Answer: You can allow the berries to remain - they should ripen for you. If not, don't be concerned. The canes that fruited this year will not fruit next year so should be removed. This helps keep the plant healthy by allowing air and sun to reach all of the canes. Sometimes you can identify the older canes by traces of where you picked the berries or they just look a little more weathered and old. Sometimes they die out after fruiting so certainly remove anything that is dead in the spring. Also remove anything that seems damaged or diseased. Next year, the fruit will be produced on second year canes (canes that grew this year), and you need to thin those out or the plants will be way too crowded. Thin by removing the weakest, least vigorous canes -- in other words, remove the skinnier or spindlier ones. Then shorten what is left to promote branching and thus increase the yield. If you make a few mistakes it will not kill the plants, but your harvest may not be quite as good.
After the berries ripen, remove the canes. Then tie the rest of the canes together loosely to keep them from whipping around in the wind. When they begin to leaf out in the spring you can untie them.
Hope this information clarifies things for you.
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