Mullers Ratchet is the process by which asexual organisms would accumulate mutations without bound. It is claimed that sexual organisms would slow this mutation accumulation through recombination. Is there any evidence that recombination achieves this? Preferably experimental evidence.
It's a good question and one without a wholly satisfactory answer. Here's a nice review from 2012 outlining the theoretical questions regarding Mueller's ratchet and recombination.
There also is "unequivocal evidence that deleterious mutations accumulate in low recombining regions of the genome, due to the reduced efficacy of purifying selection. " So if you accept this correlation between recombination and removal of deleterious mutations, then studies such as these are compelling evidence of what's happening in real populations .
One other thing to keep in mind that in terms of experimental evidence, it is non-trivial to translate theoretical measures of fitness (e.g. "selection coefficients") to something that we can directly measure in real populations. So even determining if there is an increase/decrease in deleterious alleles is going to dependent on having useful data in the first place. The assignment of "true" measures of selection on individual genotypes is the mainstay of experimental evolution (nice review here) and is very labor intensive. Moreover, the vast majority of this work has been carried out in bacteria (due to their short generation times) so effects of recombination are not addressed. Nevertheless there are some cool comparative studies in yeast showing how recombination can make selection more efficient.
There have been a ton of mathematical arguments and computer simulations demonstrating Muller's Ratchet and its relationship to asexual reproduction. However, as far as I know, the experimental evidence is still hotly debated. The debate generally revolves around whether a given biological system fulfills the conditions necessary for the ratchet to operate. Here are a couple of relevant papers:
Mutations that are positively selected reduce the ratchet effect in large asexual populations. They spread, eliminating everything else, and so other mutations only matter if they happen in descendants of those mutations. It's as if the average population size is smaller.
Unfavorable mutations can hitch-hike with the selected ones, but only if they are unimportant enough that the combination is still selected.
Sexual reproduction reduces the ratchet effect to single linkage groups. But it allows things like meiotic drive. Mutations that result in the mutant version distributed to more than half the offspring can still be selected even if they reduce survival of the offspring later. And that happens a lot faster than the ratchet.
Experimental evidence -- that's hard. Maybe you could grow haploid yeast that don't do sex over a long period in a particular environment and measure changes in fitness in that environment. (The obvious way to measure changes in fitness is to grow them mixed with the wild-type and see how long it takes one to outcompete the other.)
Grow other yeast that do some recombination in the same environment and see whether they evolve faster. (Again, grow them together and see which one consistently wins.)
Some yeast that look reliably asexual have rare events that turn on sexuality. For example if they are all the same mating type, they can rarely have something that turns an individual into the other mating type. If your asexual populations have that happen while the experiment is running it contaminates your results. So be careful about that.
It looks like a whole lot of work. If the sexual form usually evolves faster then you have done a whole lot of work to show what almost everybody already believed.