The "punctuated equilibrium" theory of Niles Eldredge and Stephen Jay Gould was proposed as a criticism of the traditional Darwinian theory of evolution. Eldredge and Gould observed that evolution tends to happen in fits and starts, sometimes moving very fast, sometimes moving very slowly or not at all. On the other hand, typical variations tend to be small. Therefore, Darwin saw evolution as a slow, continuous process, without sudden jumps. However, if you study the fossils of organisms found in subsequent geological layers, you will see long intervals in which nothing changed ("equilibrium"), "punctuated" by short, revolutionary transitions, in which species became extinct and replaced by wholly new forms. Instead of a slow, continous progression, the evolution of life on Earth seems more like the life of a soldier: long periods of boredom interrupted by rare moments of terror.
instead of a slow, continuous movement, evolution tends to be characterized by long periods of virtual standstill ("equilibrium"), "punctuated" by episodes of very fast development of new forms.
Punctuated equilibrium is more an observation than a theory of evolution. However, this observation is easy to explain by using some general insights from the systems approach. Consider a typical fitness landscape, in which there are valleys separated by ridges. If the evolving system has reached the bottom of a deep valley, there will be almost no change, since variation will fail to pull the system out of that hole. This is a negative feedback regime, in which chance fluctuations will be counteracted, pulling the system back to its equilibrium position at the bottom of the valley.
On the other hand, if there is only a small ridge separating the valley from a neighboring, deeper valley, then a chance event may be sufficient to push the system over the edge so that it enters the other valley. Such a lucky variation will become increasingly likely when the fitness landscape changes so as to reduce the height of the ridge. Once over the ridge, the descent into the new valley will go very fast. This is a positive feedback regime in which deviations from the previous position are amplified. This means that the system will evolve very quickly to a new, fitter configuration. If we would check the evolution of the species in the geological record, we would find many fossils corresponding to the position at the bottom of the valley where the organism remained for so long, but few or none corresponding to the crossing of the ridge, which happened very fast on the geological time scale.
The systems approach can help us to understand more profoundly how a small variation can produce a major change. Indeed, organisms, like all systems, are organized in levels, corresponding to their subsystems and subsubsystems. Each subsystem is described by its own set of genes. A mutation in one of the components at the lower levels will in general have little effect on the whole. On the other hand, a mutation at the highest level, where the overall arrangement of the organism is determined, may have a spectacular impact. For example, a single mutation may turn a four-legged animal into a six-legged one. Such high-level mutations are unlikely to be selected, but potentially they can lead to revolutionary changes.
A fundamental example of such a major change is the metasystem transition, where a system evolves in a relatively short time to a higher level of complexity.
Gould S.J., and N. Eldredge. 1977: Punctuated equilibria: the tempo and mode of evolution reconsidered. Paleobiology 3, pp. 115-151.
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