Horizontal gene transfer is much more common in non-eukaryotes. When a gene is transferred, it is more likely to be retained by its new host if it confers a fitness benefit. Most genes, though, are parts of pathways, and can only confer a benefit if the other genes in the pathway are also present. Therefore, it's in the gene's best interest to be physically close to the other members of the pathway so that they're more likely to be transferred together. This was considered years ago in a paper called "The Selfish Operon" by Lawrence and Roth.

I think this is an interesting question, it's not exactly my core area of speciality, so these are just some thoughts.

First, a little caution - the operons model came from E.coli I think, and other prokaryotes don't necessarily rely on operons to the same degree (although they do use them). I am thinking here of Streptomyces coelicolor, which has a more complex metabolism than E.coli, and where there is not so clear evidence about the pervasive use of operons. We might be a little biased by looking at E.coli first, and we may have missed operons in eukaryotes by not sequencing and assembling enough transcriptomes yet, in fact I just saw a reference that C.elegens does use operons.

I'm assuming that operons is the ancestral state, then presumably early eukaryotes gained the ability for finer control of transcription whilst losing the ability for RNA processing into individual proteins.

It strikes me now that eukaryotes have introns, and hence splicing machinery to excise them, whereas prokaryotes don't, but prokaryotes do have splicing machinery to turn an operon into individual proteins. I wonder whether presence of introns and lack of operons, are related, and have evolved through mutation in the splicing machinery in early proto-eukaryotes.

I guess the reason why eukaryotes preferentially selected no-operons may be to do with the selective advantage gained through more flexible regulation of transcription, or possibly, it might be related to multicellularity and the ability to maintain much larger genomes, which can then accommodate a much richer set of regulatory regions.

I think finding transition states is one of the keys to understanding this. These might be helpful reads: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2881147/ and http://bfg.oxfordjournals.org/content/3/3/199

Why is there the notion that operons were lost in Eukaryotas. Is it not more likely they changes and were selected for novel mechanisms (such as splicing). In addition with the increase in gene duplications and transposable elements, the classical operons were chewed up into individual regulatory elements.

Good question, yes...

In addition to what Jonathan said, one must have in mind that eukaryotes did not "simply came" from prokaryotes, and that the transitional states from "the" ancestor through multiple proto-symbiotic events (i.e. association between multiple genomes) is probably complex and somehow multiple.

But we may also think to "complexity", that operatic regulation do restrain: when you group genes into a regulatory structure such an operon, you loses the versatility of each individual gene (pretty much in the same way that when you group protein modules into a single more complex protein, you lose some of the initial properties of the module). In other terms, you specialize.

Thus, in this specialization process (one gene being more linked to its operon neighbors than if it was alone; trivial), you lose some selective advantages that are retained by the eukaryotes.

In my opinion, the most striking difference is linked to multicellularity and tissue-specifc expression (also a + of the organisation in introns, that puts "another level" or regulation in between the gene and the protein). Jonathan pointed to it at the end of his comment.

I would say that there is "some amount" of literature on the subject (and I am not a specialist of this, although dealing with both type of organisms through symbiotic associations...)

Horizontal gene transfer is much more common in non-eukaryotes. When a gene is transferred, it is more likely to be retained by its new host if it confers a fitness benefit. Most genes, though, are parts of pathways, and can only confer a benefit if the other genes in the pathway are also present. Therefore, it's in the gene's best interest to be physically close to the other members of the pathway so that they're more likely to be transferred together. This was considered years ago in a paper called "The Selfish Operon" by Lawrence and Roth.

Also, a lot of eukaryotes are not haploid, so there is opportunity for recombination that might tend to disassociate functionally integrated stretches of the genome.

Eukaryotes evolved splicing to expand the proteome. Presence of splicing as well as operons is possibly not a viable option. That may be the reason why evolution opted for splicing over operons in most eukaryotes. Of course this is just a speculation.