around a mean and does not accumulate. Likewise PE's tenet that instances of change will appear instantaneous implies that such change will be rapid relative to geological terms but will in reality take many generations to occur.
Punctuated equilibrium is not synonymous with theories of mass extinction, catastrophism, George Gaylord Simpson's quantum evolution, or Richard Goldschmidt's saltationism, which invoked large scale macromutations. PE does not require any new or extreme explanatory mechanisms such as macromutations or saltations but rather relies on the genetic mechanisms for allopatric speciation observed by Ernst Mayr.
Punctuated equilibrium is not an admission that there are no intermediate forms in the fossil record, as claimed by creationists. Gould explains, "Transitional forms are generally lacking at the species level, but they are abundant between larger groups.  PE is founded on the positive evidence of paleontological studies that show periods of stasis and rapid evolution of evolutionary lines.
PE and creationists
Creationists perpetuate many of the misconceptions about punctuated equilibrium. Additionally, creationists characterize punctuated equilibrium as a desperate effort to save the theory of evolution from the apparent contradiction of the lack of transitional fossil forms. For example the website Darwinism Refuted.com reports:
In the 1970s, some paleontologists accepted that...the "gaps" in the fossil record had to be accepted as a reality. However, because these paleontologists were unable to relinquish the theory of evolution, they tried to explain this reality by modifying the theory. And so was born the "punctuated equilibrium" model of evolution, which differs from neo-Darwinism in a number of respects. 
This claim fails to note that modification of a theory is a requirement of the scientific method, and additionally as a theory punctuated equilibrium in fact makes useful predictions that are verifiable by observation of the fossil record.
Creationists have exploited the fact that elements of punctuated equilibrium appear to differ from those of the standard theory of evolution as proposed by Darwin. Taken out of context, quotes from proponents of punctuated equilibrium are presented to make it appear as though scientists doubt the historical fact of evolution. See for example a misquote of Steven Stanley.
The theistic evolution book Natural Creation or Natural Selection?: A Complete New Theory of Evolution claims that the "formative mind" is the cause of punctuated equilibrium and geologically rapid events of evolutionary change.
- Scottish Horticulturalist Patrick Matthew Proposed More Accurate Theory of Gradual Evolution Before Charles Darwin Did, Geologist Argues
- Eldredge, Niles and S. J. Gould (1972). "Punctuated equilibria: an alternative to phyletic gradualism" In T.J.M. Schopf, ed., Models in Paleobiology. San Francisco: Freeman Cooper. pp. 82-115.
- Rhodes, R. H. T. (1983). "Gradualism, punctuated equilibrium and the Origin of Species". Nature 305 (5932): 269–272.
- Gould, Stephen Jay. "Evolution as Fact and Theory". The Unofficial Stephen Jay Gould Archive.
- The Invalidity of Punctuated Equilibrium, Darwinism Refuted.com
- Gould, Stephen Jay. "Opus 200". The Unofficial Stephen Jay Gould Archive.
- Elsberry, Wesley R. (1996). "Punctuated Equilibria". TalkOrigins.
- Douglas, Theobald (2010). "All you need to know about Punctuated Equilibrium (almost)". Brandeis University.
- Stanley, Steven M. (1981). The New Evolutionary Timetable. Basic Books, Inc. New York.