## 1 Introduction  
The morphological characteristics exhibited by growing microbial communities arise from complex interactions between genetic, epigenetic, environmental and cellular determinants [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14] (Figure 1). For example, the emergence of large regions of a single genotype in bacterial colonies is most often associated with the chance loss of certain genes as individuals die or do not reproduce due to nutrient limitation [8; 9; 11]. In this scenario, the survival or extinction of an individual depends on relative fitness or physical interactions with neighboring cells [5]. In yeast colonies, sectoring patterns appear when cells transition between different phenotypic states [2; 3; 15; 16; 17; 18; 19; 20; 21]. One example in _Saccharomyces cerevisiae_ is the appearance of sectoring in yeast prion phenotypes. In the non-prion state ([_psi_-1]), cells establish red colonies: however, when prion aggregates are present ([_PSI_+]), _S. cerevisiae_ colonies exhibit different colors ranging from white (strong) to shades of pink (weak). Under certain experimental conditions, changes in protein aggregation dynamics between neighboring cells result in sectors corresponding to loss of the prion phenotype (Figure 1D). Other examples of sectoring in yeast colonies include spontaneous mitotic crossover [18; 19] and the white-opaque switch in _Candida albicans_[2; 16; 17; 20; 21]. In each case, the complex phenotypic organization that arises from an initially small group of cells, provides a rich data set that can be used to uncover relationships between molecular processes, individual cell behaviors and phenotypic transitions at the colony level (Figure 1). At this point, most biological studies do not provide rigorous quantification of shape, size and structure between different sectoring phenotypes. As such, characterizing the role of individual cell behaviors in directing spatial organization of cells, as well as quantifying their impact on overall heterogeneity and disease progression within microbial communities is an underexplored opportunity for discovery. In this study, we propose a novel mathematical and computational framework that depicts realistic biophysical division processes and the effect of nutrient limitation, and use our model to study how these processes impact colony organization. In yeast, and other microbial colonies, cells grow closely together, and the cumulative effect of mechanical interactions at the microscopic scale impacts the overall shape and organization of growing colonies [5; 22]. For example, patterns of polarized growth and division have been shown to impact cellular organization, and cell-cell adhesion forces have been shown to impact how the population expands outward and how cells divide [23]. An interesting feature of _S. cerevisiae_ is that cells undergo an asymmetric division process called budding (Figures 1 and 14) [24; 25; 26; 27; 28]. During budding division, new daughter cells form as protrusions on the surface of the mother cell and stay attached until they reach a mature size and physically separate. After separation the resulting mother and daughter cells are unequal in size and the daughter cell does not inherit the replicative age of the mother. The creation of a large mother-daughter cell pair during budding division results in distinct biophysical properties from fission (i.e., non-budding division), a process by which cells split symmetrically into two daughters. Moreover, this difference leads to small perturbations in the physical interaction between neighboring cells and could act as a mechanism driving emergent patterns of organization. Thus, in the case of _S. cerevisiae_, understanding the impact of budding division and other individual  
Figure 1: Spatial Phenotypes are the Consequence of Processes at Different Scales. (**A**) Cells transition between different phenotypic states due to genetic mutations or epigenetic determinants. For example, alternative conformations of the prion protein in _S.