Answer: 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. 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.
If you really can't tell which is which, just thin them out next spring and then tip them back and hope for the best. Next year, be sure to remove the ones that have fruited right after you pick the berries -- when you can still tell easily which are new growth and which are not.
Canby bears a single crop. Canby is somewhat unique in that it is nearly thornless.
Here is a quick and concise illustrated guide you may find useful, it shows what you need to do the first year and then in subsequent years. You may need to cut and paste the complete url into your browser to make it work correctly.
I hope this helps!
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