13Background In planarian flatworms, the mechanisms underlying the activity of collec-14 tively pluripotent adult stem cells (neoblasts) and their descendants can now be studied 15 from the level of the individual gene to the entire animal. Flatworms maintain startling 16 developmental plasticity and regenerative capacity in response to variable nutrient con-17 ditions or injury. We develop a model for cell dynamics in such animals, using methods 18 of nonlinear dynamics, assuming that fully di↵erentiated cells exert feedback control on 19 neoblast activity. Results Our model predicts a number of whole organism level and 20 general cell biological and behaviours, some of which have been empirically observed or 21 inferred in planarians and others that have not. As previously observed empirically we 22 find: 1) a curvilinear relationship between external food and planarian steady state size; 23 2) the fraction of neoblasts in the steady state is constant regardless of planarian size; 24 3) a burst of controlled apoptosis during regeneration after amputation as the number 25 of di↵erentiated cells are adjusted towards their correct homeostatic/steady state level. 26 In addition our model describes the following properties that can inform and be tested 27 by future experiments: 4) the strength of feedback control from di↵erentiated cells to 28 neoblasts (i.e. the activity of the signalling system) and from neoblasts on themselves 29 in relation to absolute number depends upon the level of food in the environment; 5) 30 planarians adjust size when food level reduces initially through increased apoptosis and 31 then through a reduction in neoblast self-renewal activity; 6) following wounding or exci-32 sion of di↵erentiated cells, di↵erent time scales characterize both recovery of size and the 33 two feedback functions; 7) the temporal pattern of feedback controls di↵ers noticeably 34 during recovery from a removal or neoblasts or a removal of di↵erentiated cells; and 8) 35 the signaling strength for apoptosis of di↵erentiated cells depends upon both the absolute 36 2 and relative deviations of the number of di↵erentiated cells from their homeostatic level. 37 Conclusions We o↵er the first analytical framework for organizing experiments on 38 planarian flatworm stem cell dynamics in a form that allows models to be compared with 39 quantitative cell data based on underlying molecular mechanisms and thus facilitates the 40 interplay between empirical studies and modeling. This framework is the foundation for 41 studying cell migration during wound repair, the determination of homeostatic levels of 42 di↵erentiated cells by natural selection, and stochastic e↵ects.43 Background 46 Stem cell systems operate by demand control [1-3] in which the needs of the organism 47 determine in large part the behavior of the stem cells. Indeed, both cancer and ageing 48 may be understood as failures of this feedback control, albeit in di↵erent ways. The 49 highly regenerative planarian flatworms (Tricladdida), particularly Dugesia a...