The idea of slow gradual change is an essential component of most people's thinking about evolution.1 The debate over gradualism began in earnest with the publication of Punctuated Equilibria: an Alternative to Phyletic Gradualism by Eldredge and Gould (1972).
They defined phyletic gradualism as ...
Paleontology's view of speciation has been dominated by the picture of "phyletic gradualism." It holds that new species arise from the slow and steady transformation of the entire population.They illustrate this point with two "classic" views of gradualism.
In the first view (left) we see speciation by gradual transformation of a single population. This form of speciation is called anagenesis.
This kind of thinking still dominates today. It's the way most people picture the result of natural selection working on a species over time. The species gradually adapts to a changing environment until its descendants come to look very different from its ancestors. This is the way most people think when they're talking about human evolution over the past several million years. It's the model you probably have in mind when you envisage arms races.
The other form of speciation is called cladogenesis. It's when an ancestral species splits into two parts—often due to geographical separation—and each separate population evolves gradually into distinct species. This is the way most people think about adaptive radiations. The key point, according to Eldredge and Gould, is the slow and steady change in each lineage as they diverge from one another.
Eldredge and Gould (1972) proposed a different way of thinking about evolution and speciation based on their observations of numerous fossil lineages. They suggested that speciation normally takes place via geographic separation of a subset of individuals in a species (allopatric speciation). This isolated group can evolve fairly rapidly so that within a relatively short time (tens of thousand of years) it comes to look very different from its ancestors.
If this geographically isolated population becomes reproductively isolated as well, then it forms a new species, distinct from its parents. The new species may then flow back into the same geographical location as the parent and there won't be any mixing of the gene pools. Meanwhile, the parent species has not changed much, so the effect on the fossil record is the rapid appearance of a new species while the old one continues to exist.2
At that point, both species will persist unchanged for millions of years (stasis) until the process of rapid speciation by cladogenesis repeats in one of both lineages. The pattern observed in the fossil record is called punctuated equilibria. It's a pattern that's very different from classic gradualism.
Here's how they illustrate it in their paper.
The important initial claims of the punctuated equilibria model are: (1) most change takes place rapidly during speciation by cladogenesis, and (2) for most of their existence species do not change very much. Later on, the implications of these two observations became more obvious. If the number of species is constantly increasing by splitting then why aren't we overwhelmed by species? The answer is that not only are species "born", they also "die" (become extinct). The overall pattern of evolution is characterized by the differential birth and death of species and this leads to species sorting as an important mode of evolution.
Lot's of people don't like punctuated equilibria and there are legitimate debates over interpretations of the fossil record. Some people say that the pattern is rarely seen, even when you have a complete record over millions of years. Others say that PE occurs in some lineages but it's not common.
Those who oppose punctuated equilibria are often upset about the claims concerning gradualism. The dispute often boils down to denying that anyone was ever a gradualist. The implication is that there's nothing new about punctuated equilibria so why all the fuss?
Much of the dispute hinges on whether Charles Darwin was a gradualist. It's often based on a misunderstanding of the word "gradualism" as it is used by Eldredge and Gould. Some people interpret it to mean "constant speedism" and they comb Darwin's works to find examples where he wrote about different rates of evolution in a lineage. "Aha!", they say, "see, Darwin wasn't a gradualist at all."
Gould addresses these critics in The Structure of Evolutionary Theory. He points out that there are some trivial examples of gradualism in Darwin's writings but the important definition is ...
Slowness and Smoothness (but not Constancy) of RateGould goes on to support his claim based, in part, on Darwin's commitment to Lyell's uniformitarianism. Gould also points out that Huxley was vexed with Darwin for adopting such a gradualist approach to evolution.
Darwin also championed the most stringent version of gradualism—not mere continuity of information, and not just insensibility of innumerate transitional steps; but also the additional claim that change must be insensibly gradual even at the broadest temporal scale of geological durations, and that continuous flux (at variable rates to be sure) represents the usual state of nature.
You can tell from reading The Structure of Evolutionary Theory that Gould was annoyed at some of his critics. Bear in mind that Gould was a student of the history of biology and a collector of old books on the subject. He wrote numerous essays on the misinterpretation of historical figures (e.g. Goldschmidt). When he makes a claim about what Darwin thought, it shouldn't be dismissed as the deranged delusions of an uniformed scientist.
The same might not be true of other scientists, or philosophers, who write about history ....
Since Darwin prevails as the patron saint of our profession, and since everyone wants such a preeminent authority on his side, a lamentable tradition has arisen for appropriating single Darwinian statements as defenses for particular views that either bear no relation to Darwin's own concern, or that even confute the general tenor of his work....For more on this debate, see John Wilkins on Myth 4: Darwin was a gradualist.
I raise this point here because abuse of selective quotation has been particularly notable in discussions of Darwin's views on gradualism. Of course Darwin acknowledged great variation in rates of change, and even episodes of rapidity that might be labelled catastrophic (at least on a local scale); for how could such an excellent naturalist deny nature's multifariousness on such a key issue as the character of change itself? But these occasional statements do not make Darwin the godfather of punctuated equilibrium, or a cryptic supporter of saltation....
1. The words on the poster are a take-off on one of the campaign slogans of Barack Obama.
2. There are other models that can account for the observations. In other works, Eldredge and Gould have explained how punctuated equilibria is also compatible with sympatric speciation.
Eldredge, N. and Gould, S.J. (1972) Punctuated Equilibria: an Alternative to Phyletic Gradualism. in "Models in Paleobiology" T.J.M. Schopf ed., Freemna, Cooper & Co., San Francisco pp. 82-115. [PDF]