That is the question...First off, know your variety! Never prune a 'determinate' type tomato, or you will lose production!
Indeterminate varieties vary in their response to pruning, some reportedly have increased yields when the young plant is pruned back to three or four vines. Experiment with your favorite varieties to see how they respond.
Also,removing new flowers and immature fruit near the end of the growing season can help speed ripening of mature fruit.
Is pruning necessary at all? No. Tomatoes will do just fine left to sprawl, though fruits that touch the ground are far more likely to be lost to insects, disease or rot.
But if you have the memory of your ancestors' glorious 7-foot-tall staked tomato plants and want to grow them that way, you'll need to prune a bit. By pruning, I mean removing the excess vines, which form where a leaf meets the main stem. A simple pinch does the job, but if you use pruners be sure to disinfect them with bleach to prevent spread of disease.
When plants are large enough to begin staking, you'll want to remove all but 2-3 vines, and tie them to the stake, with supports about every 10 inches. You'll likely need to remove some top growth later, to keep the overall weight down. On some varieties, pruning and staking will result in larger, cleaner fruit, but yields will be lower, and subject to sunscald due to losing the protection from the foliage.
A good compromise is growing in cages. The fruit stays clean, no pruning is necessary, and yields are large. Building or buying tomato cages is a bit of an outlay initially, but well-made cages will last many years. Another solution is growing on wooden ladders or trellises, some time is required each week to work the vines between the supports.
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