Punctuated Equilibria ("Punk-Eek" for short) is the new de-facto version of evolutionism.
It was devised by Steven Gould, Niles Eldridge, Ernst Myer, and a handful of others and there were two primary motivations, i.e. to account for the total lack of the intermediate fossils (missing links) which classical Darwinian gradualism requires, and also to try to eliminate the problem of the gigantic time frames which are known to be required for spreading ANY genetic change through any large group of animals spread out over vast areas.
The claim, basically, is that all meaningful evolutionary change occurs amongst "peripheral isolates", that is, amongst tiny groups of animals which somehow or other get trapped into isolated areas. The claim is that such tiny groups cannot be expected to leave enough fossil evidence for anybody to find and that, at the same time, the need to spread genetic change through large groups is eliminated. Myer in particular noted the Haldane Dilemma from population genetics as a major motivation. The claim is that such minuscule groups develop some evolutionary edge and then break out, spread out, outcompete and overwhelm the pre-existing and much larger herds of animals.
The theory to my knowledge does not provide any sort of new AGENCY/CAUSE for these changes which supposedly occur amongst the tiny groups and there are several other similarly gigantic problems with it:
It amounts to a claim that inbreeding is the most major cause of our entire biosphere.
It requires animals adapted to a local set of conditions to defeat globally adapted animals on a quasi-infinite basis and in real life, that never happens. In real life the first time ordinary dogs, cats, and rats ever get introduced to one of Darwin's little paradise islands, the exotic animals get wiped out within 100 years.
It violates the laws of probability. In real life other than for cosmic catastrophes, the only agency known to have ever wiped an entire species of animals off of entire continents is man and man only acquired such capabilities recently. A tiny group of animals penned into some small area on the other hand is vulnerable to everything nature has to offer. Any sort of a disease, a local flood or lightning fire, or anything at all, even a skewed sex ratio in one generation which can happen seemingly for no reason, and the tiny group is decimated or wiped out. Thus the little heath hen in North America was in good shape so long as it was spread out over the East coast but the first moment it got penned into one of Gould's little peripheral areas (Martha's Vinyard in this case) it was all over; the protection which being spread out over large areas had formerly given them was gone.
Alexander Mebane of the Tampa Skeptics notes another problem which the dynamic trio of Gould/Eldridge/Myer have with the laws of probability:
..."But it may be questioned, on obvious probability grounds, whether this way of accounting for the observed absence of intermediates will really wash. Admitting that every intermediate stage "must have" a small population, we may nevertheless observe that there must have been a far greater number of them than of the stable, " finished" species known to us, since (according to the Darwinist picture) every species-transition must necessarily pass through several intermediate stages. That greater number would increase the likelihood that some intermediate forms, here and there, would chance to be preserved as fossils.
And the dogma further requires that the larger transitions - between different genera, families, orders, classes, and even different phyla, must all have come about in just the same gradual and continuous manner, simply by a long-continued succession of normal species-transitions! We have all seen "genealogical trees" drawn by evolutionists, to show the order in which these taxonomic groups have all come into existence over a long period, by successive "branchings from a common root". But it must be asked: Where are all the fossils that should have been left by the many millions of species that this tree requires to have once existed on its trunk, boughs, and branches, before its final branchings took place? Why are none of these seen in the fossil record of the period during which the evolutionists' tree requires them to have lived?....
Moreover, why have none of this great multitude of Darwinian intermediate species chanced to survive unchanged to our own time, among the considerable number of ancient life-forms that, as we know, have had the luck to do so?
"The most recent episode of great changes, the advent of the modern (Cenozoic) mammals after the death of the dinosaurs, is the one that we should expect to have left the best-preserved fossils of intermediate species. At the catastrophic end of the Cretaceous, 65 Myr ago, mammals were small nocturnal "tree-shrew"-like animals, none larger than cats; roughly ten million years later, we find essentially "modern" bats*, bears, and lions18. "All modern orders of mammals seem to have arisen independently and at about the same time": Wesson, p. 40, quoting Bonner 1988 and Carroll 1988.
