I have recently made an egyptian angular composite bow and also made a set of 5 arrows with it (only show 4 on pics). The arrows are made with arundo donax. Pat B asked if I could write something about them as he said he can only find larger diameter shafts. I wrote a blog post some time ago about where the smaller shafts are located at in the patch. here is the small article I wrote. The cane I talk about is the Arundo but do not explicitly mention it.
"It can be a real nightmare trying to figure out the proper diameter when making arrow shafts from cane and or bamboo. In contrast making arrows from shoots or shafts all you have to do is reduce your shafts to a certain diameter and you are set to go. Cane and bamboo is not quite the same. With rivercane (especially with the one we have here in Cali) you can't really take much material from the shaft without weakening the outer wall of the shaft and possibly ruin it. Bamboo is also a type of cane, which you can take material of its outer wall especially if the pith in the center is rather small and the outer walls are thick. This technique of taking of material from the outer wall of boo shafts is used amongts Japanese arrow makers and it seems not to affect the arrow. You can actually lower the wight and reduce your diameter.
This article however is more concentrated on Cane shafts. Usually cane can be found growing in areas where the soil is constantly wet and humid. The more water there is the larger the cane grows and the faster it does. For this reason cane growing in areas that are to wet is not suitable for making arrow shafts. Usually they will outgrow arrow diameter in a few days or weeks. You must find an area that has sufficient water to foster the cane growth but not so much that it will overgrow the maximum diameter. The maximum diameter on cane arrows, and probably the ideal diameter is 3/8 on the thicker end and 5/16 on the smaller end. Sometimes you will have canes growing 3/8 almost all the way through your shaft without tapering. You must remember to put the weight foward, which means that on cane and bamboo arrows the thicker end goes in the front. There are also a multitude of other factors that you must take into consideration when matching arrow shafts, these include weight, stiffness, and balance point. If you want your arrows to match fairly well for 15-20 yard shots make sure that atleast your weight and stiffness is similar. Stiffness for some reason does not affect cane shaft as much as it does regular wooden arrow shafts. you can group your shafts into 3 groups, weak, medium and strong and have fairly well matched shafts if your weight is the same, no real need to spine them. So to reiterate the point, the diameter of cane shafts must be between 5/16 to maximum 3/8 inch in diameter."