Frank R. Ettensohn in the department of geological sciences at the University of Kentucky offers this response, which probably captures the view of many in the scientific community:
"The idea of periodic extinctions is still with us, but it remains in limbo, still awaiting full proof. Most scientists are unconvinced. There certainly are series of extinctions of varying severity that seem to occur with a periodicity of 26 to 34 million years. The inferred period is obviously inexact; some researchers consider this uncertainty a detraction from the theory, but when you are dealing with such a large time range, a few million years of error is not that big a deal.
"The biggest question is what could cause periodic extinctions. Those who support the theory of periodic extinctions commonly attribute these events to periodic influxes of meteorites. The most famous mass extinction--the Cretaceous-Tertiary event, which marked the end of the dinosaurs--is certainly related to a meteorite impact, and impacts appear to be possibly implicated in a few other extinctions. But there is no widely accepted mechanism that would explain periodic episodes of impacts, so the idea has floundered for want of proof and of viable causes.
"The theory of episodic extinctions is an interesting one, and there are some tantalizing suggestions of what might cause them. Nothing has really panned out yet, however, so most scientists remain skeptical."
J. John Sepkoski, Jr., is a professor of paleontology at the University of Chicago; he is also one of the co-discoverers of the apparent cyclic nature of mass extinctions. Here is his take on the status of his controversial idea:
"The question of a 26-million-year periodicity of extinction generated considerable interest in the 1980s. David Raup, now professor emeritus at the University of Chicago, and I arrived at this hypothesis empirically, based on our statistical analysis of data from the fossil record. The best information on extinction rates comes from a compilation of 36,000 marine animal genera from the past 600 million years. I continue to update and improve this compilation.
"The fossils show a statistical variation in extinction rates having a period of approximately 26 million years. The two periodic peaks of extinction after the Cretaceous-Tertiary boundary, 65 million years ago, are at the end of the Eocene (roughly 37 million years ago) and in the Middle Miocene (about 17 million years ago).
"Raup and I had initially performed a coarser analysis of the fossil record, focusing on extinctions at the family level (one level above genus in the taxonomic hierarchy). That analysis conformed to a 26-million-year periodic series, but it was missing two beats: one in the late Middle Jurassic (170 million years ago) and one in the Early Cretaceous (95 million years ago). Our hypothesis predicted that more extensive data offering finer time resolution would reveal that small extinction events occurred at those times. Indeed, the better, more voluminous genus-level data subsequently confirmed the prediction.
"Why has interest in this hypothesis subsided? There are two reasons. First, there are statistical questions about extinction rates that just cannot be answered. It is not clear whether other hypotheses can fit the empirical data as well as does the hypothesis of periodicity. The distribution of extinction events in time is certainly not random, but there is more than one way to analyze the data. Does the fact that the data appear to fit well to a model of periodicity mean that the events truly are periodic? This question was debated throughout the late 1980s without reaching a resolution
"The second reason for the loss of interest is one not uncommon to science: Here is an intriguing observation that no one knows how to explain. Researchers formulated a number of very interesting astronomical hypotheses to account for the 26-million-year periodicity of extinction. The most famous of these was the Nemesis, or 'death star,' hypothesis, which stated that the sun has a distant companion whose highly elliptical orbit brings it into the Oort Cloud (a swarm of frozen comets orbiting far from the sun) once every 26 million years. During each pass through the Oort Cloud, the companion's gravity would scatter huge numbers of comets, some of which would crash into Earth. The environmental damage caused by these impacts would lead to an elevated rate of extinctions.