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Neural organoids model the development of the human brain and are an indispensable tool for studying neurodevelopment. Whole-organoid lineage tracing has revealed the number of progenies arising from each initial stem cell to be highly diverse, with lineage sizes ranging from one to more than 20,000 cells. This high variability exceeds what can be explained by existing stochastic models of corticogenesis and indicates the existence of an additional source of stochasticity. To explain this variability, we introduce the SAN model which distinguishes Symmetrically diving, Asymmetrically dividing, and Non-proliferating cells. In the SAN model, the additional source of stochasticity is the survival time of a lineage's pool of symmetrically dividing cells. These survival times result from neutral competition within the sub-population of all symmetrically dividing cells. We demonstrate that our model explains the experimentally observed variability of lineage sizes and derive the quantitative relationship between survival time and lineage size. We also show that our model implies the existence of a regulatory mechanism which keeps the size of the symmetrically dividing cell population constant. Our results provide quantitative insight into the clonal composition of neural organoids and how it arises. This is relevant for many applications of neural organoids, and similar processes may occur in other developing tissues both in vitro and in vivo. Author summary: Organoids are tissue that is grown in vitro, but which replicates many aspects of a specific organ. Neural organoids grown from around 20,000 human pluripotent stem cells in particular replicate many aspects of the developing human brain, and have become an important tool for studying human neurodevelopment. Lineage-tracing allows the contribution of each ancestral stem cells to the organoid to be measured quantitatively. Surprisingly, these contributions vary between a single and more than 20,000 cells, which affects many applications of neural organoids. In this paper we study how these variations arise. We introduce the so-called SAN model, named after the symmetrically, asymmetrically, and non-dividing cells it distinguishes. This model explains the large variation in lineage sizes as being caused by neutral competition between symmetrically dividing cells, i.e. by random chance as cells divide and differentiate. Our model helps to understand the growth of neural organoids quantitatively, and provides way to account for the large difference in lineage sizes in applications of neural organoids. Neutral competition as the cause of large lineage size differences may also be relevant beyond neural organoids, and possibly in the development of tissue in vivo. [ABSTRACT FROM AUTHOR]