Firstly, it must be noted that punctuated equilibrium does not contradict phyletic gradualism. It is an expansionist theory, not a mutually exclusive one. Secondly, the differences within the theory of evolution does not jeopardise the theory itself. In other words, the theory does not change significantly if Gould and Eldredge are right. The difference is that they tend to emphasise certain trends rather than those advanced by the traditional Darwinians (Dawkins, Maynard Smith).
Basically, Eldredge and Gould, the paleontologists say that the population genetics experiments do not yield results that can be successfully extrapolated to the real world in evolutionary time. As George Gaylord Simpson (the early version) stressed, we can know what happens to a hundred mice over a period of ten years in controlled laboratory conditions, but we cannot extrapolate their subsequent evolution to yield results which would be the same as that of one billion mice over the period of tens of millions of years.
PE(Punctuated equilibrium)believers basically believe that gradualism does not account for the variety of species, orders, families, genera of organims that exist today. They cite stasis from paleontological evidence that species do not accumulate noticeable change gradually over a period of many millions of years. What they observed was that when there was gradual change, the change was not linear, but tend to wobble about a phenotypic mean. In essence, this means that the species do change very slightly over the ages and end much looking much like they did when they started off. This is where PE conflicts with PG(phyletic gradualism). Speciation, PE claims, is much more likely to happen by way of cladogenesis, than by anagenesis. Basically, this means that the a group splits with the parental species due to some accident, eg. perhaps some climate change that segregates them. When the group comes back into contact with the parental species, there is reproductive isolation. When this happens, going by the Mayr-Dobzhansky definition of "species", a new species is formed.
The mechanism by which this occurs is that when populations of a species that live on the edge of the ancestral range may either be isolated by some mechanism (geographical) or persevere living as they do at the edge of the geographical range. When the population becomes isolated, they are subjected to environmental conditions harsher than those faced by the ancestral species. As such, they face a choice they cannot choose, evolve or die. If a sufficient number of organisms survive, their altered phenotype corresponds with the evolution of a species. Unfortunately, most of the time, when these groups are exposed to a different environment, they tend to die off. This explains why you do not find intermediate fossils. The fact that they survive is due to luck and some other biological factors. The rate of speciation of such isolated groups is very fast, since they have to either evolve to a modified state whereby they can survive in the environment or become extinct. The other scenario is that the populations on the brink of the geographical range is modified over time by natural selection to improve the species adaptations to the environment. It is important to note that the population at the centre of the species' geographical range do not undergo lasting change in the course of evolutionary history. Stasis is the rule for such populations.
PG tells a different story. In this picture, evolution is taking place all the time, such that evolutionary change over time accumulates until a new species is formed. Basically, PG tells much the same story Darwin told in the Origin.
The other feud Gould/Eldredge has with Dawkins is over the degree of importance of genes in evolution. Dawkins believes that genes play the most important role in evolution, that natural selection acts on genes, and that the purpose of species perseverance is to do nothing other than to propagate their genes. The vehicle (body of the organism) is important as well, since without the vehicle, there can be no reproduction. Thus in this picture, natural selection is really acting on genes and not organisms and species in the long run. Different species survive due to a better genetic makeup they possesses with respect to the phenotypic changes they cause and the adaptive fitness conferred on the organism with respect to the environment. Gould disputes this part, for although he believes genes are important, because they are the units of heredity and possible variation, the influence of a gene on the organism in later development depends on much more than what it does. The influence of a gene is limited by the the presence of other genes, and by other factors. Gould believes that species selection is more important than gene selection. The gene pool, after all, does not exist unless it is expressed though some vehicle, which then competes directly with other organisms in nature. Competition in nature is defined more by the interconnecting network of species and the ecological energy cycles, than the propagation of genes. This diminishes the influence of any gene on the outcome in the evolutionary long run. This controversy extends to sociobiology as well.