If these vast changes really proceeded in the manner prescribed by Darwin, surely many hundreds (at the least!) of intermediate species in each lineage must once have lived during that protracted period of radical transmogrification. None of them have ever showed up in the fossil record.
And not only are all traces of intermediate species' missing, but anyone who seriously tries to imagine a believable sequence of viable intermediate animals between a tree-shrew and a bat-every one of which, according to Darwin, supplanted its predecessor by virtue of being "better adapted"! -wiII very soon be convinced that such a sequence is simply inconceivable
Walter Remine notes that no variant of evolutionism is logically consistent or believable in itself and that therefore what evolutionists are actually presenting to the public these days is what he calls a "smorgasbord" consisting of bits and pieces of Darwinian gradualism, punk-eek, and possibly one or two other kinds of things. In other words, if you can't dazzle the world with brilliance, baffle it with bullshit.
Remine also notes that statistically, a tiny group in an isolated area would never see the "beneficial mutation" on which all versions of evolution still depend but, at some part, more such arguments amount to overkill...
Gould of course made an art form out of crying "they're quoting me out of context" whenever anybody tried to quote his statements regarding intermediate fossils or Darwinian gradualism and, generally, evolosers scream "quote mining" whenever anybody publishes any sort of a compendium of what real scholars have had to say about evolution over the last 60 years.
The question is whether a man can have his cake and eat it at the same time; Gould insisted he was entitled to such a power.
Consider the famous case of the Uncle Don (Carney) radio show back in the 30s. Snopes claims that is an urban legend but I've spoken with people who heard the broadcast. Uncle Don finished his childrens' show broadcast and then, not realizing the mike was still on, said something like 'Well, I guess that'll hold the little bastards for another day!', which in those days was all she wrote for a radio career.
The case of Stephen J. Gould is similar. In the 1960s and 70s, evolutionism lay like a wet blanket over the entire field of paleontology. Guys like Gould were prohibited from publishing significant kinds of material because ramifications of that material conflicted with the dictates of Darwinism.
And so, Gould and one or two others got together and devised what they call "Punctuated Equilibria" or "punk-eek".
The thinking clearly had to be similar to that of Uncle Don, i.e. something like 'Well, if the little bastards have to have some sort of a version of evolutionism to be happy, let's concoct a version which won't interfere with the serious business of paleontology. The fact that it (punk-eek) was patently idiotic mattered not an iota since the authors of the theory clearly viewed the intended audience as idiots.
In fact there actually are salesmen who try to keep their consciences clean by telling such outrageous lies that they figure nobody could feel sorry for anybody who buys off on any of them, and God will not punish them for it. The thinking which went into punk-eek had to be similar.
Now, having thus taken care of the "little bastards" for another day, Gould, Eldredge et. al. thereupon figured they could get on with the business of paleontology (which they get paid for) without having to deal with evolution anymore. Nonetheless there remained the problem of creationists and other non-believers quoting them. In establishing their new "punk-eek" variant of evolutionism, Gould and his associates had of necessity made a fairly large number of statements regarding the inadequacies of standard Darwinism (gradualistic evolution), and creationists were having a field day pulling juicy quotes out of such literature.
And so, over the last 20 years or so which you asked about, Gould has made various kinds of statements to the effect that creationists who quote him are all liars, are all quoting him out of context etc. etc., and that there is no lack of intermediate fossilss BETWEEN HIGHER TAXONOMIC GROUPS, which is a sort of mumbo-jumbo meaning that you might could look at a worm, and a fish, and a human and figure that the fish was some sort of an intermediate form between the worm and the human. Again, that's basically just lip service.
Moreover there are other claims that you will read of people having found the long missing intermediate fossil but, invariably, such claims turn out to be fakes or wishful thinking. The hard reality is that Darwinism demanded that the vast bulk of all fossils should be clear intermediate forms, and there is no rational way to think that even Gould's punk eek version would produce a world totally devoid of such, nonetheless that's the world we have.