In horticultural varieties the function is ornamental :-) 

More seriously, in some species it's thought to be a product of viral infection, so not an adaptation at all.  In others it could be to break up the outline of the leaf to make it less conspicuous to herbivores.  There's been a few published studies on this but not a huge number.

If variegation can be the product of viral infection, then not all leaves should be affected but only the infected ones. The question arises, wether variegation can also mimic viral infection and thus reduce the attrctiveness to  herbivores.

Dear Klaus:

Variegation in leaf color may be based on somatic mutation in meristems (chimeras) but plant ecologists insist that variegation is precise and genetically based in many species growing as flowering herbs and vines in deep shade on forest floors.  Please see Gurevitch et al. (2006) "The Ecology of Plants" (second edition) pp. 36-40.  Variegated leaves help capture "sun flecks." Yellow or red portions of the leaf epidermis also allows the plant to capture the green end of the white-light spectrum.  As for the variation of leaf-color to attract pollinators to flowers please consider...Ren, ZX., Li, DZ, Bernhardt, P. & Wang, H. 2011. Flowers of Cypripedium fargesii (Orchidaceae) fool flat-footed flies (Platypezidae) by faking fungus-infected foliage. Proceedings of the National Academy of Sciences. 108: 7478-7480.

The Chinese entomologists did NOT identify the fly correctly.  The flies associated with this orchid are really syrphids that eat fungus spores as adults.  

Peter

"Flowers of Cypripedium fargesii (Orchidaceae) fool flat-footed flies (Platypezidae) by faking fungus-infected foliage."

That's an impressive bit of alliteration!

I guess this is a great and difficult to answer question. The "sun flecks" hypothesis may explain some of the variegated or other-than-green coloured leafs we find in nature. However, it would fail to explain why some leafs are naturally perforated or full of holes (as Monstera deliciosa and other Araceae: https://felipedelbosque.files.wordpress.com/2013/09/monstera_deliciosa_fdb_6390-copy.jpg ). I hypothesize that both variegation (as the case of Musa sumatrana: https://gardencoachpictures.wordpress.com/tag/sun-to-part-shade/ compared with really damaged Musa: http://sistemasdeproducao.cnptia.embrapa.br/FontesHTML/Banana/BananaFormoso/pragas.htm) and natural leaf perforation may be traits adaptive in the sense they would reduce herbivory both by inhibitting oviposition by visual oriented herbivores and by attracting more visually oriented parasitoid predators. These ideas came from the fact that, in Brazil we have lots of Lepidoptera that feed on Musaceae, but I ve never seen signals of herbivore damage in the variegated Musa sumatrana here. Some insights about that are in: 

http://link.springer.com/chapter/10.1007/978-1-4615-2814-2_3

http://www.annualreviews.org/doi/abs/10.1146/annurev.en.36.010191.000433?journalCode=ento

http://www2.ib.unicamp.br/profs/pso/PDFS/Sendoyaetal_2009.pdf

Other cues: other Musa species or cultivars are variegated only at the seedling stage, when they may be more suceptible to heavy herbivory by caterpilars, loosing this trait when adult...

Idea of experiment: In a common garden with both variegated and non-variegated Musa spp. subjected to visual oriented lepidoptera herbivores, measure the herbivory/oviposition/parasitoid infection rates in both phenotypes. Then, in the lab, feed the herbivores (mostly caterpilars) with both phenotypes and look if is there differences in the fitness of larvae under both diets. That would give an idea of the function of the variegation in Musa and asure that differences in herbivores damage/preferences are not due to difference in the nutriotional value of the variegated and non-variegated Musas.

I could not think about hypothesis envolving pollination. In my garden I have a hummingbird-pollinated Stromanthe, a genus famous by it is fascinating varietation patterns. I guess most of the Maranthas have white/cream flowers folded in green or brown bracts and are insect pollinated. However this species have bright vine bracts contrasting with bright white flowers. Curiously, this species has no variegation: leaves are dark green upside and dark vine downside. The reason this species has no variegation may be related to the reason that it is hummingbird pollination: it may come from the highlands, where both insect activity as pollinators or herbivores is lower than in lowland.

Whow, many good answers! Is it known whether there are costs of variegation due to reduced photosynthesis?

Dear Klaus and Jeff:

Yes, there are ALWAYS costs.  Once again read Gurevitch for the evolutionary ecology of variegations and perforated leaves.

An YES, my alliterative titles are Always impressive.  What a pity those Chinese entomologists mistook a syrphid for a platypezid.

Yang Niu mentioned an intersting aspect which I want to shere here:

Dear Klaus,

I'm interested in your question, but there is something wrong when I response your in the "question-answer system". I was believed that there must be a cost for the "non-green" green plant. But after I investigated a plant with color dimorphic leaves (green and grey), I failed to find any cost in the non-green morph. https://www.researchgate.net/publication/262077098_Grey_leaves_in_an_alpine_plant_a_cryptic_colouration_to_avoid_attack

And I was still seeking for the potential cost ...

Yang

Article: Grey leaves in an alpine plant: a cryptic colouration to avoid attack?

Yang Niu, Gao Chen, De‐Li Peng, Bo Song, Yang Yang, Zhi‐Min Li, Hang Sun

New Phytologist 05/2014;

I answered to him:

Dear Yang Niu,

I agree that a leaf area where there is no chlorophyll means a cost for the plant. However, I think that in many variegated leaves there are differently coloured areas which both may possess chlorophyll are hypothetically adapted tosdifferent light conditions: then the costs turn into benefits.

Klaus

Article Grey leaves in an alpine plant: A cryptic colouration to avoid attack?

I just saw this thread (10 months late!), and probably Klaus has found much more information by now. I just want to point to a popular article in which I reviewed some of the hypotheses about the ecological implications (and putative adaptive function) of leaf variegation, more specifically on the type of variegation expressed as leaf mottling. In it, I cite some important papers (Allen & Knill 1991, Benzing & Friedman 1981, Givnish 1990, Stone 1979) not cited by Niu et al. (2014), that are not related to pollinator attraction.

Data Geonoma epetiolata PALMS