This research is part of my PhD thesis which I started in 2007, in part inspired by the creationist claim that deleterious mutations are only bad and prohibits evolution. My first objection was that they can of course exist on the line of descent as hitchhikers - deleterious mutations that go to fixation because they occur in close temporal proximity* to a beneficial mutation, so the combined effect is beneficial. Then I learned about epistasis - the interaction between mutations - which is ubiquitous and essential for non-trivial adaptation. Trivial adaptation is when evolution occurs by accumulating only beneficial mutations, as when a single fitness peak is ascended. But if the fitness landscape is rugged with many local peaks (as it necessarily always is in reality), then it is of great benefit to be able to climb down one peak and up another higher one.
The study is also highlighted in MSU Research**: Evolutionary kings of the hill use good, bad and ugly mutations to speed ahead of competition.
On Uncommon Descent, someone called PaV says
Second, here’s what the lead author had to say:The level of ignorance comes as a surprise to me, but that is of course entirely my own fault. Never underestimate these people's denseness.
“These fitness landscapes simply could not be traversed with mutations that did not interact.”
This wasn’t a ‘main conclusion’ of the study; however, I don’t know about you, but this sounds to me like any ‘single’ mutation cannot get you across any fitness valley, and, therefore, seems to rule out having a single mutation ‘sweep’ across a population to fixation.
IOW, without epistatic effects, evolution cannot move forward. This is unexpected. It makes simple neo-Darwinian evolution that more complex with more hurdles to get over. And, it is another nail in the coffin of neo-Darwinism. That is: “Another day, another bad day for Darwinism.”
That a single mutation cannot get you across a valley should rule out that a single mutation can go to fixation reveals a gaping hole in the writer's understanding of very basic population dynamics. It is a complete non-sequitur. Crossing a valley is not necessary for a mutation to go to fixation; if a mutation is beneficial it can (but doesn't always) go to fixation by selection, and whether this is one step in crossing a valley or not is besides the point.
In this study we only allowed single point mutations, which is why it is true that no single mutation can cause an organism to jump from one peak to another (this is short-hand for the parent sitting on one peak has an offspring with one mutation). In order to move from one peak to another, at least two mutations are needed - otherwise the genotypes of the two organisms would be adjacent, and so one of them would not be sitting on a fitness peak. With larger-scale mutations such as insertions, deletions, transposons, etc., it would not be impossible to go from one peak to another in a single mutational event.
Another possible misunderstanding is that evolution never occurs up one peak. It does of course, as recently reported in two papers on experimental evolution side by side in Science [2,3]. In those cases, evolution can proceed by beneficial single point mutations, until the peak has been ascended (which in non-digital evolution often takes a very long time).
Lastly, PaV says it is unexpected that evolution cannot move forward without epistasis. It isn't at all. There are cases where epistasis is not important, but overall we already knew that epistasis was required.
I picture a game of King of the Hill where the ID creationists stand atop a little hill of faulty understanding of evolutionary theory claiming victory, while the rest of us have long ago ascended an adjacent and much higher peak that the ID creationists aren't able to locate.
Apologies to Randall Munroe.
 Østman, B., Hintze, A., & Adami, C. (2011). Impact of epistasis and pleiotropy on evolutionary adaptation Proceedings of the Royal Society B: Biological Sciences DOI: 10.1098/rspb.2011.0870
 Chou, H., Chiu, H., Delaney, N., Segre, D., & Marx, C. (2011). Diminishing Returns Epistasis Among Beneficial Mutations Decelerates Adaptation Science, 332 (6034), 1190-1192 DOI: 10.1126/science.1203799
 Khan, A., Dinh, D., Schneider, D., Lenski, R., & Cooper, T. (2011). Negative Epistasis Between Beneficial Mutations in an Evolving Bacterial Population Science, 332 (6034), 1193-1196 DOI: 10.1126/science.1203801
* I am no popular science writer, but if you don't know what I mean, feel free to ask.
** And on PhysOrg, Science Daily, Irish Weather Online, and NSF.