cherries and plums!... LOLYeah thinning is a huge thing with fruit trees. A lot of stone fruit will overset if you let it. If this happens it will reduce fruit quality and Brix (sugar) and occasionally ends up making the tree biennial. Like you say the tree can only support so much fruit. But yeah apples, peaches, plums etc will only get their best and biggest fruits if you thin.
Lots of big commercial ops use chemical sprays to kill/thin the fruitlets, usually right after shuck split. Its wild reading and learning about all the chemicals needed and used to grow some fruit commercially.
The tree will naturally abort some and some will fall prematurely but on a mature tree its usually important to thin, especially dwarf/semi-dwarf fruit trees. Heres an example- A green gage plum, this fruit spur was pollinated but 3 plums was too much fruit for this tree to handle from this spot. So it put its energy into one and aborted the other two- you can see the small aborts still attached to the stem but they stopped developing.
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Never heard about thinning for tomatoes, interesting. Only thing I make sure to do is prune the suckers and try to keep a single stem and grow vertically with trellis.
edit: lol just read you wrote cherries and plum tomatoes I read it as just cherries and plums!
We have a Plum tree too. Same story. It has some kind of blight now. But yeah, I learned alot but the main thing is, not everyone agrees (Imagine that) So I an trying all kinds of things I never did, to teach myself. Also, never knew there are Determinate vs Indeterminate Tomatoes. Det* sets fruit all at once, so if you remove any flowers they will be lost. Indet* keeps growing until the frost kills it.
Not sure what is on this Plum tree