None of the earthworms propagate by self-division, although occasionally, under unfavorable conditions, pieces may pinch off at the posterior end.[68] Lumbriculus, on the other hand, propagates by self-division, although it has been disputed whether the division takes place without the intervention of an external injury or disturbance of some sort, or whether the division may take place entirely from internal causes, that is, spontaneously. Von Wagner has shown that at certain seasons lumbriculus breaks up much more readily than at other times, which may only mean that it is more sensitive to stimuli at one time than at another. The pieces into which lumbriculus breaks up regenerate after separation. In another form, _Ctenodrilus monostylos_, division takes place first in the middle of the body behind a cross-septum. Each half may again divide in the same way, and the same process may be repeated again and again until some of the pieces are reduced to a single segment. A new anterior and posterior end may then develop on each piece. In _Ctenodrilus pardalis_ each segment of the middle region of the body constricts from the one in front and from the one behind, and each produces a new head at its anterior end and an anal opening at its posterior end. The worm then breaks up into a number of separate worms. In this series, self-division of the individual is not associated with the development of sexual forms, but seems to be a purely non-sexual method of reproduction. In the leeches self-division does not occur, and no cases are known in the mollusks. In the echinoderms several forms reproduce by voluntary self-division. In the brittle-stars some forms divide by the disk separating into two parts, one having two and the other three of the old arms. Each piece of the disk then regenerates the missing part of the disk as well as the additional arms. In the starfishes the arms may be thrown off if injured, and, while in certain forms the lost arm does not regenerate a new disk, yet, according to several writers, it may in other species regenerate a new animal. Dalyell observed a process of self-division in a holothurian, each part producing a new individual, and more recent observers have confirmed this discovery. No cases of self-division are known in the groups of myriapods, insects, crustaceans, spiders, polyzoans, brachiopods, enteropneusta, or vertebrates.