## 2 Results
### Nutrient-Limited Growth: Differential Growth Rates Impact Global Organization of Yeast Colonies
#### 2.2.3 Nutrient-Limited Growth Promotes Colony Connectivity  
As for nutrient-rich growth conditions, the colony connectivity decreases in time and is significantly higher in budding colonies (compare Figure 5A with Figure 9A). However, we observe that nutrient-limited growth promotes colony connectivity as both budding and non-budding colonies have higher connectivity in this growth condition at the 24 h time point. In addition, the difference in colony connectivity is observable much earlier on in the life of the colony (12 h vs. 18 h). Figure 8: Age and Spatial Organization of Cells in Nutrient-Limited Colonies. **(A)** Empirical probability density function for cell ages in synthetic colonies after 28 h of colony growth. We observe that the probability that a given cell is \(\leq\) 12 h old is 0.9454: **(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 0.889: **(C)** Cell age (\(\eta\)) versus cell distance from the colony center of mass for budding (red) and non-budding (blue) colonies at the 28 h time point. In both **(C,D)** average values were determined for different age groups using a sliding window with a fixed window size of 20 min. We conclude that distance from the colony center of mass at 28 h is strongly correlated with age. However, we see that cell distance from the colony center of mass is not impacted by budding division since 95% confidence intervals overlap: **(D)** Cell age (h) versus cell distance from its mother for budding (red) and non-budding (blue) colonies. The difference between budding and non-budding colonies is given for ages 2, 4, 6, 8, 10 and 12. We conclude that this difference is significant since 95% confidence intervals do not overlap. Moreover, since nutrient-limited colonies are smaller than nutrient-rich colonies, this difference becomes even larger when it is considered relative to the size of the colony. (See Section 2.2.2 for details. )As above, we analyzed connectivity between mother and daughter pairs in two distinct phases: when they are attached for budding cell division (budded cells, Figure 9B) and after separation (un-budded cells, Figure 9C). We observe that, as in nutrient-rich growth, the connectivity between mother and daughter cells in both phases was higher for budding cell division, and that this difference is due to the fact that the number of daughter cells in the population is larger than the number of daughter cells in the population. Figure 9: Colony Connectivity in Nutrient-Limited Colonies. Comparison of colony connectivity between budding and non-budding colonies in nutrient-limited conditions at 12 h, 18 h, 24 h and 28 h. We compared connectivity for all cells in (**A**), as well as cells in two distinct phases: during the time when cells are attached for budding colonies in (**B**) and after separation in (**C**). (See Section 4.2.2 for how we define connectivity). (**A**) We observe a statistically significant difference in colony connectivity at 12 h (\(p=3.602\times 10^{-04}\)), 18 h (\(p=8.921\times 10^{-29}\)), 24 h (\(p=1.094\times 10^{-79}\)) and 28 h (\(p=3.389\times 10^{-110}\)). (**B**) We observe a rapid decrease in connectivity for non-budding colonies between 12–18, 18–24, and 24-28 h. This decrease leads to a statistically significant difference between budding and non-budding colonies at 12 h (\(p=6.834\times 10^{-05}\)), 18 h (\(p=4.670\times 10^{-40}\)), 24 h (\(p=1.050\times 10^{-92}\)) and 28 h (\(p=2.658\times 10^{-122}\)). (**C**) We observe a statistically significant difference in connectivity at 18 h (\(p=1.144\times 10^{-15}\)), 24 h (\(p=1.888\times 10^{-56}\)) and 28 h (\(p=2.140\times 10^{-83}\)). (**\(p\)**-values for connectivity were computed using independent \(t\)-tests. \(p\)-value annotation is as follows.