## 3 Discussion
Our results suggest that nutrient-rich colonies have less structure and therefore allow a greater number of lineages to be maintained as the colony expands. This is in contrast to our simulations of nutrient-limited colonies where the number and sizes of subcolonies undergoes a lot more variation. An interesting avenue of further study would be to run simulations for a longer amount of time and assess how nutrient limitation impacts overall colony fitness and survival other than the overall slower growth we describe in our results. We note that there are many cellular processes that our model did not explicitly consider. First, we did not include cell rotational forces in our model. Based on results in this paper, biophysical properties of attached mother-daughter cell pairs play a role in local organizational properties of colonies. Thus, we believe extending our model to include rotational forces and capture more detailed geometry of attached mother-daughter cell pairs may further impact local organization dynamics. In addition, in nutrient-limited conditions, cells may enter a state of quiescence where they choose not to enter the \(G\)1 phase of the cell cycle [54]. Although we did not directly include quiescence as a state in our model, cells in our simulations do attain an effective \"quiescence\" state as they stop growing and creating new buds due to limits on their cell cycle progression. Third, our model does not include cell death. Although cell death is definitely a contributor to colony structure, specifically the 3D structure of colonies where the middle section is nutrient-starved, because the average lifetime of yeast cells exceeds the time-scale of our simulations [55; 56], the impact of cell death on the organization phenomena we observe is negligible. Finally, we have included only one type of budding behavior. Yeast are capable of multiple budding strategies. For example, we do not consider multiple cell mating types and only consider diploid cells. While diploid yeast cells primarily divide in a bipolar budding pattern [57], haploid cells can bud in an axial pattern [27] and have been shown to divide faster than diploid cells [58]. If we only considered diploid cells with no variance in the location of the new birth scar, all cells would appear co-linear to each other. However this extreme case is unlikely to occur within large diploid colonies [27]. We model new budding sites in a manner similar to the implementation by [PERSON] et al. [42], but we consider only daughter cells to be limited to bipolar cell division. In addition, we assume that a mother cell has at most one daughter cell attached, but this is not guaranteed for all strains [59]. Furthermore, we also neglect environmental factors in influencing budding strategies. While cells in larger yeast colonies have been shown to exhibit pseudohyphal growth through switches in budding strategies under nutrient-limited conditions [60; 61; 32], it was reported by [PERSON] et al. [60] that colony expansion appears to evolve non-uniformly after approximately 100 h. Because this far exceeds the time scales of the colonies we produced, we believe this effect to be negligible. However, we conjecture that for large colonies, pseudohyphal growth under nutrient-limited conditions will induce rapid changes in colony organization near the colony periphery. Indeed several agent-based modeling frameworks have been developed to study the factors impacting yeast colony growth. [PERSON] et al. developed a similar center-based model to study the impact of biophysical factors and growth inhibition by neighboring cells on colony expanse and sparsity [41]. Their results show that cell-growth inhibition by neighboring cells and bipolar division patterns are the most significant factors impacting colony sparsity where they used colony sparsity as a measure of exploratory behavior of the colony.