An amalgam tree could exist naturally, as multiple species! This actually exists in nature!
Well, on a modest scale. I'm refering to hemiparasitic plants, like mistletoe.
Let's imagine the evolutionary steps needed to get to an amalgam tree, and work out the details.
Step: mistletoe like parasite
Mistletoe is a "obligate stem hemiparasite". Meaning it can't live on it's own, but grows on the trunk of other trees. It steals nutrients and water from them, but has it's own leafs and off course fruits.
Mistletoe grafts itself on another tree, all that is needed is a bird pooping out its seed on another tree trunk.
Step: Parasites starts feeding the host
Now imagine the parasite is too successfull. The hosts would eventually die because the parasites steal to much water and nutrients. The parasite could evolve to prevent this by feeding the host sugar, to keep it alive. In a way, the parasite is not much different then a man-made fruit tree graft. The relation is getting more symbiotic then parasitic now.
Step: Full symbiosis evolves
The host and symbiont (no longer parasite) could further evolve together at this point. Some things that might happen:
- No more leafs of it's own. The symbiont provided all needed nutrients
- Special spot places where the symbionts can graft themselves, while other places on the trunk are impossible for the symbiont to graft itself to.
- Host tree could grow bird nests on it's trunk to encourage bird droppings on graft sites.
One possible requirement is that the host tree and the symbiont don't compete too much for pollination and fruit. This is easily possible:
- Host tree might use wind pollination while symbiont uses insects
- Symbionts might have fruits, while host tree has sticky seeds that stick to the creatures gathering the fruit (birds, monkeys...).
Step: evolutionary success
If the symbiosis is very successfull, it might drive out all other normal trees. One reasons this could work is that if this happens in a very high jungle, symbionts can evolve faster, as they start at the top of the canopy instead of from the bottom.
Step: multiple host and symbiont species
Both the host and symbiont species could evolve into different species. The host could evolve to handle multiple terrains, while the symbionts could evolve to handle multiple canopy/wildlife situations.
This would become another possible reason that the amalgam tree is more successfull then regular trees: imagine that serious viral (or bacteria, insect or other wilflife) plagues are a common threat for all plant species, but typically only hit one species at a time. The host tree would be at an advantage because it has multiple symbionts and can thus easily handle the loses to just one of the symbiont species. One symbiont species could be hit hard by a plague, but can recover quicly afterwards, thanks to the nutriants and water supplied by the host (and thus survive thanks to the other species of symbiont!).
A forest full of extremely diverse amalgam trees is actually not that far fetched in this scenario!
All of this would require no sentient being to grow it, it would all work by seed scattering by creatures. (so bird poop on tree trunks)
But this could perhaps evolve further.
Step: One seed, multiple species
The host tree could have special spots where it gathers bird droppings, and incoporates the small symbiont seeds in these into a large seed of it's own.
(I imagine this is possible, there are multiple species where the female stores male sperm for later usage.)
The big host tree seed would contain a lot of symbiont seeds, and when it hits the ground, it would start growing, spreading the symbiont seeds inside its trunk, and activating them at the spots where they are needed.
Final Step: One amalgam species
When this evolves further, it could become even more complex, and the boundaries between species will blur. The only problem I see is that the need to have fruits on the symbiotic species might probably dissapear.
Just look at mythocondria, the energy sources within our cells, for inspiration. They started of as completely seperate organisms, and now replicate together with the host cells as one species!
(note: I've edited my original answer to show how this could evolve into one seed for an amalgam tree.)