## 2 Results
#### 2.1.2 Budding Does Not Change Global Age and Spatial Structure but Impacts Local Connectivity  
Next we analyzed the relationship between cell age and spatial location within the colony after 24 h of growth. First we computed the empirical probability density function for the ages of cells in the colony (Figure 4A). We find that over 93% of cells are less than 8 h old, and thus we focus on this subpopulation. (Note, because cell cycle timing is unchanged between budding and non-budding colonies, as expected we find no difference in the distribution of cell ages between these two conditions). Figure 3: Population Growth, Expanse and Sparsity of Simulated Yeast Colonies in Nutrient-Rich Conditions. (**A**) Colony growth is exponential with doubling time \(\sim\)105 min (inset). Bar plots represent average number of cells in each colony across all 50 simulations for both budding and non-budding colonies under nutrient-rich conditions calculated at 4.5 h intervals: (**B**) Colony expanse increases over time for both budding and non-budding colonies; (**C**) Colony sparsity decreases to 1 (implying that the colony is becoming more circular) as the size of the colony increases over time for both budding and non-budding colonies. (See Section 2.1.1 for details.) Next, we quantified the birth location of cells within the colony (Figure 4B). To do this, we analyzed the empirical probability density function for the normalized distance from the colony center of mass to the birth location of cells born in the last hour of colony growth. We observe that in both conditions, cells are more likely to be born closer to the perimeter of the colony. We note that this empirical distribution has a nearly linear increase, consistent with a uniform probability per area of the colony, with the exception of the decreased probability at the moving front of the colony. Similarly, we find no difference in birth location of cells between budding and non-budding colonies demonstrating that the budding mechanism has no impact on birth locations within the colony. Finally, to ensure that this distribution itself is not age structured, we examined the distance from the colony center of mass (Figure 4C) and note that both budding and non-budding cells display uniform probabilities with respect to distance from the colony center of mass for all ages. While there are no differences in the large-scale age structure between budding and non-budding colonies, we note that there are significant differences within the local neighborhood of a cell. More specifically, we observed a small, but statistically significant (non-overlapping 95% confidence intervals) difference in the distance a cell less than 8 h old was from its mother (Figure 4D). Although this difference is quite small (less than the average radius of a cell), because most cells in the colony fall into this age group, this suggests significant differences in the local spatial arrangement and organization of budding versus non-budding colonies. Note, for both average distance from the colony center of mass (Figure 4C) and average distance from cells to their mother (Figure 4D), average values were determined for different age groups using a sliding window with a fixed window size of 20 min. In addition, 95% confidence intervals are shown for each window. Figure 4: Age and Spatial Organization of Cells in Nutrient-Rich Colonies. (**A**) Empirical probability density function for cell ages in synthetic colonies after 24 h of colony growth. We observe that the probability that a given cell is \(\leq\) 8 h old is 0.9388: (**B**) Empirical probability density function for the normalized distance from the colony center of mass to the birth location of cells born in the last hour of colony growth (\(D_{norm}\)). We observe that the probability that \(D_{norm}\) is \(\geq\) 0.5 is 0.6844: (**C**) Cell age (h) versus cell distance from the colony center of mass for budding (red) and non-budding (blue) colonies at the 24 h time point.