Code for regional fitting the symmetric division ratio

Quantification of symmetric ISC division probability r using clone data simulationTo quantify symmetric ISC division probability r {O'Brien, 2011 #709}{de Navascues, 2012 #55}, MARCM FRT82B clones were induced by a 1-hour heat shock at 72 h APF. Midguts were dissected at 5d, 7d, and 12 d post‑eclosion and subjected to immunofluorescence staining for Dl, GFP, and Pros. The midgut was segmented into the R1, R2, R3, R4ab, R4c, and R5 regions based on anatomical constriction sites{Buchon, 2013 #66}. For each clone, the following parameters were recorded: (1) the anatomical region in which the clone was located, (2) clone size t (total number of GFP+ cells), (3) number of Dl⁺ cells (ISCs), and (4) number of Pros⁺ cells (EECs).To assess the regional probability of symmetric ISC divisions, we performed a computational simulation based on experimentally derived MARCM clone datasets. The fitting aimed to determine the optimal symmetric division probability parameter r (where the probability of an ISC undergoing a symmetric division is 2r), such that the simulated distribution of ISC numbers per clone size best matched the experimental observations.Data processing and simulation framework For each region (or region combination), the experimental data were summarized as the conditional probability distribution of observing a given number of ISCs within clones of a specific size t. Clones with fewer than 3 occurrences for a given (t, ISC number) pair were excluded from fitting due to limited statistical reliability.A stochastic simulation was implemented to generate synthetic clones under a defined r. Starting from a single ISC, each division was modeled as either symmetric (producing two ISCs or two differentiated daughters with probability 2r) or asymmetric (producing one ISC and one differentiated daughter). The simulation continued until the clone reached a predefined maximum size or contained no further ISCs. For each tested r, 100,000 independent lineage simulations were performed to obtain a stable distribution of ISC counts across clone sizes.Optimization and validation The optimal r was identified by minimizing a weighted mean squared error (MSE) loss function comparing the simulated probability distribution with the experimental one. The weighting accounted for the sample size in each experimental bin, giving higher confidence to probabilities derived from larger clone counts. A hierarchical grid-search approach was employed to efficiently explore the parameter space.Goodness-of-fit was evaluated by comparing simulated and experimental distributions across clone sizes (see Fig. S10 for regional fitting results and validation plots, including loss history, probability distribution comparisons, and correlation analyses). This simulation-based fitting provided region-specific estimates of r, which informed the exclusion of the high-symmetry region R4ab and supported the use of clones containing only one Dl⁺ ISC (in non‑R4ab regions) for analyzing division‑counting behavior.