As I think I said pages and pages back or on another version of this same question, herbivores frequently eat animals. Mollies certainly come into this category, no question. What I have been trying to clarify is that herbivores (in the wild) are not the same thing as vegetarians (a human choice). You're right, mollies would be difficult to keep purely on algae. I am sure you could do it, you would just need a wide range of algae, and that algae would have to be growing thick and fast to support the fish. Once the algal turf is growing it would have its own microscopic community of life, rotifers and the like, and mollies would do fine on that. It would basically be eating "aufwuchs", which is what a lot of poecilids, killifish, catfish, and cichlids eat in the wild anyway. Phenomenally difficult to recreate in an aquarium, but certainly possible in theory.
Lots of animals feed exclusively on algae, including some fish (desert pupfish is the example that springs to mind). Among the animals: bivalve molluscs feed largely on phytoplankton, and many gastropods feed on algae that they scrape off rocks. Sea urchins feed heavily on algae. Practically all zooplankton -- including baby fish -- feeds on phytoplankton. In terrestrial ecosystems, the majority of ungulate mammals feed primarily or exclusively on plants, taking in animals only indirectly. Sheep and cows are classic plant-eaters, though presumably they eat ants and bugs and other little things stuck to the grass they eat. In fact, in terms of biomass most animals feed on plants all or most of the time. It has to be this way, because only 10% of the energy gets passed up each level of the tropic pyramid. So plant eaters get 10% of the energy that plants take from sunlight, the first level of meat eaters get 10% of that, and the next level 10% of that, and so on. So a meat eater 3 steps up, like a tuna fish, which ate an anchovy, which ate a krill, which ate a diatom (the "plant") is only able to use 0.1% of the sunlight energy the diatoms turned into its body. Hence, meat eaters have to be rare, or ecosystems would collapse.
Among aquarium fish, the only two I can think of that could be kept as "vegetarians" in the human sense are scats and Panaque catfish. The latter have to kept on wood and plant food anyway, and the former could be fed anything, including, I'm sure beans, corn, tofu, or whatever else.
Cheers,
Neale
Nmonks, mollys are not herbivores, they are known omnivores, and will not do well on an all-veg based diet (think slow growth and weak imune system, lower fry birth rates and more pregnancy complications)- in the wild they are primarily insectivores with a large bulk of their diet consisting of critters they find swimming aroundin the water as well as other fishes fry.
Practically all food chains stem back to algae, but there are few animals or fish for that matter in this world that live directly and only off algae or plant matter.