## 2 Results
### Nutrient-Limited Growth: Differential Growth Rates Impact Global Organization of Yeast Colonies
#### 2.2.4 Nutrient Limitation Further Promotes Subcolony Connectivity
We observe a statistically significant difference between budding (red) and non-budding (blue) colonies for subcolony 1 (\(p=8.967\times 10^{-05}\)), subcolony 2 (\(p=6.246\times 10^{-08}\)), subcolony 3 (\(p=8.636\times 10^{-05}\)), and subcolony 4 (\(p=9.154\times 10^{-06}\)). (**C**) Comparison of the number of cells in a connected component with less than 10 cells. Note that nutrient-limited growth results in a large decrease in the total number of cells in small components at the 24 h time point compared to nutrient-rich growth. However, we still observe a statistically significant difference between budding (red) and non-budding (blue) colonies at 18 h (\(p=3.537\times 10^{-02}\)), 24 h (\(p=9.040\times 10^{-07}\)), and 28 h (\(p=5.410\times 10^{-18}\)). (**D**) Kaplan-Meier survival curves for the length of time a subcolony is made up of less than 5 connected components for budding (red) and non-budding (blue) colonies. The \(y\)-axis is the probability that a subcolony consists of less than 5 connected components for longer than \(t\) hours, where time is on the \(x\)-axis. We observed that the survival curves are different between the budding and non-budding colonies (\(p=2.428\times 10^{-23}\)) indicating that the probability that a given subcolony remains connected (i.e., less than 5 connected components) for longer than \(t\) hours is greater for budding colonies. (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 2.2.4 for details.) subcolonies that grow in a \"sector-like\" formation (compare Figure 11 (top and middle) with Figure 2 (middle and bottom)). Namely, subcolony boundaries in nutrient-limited simulations are more linear. This is especially visible in the last time point at 28 h.  
Figure 11: Nutrient Limitation Drives Spatial Organization of Cells. We compared growth and overall spatial organization between four different types of colonies (budding/non-budding, nutrient-rich/nutrient-limited). Cells in colonies are colored according to the unique subcolony each cell belongs to: Subcolony 1 (dark green), Subcolony 2 (blue), Subcolony 3 (cyan), Subcolony 4 (teal), Subcolony 5 (light green), Subcolony 6 (yellow-green), Subcolony 7 (yellow), Subcolony 8 (gold), Subcolony 9 (orange), Subcolony 10 (red), Subcolony 11 (magenta), Subcolony 12 (purple) and Subcolony 13 (pink). Typical simulation output from budding and non-budding colonies grown in nutrient-limited conditions: 12 hours (**A**), 18 hours (**B**), 24 hours (**C**), 28 hours (**D**). (**E**) Nutrient limitation results in more variation in the percentage of the population contained in each subcolony (Subcolony 1 (\(p=2.779\times 10^{-20}\)), Subcolony 2 (\(p=6.143\times 10^{-25}\)), Subcolony 3 (\(p=4.636\times 10^{-23}\)), Subcolony 4 (\(p=6.574\times 10^{-32}\)), and Subcolony 5 (\(p=2.985\times 10^{-09}\)). (\(p\)-values were calculated using the Levene test for equal variances. \(p\)-value annotation is as follows. *: \(1.0\times 10^{-2}\)\(p\leq 5.0\times 10^{-2}\), **: \(1.0\times 10^{-3}\)\(p\leq 1.0\times 10^{-2}\), ***: \(1.0\times 10^{-4}\)\(p\leq 1.0\times 10^{-3}\), ***: \(p\leq 1.0\times 10^{-4}\). (**F**) Birth Location of cells born within the last hour of colony growth changes significantly between nutrient-rich (red) and nutrient-limited (cyan) conditions (\(p<1.0\times 10^{-32}\)). (\(p\)-value was calculated using the Kolmogorov-Smirnov statistic in python. See Section 2.2.5 for details.) In addition, unlike colonies grown in nutrient-rich conditions, colonies grown in nutrient-limited conditions have highly variable subcolony sizes as a percentage of the colony. For example, consider the different sizes of the first subcolony (dark green) in both the top and middle row of Figure 11. At 28 h, the first subcolony in the top row appears to consist of close to half of the total population.