## 2 Results
#### 2.1.4 Budding Division Promotes Subcolony Connectivity  
Next, we considered the impact of budding division on subcolony structure and organization. We define a **subcolony** to be the subset of all cells whose common ancestor is the same immediate daughter of the founder cell (Section 4.2.2 and Figure 17). Note that a colony has as many subcolonies as immediate daughters of the founding cell. We then analyze how well each of these subcolonies is connected in terms of the spatial layout of the colony. To do this, we considered colonies at the final time point (24 h) and compared the number of connected components of the first five subcolonies between budding and non-budding division conditions. We found that the average number of connected components was significantly lower for budding colonies (Figure 6A). This demonstrates that budding division acts as a mechanism to increase spatial adjacency within subcolonies as well as impact overall subcolony connectivity. Figure 6: Subcolony Structure and Organization in Nutrient-Rich Colonies. (**A**) Comparison of the number of connected components for the first five subcolonies between budding (red) and non-budding (blue) colonies at the 24 h time point. We observe a statistically significant difference in the number of connected components for subcolony 1 (\(p=2.885\times 10^{-10}\)), subcolony 2 (\(p=1.139\times 10^{-10}\)), subcolony 3 (\(p=3.075\times 10^{-04}\)), subcolony 4 (\(p=1.539\times 10^{-06}\)) and subcolony 5 (\(p=1.959\times 10^{-03}\)). (**B**) Comparison of time from creation until each of the first five subcolonies splits into 15 connected components. We observe a statistically significant difference between budding (red) and non-budding (blue) colonies for subcolony 1 (\(p=1.140\times 10^{-04}\)), subcolony 2 (\(p=4.727\times 10^{-04}\)), and subcolony 3 (\(p=1.581\times 10^{-02}\)). (**C**) Comparison of the number of cells in a connected component with less than 10 cells. Note that overall very few cells are in small connected components; however, we observe a statistically significant difference between budding (red) and non-budding (blue) colonies at 12 h (\(p=7.408\times 10^{-40}\)), 18 h (\(p=7.896\times 10^{-19}\)) and 24 h (\(p=1.233\times 10^{-59}\)). (**p**-values in (**A**–**C**) were computed using independent \(t\)-tests. \(p\)-value annotation is as follows. *: \(1.0\times 10^{-2}\)\(p\leq 5.0\times 10^{-2}\). **: \(1.0\times 10^{-3}\)\(p\leq 1.0\times 10^{-2}\). ***: \(1.0\times 10^{-4}\)\(p\leq 1.0\times 10^{-3}\). ***: \(p\leq 1.0\times 10^{-4}\).). (**D**) Kaplan-Meier survival curves for the length of time a subcolony is made up of less than 15 connected components for budding (red) and non-budding (blue) colonies. The \(y\)-axis is the probability that a subcolony consists of less than 15 connected components for longer than \(t\) hours, where time is on the \(x\)-axis. We observe that the survival curves are different between the budding and non-budding colonies (\(p=1.165\times 10^{-06}\)), indicating that budding promotes subcolony connectivity. (The \(p\)-value comparing survival curves was calculated using a log-rank test as described in Section 4.3. In addition, 95% confidence intervals for the survival function are shown. See Section 2.1.4 for details. )Because every subcolony begins with a single cell, which is necessarily a single connected component, we studied at what time a given subcolony would break apart. To do this, we computed the average time elapsed from creation of a given subcolony until it splits into more than 15 connected components. We observe that the average time was significantly lower in non-budding colonies for subcolonies 1, 2 and 3 (Figure 6B). These results suggest budding division impacts subcolony connectivity by ensuring cells in the same subcolony remain physically closer together for a longer period of time. Moreover, we hypothesized that the absence of budding division makes it easier for individual cells to become separated from the rest of their subcolony.