The question is far from resolved (especially since it’s likely a case of convergent evolution across many species) but there have been a couple developments that haven’t made it into the wikipedia article. The most interesting ones are that there is a positive correlation between crown shyness and tree slenderness [1] and between crown shyness and leaf shape [2].
The former is especially interesting because it implies that crown shyness is an explicit strategy for resource management beyond just responding to the availability of light, since it presumably also improves the survivability of the species. The latter is interesting because it might be an adaptation to other environmental stresses like wind damage.
The best estimate I can give you is "not many" but it hasn't been exhaustively studied, especially with tens of thousands of tree species. I would like to point out though that crown shyness is a lot easier to observe in monoculture forests that were replanted after logging. A diverse forest with lots of trees is really hard to observe tree shyness in because it's a specific adaptation between members of one or a few species. If they're standing next to another species that doesn't cooperate, the shyness might not be readily visible.
It's also not universal, which is why it's increasingly believed to be some sort of stress response. One patch of trees in a forest may exhibit it while another patch of the exact same species a few hundred feet away might not. It might even be the case that this is an old adaptation that most trees are capable of but no longer need.
Trees that display crown shyness patterns include:
* Species of Dryobalanops, including Dryobalanops lanceolata and Dryobalanops aromatica (kapur)
* Some species of eucalypt
* Pinus contorta or lodgepole pine
* Avicennia germinans or black mangrove
* Schefflera pittieri
* Clusia alata
* K. Paijmans observed crown shyness in a multi-species group of trees, comprising Celtis spinosa and Pterocymbium beccarii
The former is especially interesting because it implies that crown shyness is an explicit strategy for resource management beyond just responding to the availability of light, since it presumably also improves the survivability of the species. The latter is interesting because it might be an adaptation to other environmental stresses like wind damage.
As always, more questions than answers :-)
[1] https://pubmed.ncbi.nlm.nih.gov/33713413/
[2] https://esj-journals.onlinelibrary.wiley.com/doi/10.1111/144...