Fig 1.
Modelling frameworks commonly used for capturing the behaviour of microbial communities, with associated spatial scales.
ABM, agent-based model; ODE, ordinary differential equation; PDE, partial differential equation.
Fig 2.
Single-cell measurement techniques for microbial communities.
(a) Flow cytometers can measure cell fluorescence and morphology in large sample sizes. (b) Time-lapse microscopy allows for direct visualization of physical cell–cell interactions and quantitative measurement of single-cell characteristics over time. (c) End-point microscopy can illustrate large-scale spatial patterns and features of cell arrangements in 2 or 3 dimensions.
Fig 3.
Model calibration techniques for spatiotemporal models of microbial communities.
Manual fitting involves direct adjustment of parameter values to achieve qualitative agreement between model predictions and observations. Nonspatial calibration is often systematic (based on a goodness of fit function) but is based on experiments that do not incorporate the spatial features of the system. Spatial calibration, against spatially distributed data, can be systematic (SSE-based) but must rely on summary statistics collected from the data.
Table 1.
Summary statistics for quantifying features in microbial communities.
Fig 4.
Calculating spatiotemporal summary statistics for microbial communities.
(a) Population counts over time capture the overall dynamics in a multispecies community. (b) The frequency of adjacent species in physical contact, determined by a contact network, provides a measure of intermixing between different species. (c) Summary statistics can be calculated from data averaged within a particular cell’s neighbourhood. (d) Single-species patch metrics, such as patch width and number of sectors, are useful for quantifying spatial patterns on a larger colony scale.
Fig 5.
Panels (a-c) illustrate the topology of a dataset changing as the length scale, L, is varied. (a) For small values of L, the balls (disks) are mostly disconnected; only 2 of the 9 intersect. (b) At an intermediate scale, all 9 balls intersect, forming a single connected component, giving rise to a loop. (c) At larger scales, there is a single connected component and no loop. (d) The progression illustrated in (a-c) is documented in the persistence barcode; the blue bars correspond to separate connected components, the ends of which corresponds to intersection (merge) events, e.g., at L = L1. The red bar corresponds to the loop, which forms at L = L2 and which becomes filled in at L = L3. (e) The same information can be represented in persistence diagram in which the (x,y) coordinates of points correspond to the right and left ends, respectively, of each bar in the barcode.
Table 2.
Requirements for generating training data for microbial community models.