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The variety of blackberries we propagate produce berries on the plant stem that's called the floricane. The plants grow on a two year cycle. The first year of the cycle, the plant will push out a new stem from the root zone. This stem (or cane) is called a primocane and will not produce any berries during the year that it is growing. The second year of the cycle, that primocane gets a new name and is called the floricane. This year will be the year that floricane will produce berries.
As the berries are developing on the floricane, another primocane can be seen pushing it's way up from the root zone. And the cycle of life continues.
Part of that cycle of life is the death of the floricane. After it has worked hard producing a lot of berries, it will begin to harden and turn brown. Eventually it must be removed from the vine and destroyed.
If at all possible the discarded canes should be burned. This will ensure that any insects that are using the cane as living quarters for themselves or their offspring will all be eradicated. These canes should never be put in a compost pile or left on the ground. Any larva will be able to survive and return to do more damage.
Pruning the floricanes is pretty straight forward. All of them should be cut off about an inch or two above the ground and removed. That's it.