Muller proposed this mechanism as a theory to explain the evolution of sex. One must note, that although Muller's ratchet is proposed to explain the success of sexual reproduction over asexual reproduction, the negative effect of accumulating irreversible deleterious mutations may not be prevalent in organisms which, while they reproduce asexually, also undergo other forms of recombination. This effect has also been observed in those regions of sexual organisms' genomes which do not undergo recombination.
Asexual reproduction compels genomes to be inherited as indivisible blocks so that once the least mutated genomes in an asexual population begin to carry at least one (additional) bad mutation, no genomes with fewer mutations can be expected to be found in future generations (except as a result of back mutation). In sexual populations, the process of genetic recombination allows the genomes of the progeny to be different from the genomes of the parents. In particular, progeny genomes with fewer mutations can be generated from more highly mutated parental genomes by putting together in progeny genomes mutation-free parental chromosomes or mutation-free pieces thereof.
Among protists and prokaryotes there is a plethora of supposedly asexual organisms. More and more are being shown to exchange genetic information through a variety of mechanisms. It is instead quite clear that the genomes of mitochondria and chloroplasts do not recombine and would undergo Muller's ratchet were they not as small as they are. Indeed, the probability that the least mutated genomes in an asexual population end up carrying at least one (additional) mutation depends heavily on the genomic mutation rate and this increases more or less linearly with the size of the genome (more accurately, with the number of base pairs present in active genes). However, reductions in genome size specially in parasites and symbionts can also be caused by direct selection to get rid of genes that have become unnecessary. Therefore a smaller genome is not a sure indication of the action of Muller's Ratchet.
In sexually reproducing organisms non-recombining chromosomes or chromosomal regions like, e.g., the mammalian Y chromosome, should also undergo Muller's Ratchet. (The Y chromosome appears to repair double-strand breaks by means of template-assisted recombinational repair at its mirror-like sequences but this "self-recombination" does not neutralize this chromosome's tendency to undergo Muller's Ratchet). And indeed such non-recombining sequences tend to shrink and evolve quickly. However, such fast evolution can also be due to these sequences' inability to repair DNA damage via template-assisted repair which de facto equates to an increase in the mutation rate. Therefore it is not easy to ascribe such cases of genome shrinkage and/or fast evolution only to Muller's Ratchet sensu stricto, i.e., to an accelerated accumulation of bad mutations that is caused by an inability to generate recombinant progeny.
Muller's Ratchet turns faster in smaller populations and it is thought to set limits to the maximum size of asexual genomes and to the long-term evolutionary continuity of asexual lineages (but some asexual lineages are thought to be quite ancient: Bdelloid rotifers, e.g., appear to have been asexual for nearly 40 million years).
Note, furthermore, that a battery of additional population-genetic and ecological processes have been proposed to explain the success of sexual forms, and it is still unclear which one is truly crucial (see evolution of sex, the Red Queen hypothesis).
Although Muller discussed the advantages of sexual reproduction in his 1932 talk, it does not contain the word "ratchet". Muller first introduced the term "ratchet" in his 1964 paper, and the phrase "Muller's ratchet" was coined by Joe Felsenstein in his 1974 paper, "The Evolutionary Advantage of Recombination".