Of course, it probably varies considerably. We know that the processes at work in clusters - mainly tidal harassment and ram-pressure stripping - certainly can cause enormous damage. And we know that at least some galaxies falling into clusters look, for the time being, perfectly healthy. But of course the real question is what happens in a typical case, if there even is such a thing.
Since we can't wait around for billions of years to track individual galaxies, like most extragalactic problems we have to tackle this statistically. As we generally have rather small samples - a few hundred galaxies per cluster - we plot radial trends in galaxy properties (colour, gas content, morphology and so on) as clues to the general trends at work. The problem is that this biases us to looking for cluster-induced changes. What about processes at work more locally, or even occurring to galaxies before they've fallen into the cluster proper ? Such "pre-processing" might be very important, but would be easy to miss in radially-averaged plots.
Being outright annoyed by such seductively simple but potentially misleading techniques, my postdoc* Boris Deshev decided to try something more sophisticated and plot Voronoi maps. We can't avoid the need to bin the data due to our small sample size, but this method allows us to really see the 2D map of various properties instead of the 1D radial average. It's a sort of adaptive-gridding that's good for dealing with points that vary widely in density from place to place, whereas a uniform gridding would wipe out a lot of fine details.
* Can one own a postdoc ? Native Americans say you can't own land, but as far as I know they don't say anything about postdocs.
The main map in the paper is a Voronoi map of the fraction of star-forming galaxies. This does not show the neat, circular trend that you might expect if the cluster was dominating galaxy evolution. In earlier drafts, we saw a clear north-south filament of galaxies dominated by non star-forming objects, but sadly this largely faded from view with more accurate star formation measurements. But it re-appeared when looking at the specific star formation rate, that is, the star formation activity accounting for the mass of each galaxy.
It's even possible to show that those objects haven't had their star formation reduced recently - it must have happened in the relatively distant past (> 500 Myr ago). So it does appear that pre-processing is having a significant influence : part of the cluster is assembling along a filament in which galaxies have already had their star-formation activity reduced. This Voronoi mapping is a neat way to show things that radial plots cannot, though the disappearing filament is an important reminder that small differences can sometimes make a big difference to the result.
This cluster is also one of only two at this distance (about 2.6 billion light years) which have HI measurements. At that distance, the resolution of the observations isn't great. Even so, there are some intriguing hints of galaxies being caught in the act of gas loss, with their HI noticeably displaced, stretched, and shifted in velocity from their most likely parent galaxy. The main problem is identifying the parent galaxy : we can't be sure that it isn't actually some barely-visible little blob that's just about visible within the beam of the telescope. But a few cases look intriguing enough that it was certainly worth reporting, as no-one's detected this at this redshift before (two of them look pretty darn convincing to me). They'll be good targets for future observations at higher resolution, and there might be more candidates hiding in the data. Developing new ways to dig them out is ongoing.