Capnella sp., right, Bill?
Their diet is said to be largely phytoplankton, and indeed, disintegration with opportunistic necrosis is one result of starvation.
Fragging is easy, clean slice through the healthy branch, then you use fishing line and needle to pierce the base of the branch and then tie it to a rock anchor (firmly, but not too tightly: you don't want the line to cut through tissue, haha).
You want a good, prolonged rinse of the frag right after the cut, and pretty good circulation for the tied frag for days after.
*I've tried using scissors to frag --with only-slightly less success.
Attachment in 3-15 days, usually
