Table 1 Definitions of key variables and terms
From: Modulation of antibiotic effects on microbial communities by resource competition
Symbol | Definition |
|---|---|
\(m\) | Number of species initially present |
\(p\) | Number of types of supplied resources |
\({n}_{i}(t)\) | Abundance of species \(i\) at time \(t\) |
\({n}_{i}^{*}\) | Steady state abundance of species \(i\) |
\(\rho\) | Richness, or number of species with nonzero abundance at steady state |
\({R}_{i\mu }\) | Rate at which species \(i\) consumes resource \(\mu\) |
\({s}_{\mu }\) | Supply rate of resource \(\mu\) |
\(d\) | Dilution rate of the chemostat |
\({b}_{i}\) | Species-specific reduction factor of \({R}_{i\mu }\) values corresponding to species \(i\), interpreted as the susceptibility of species \(i\) to antibiotics |
\({d}_{i}\) | Death rate of species \(i\) |
\({E}_{i}\) | Enzyme budget of species \(i\), where \({E}_{i}={\sum }_{\mu=1}^{p}{s}_{\mu }\) |
\(S\) | Total resource supply rate (in general, assumed to be \(S=1\)) |
\({c}_{\mu }^{*}\) | Steady-state concentration of resource \(\mu\) |
\({\hat{s}}_{\mu }\) | Normalized supply rate of resource \(\mu\), where \({\hat{s}}_{\mu }=(d/S){s}_{\mu }\) |
\({\hat{R}}_{i\mu }\) | Rescaled rate at which species \(i\) consumes resource \(\mu\), where \({\hat{R}}_{i\mu }={c}_{\mu }^{*}{R}_{i\mu }\) |
\(c\) | Factor that scales all values of \({d}_{i}\) equally to mimic the concentration of an antibiotic |
\({D}_{{Ti}}\) | Magnitude of the difference between \({\hat{R}}_{i}\) and \(\hat{s}\), where species \(i\) is targeted by antibiotics |
\({D}_{T}\) | Magnitude of the difference between \({\hat{R}}_{i}\) and \({\hat{R}}_{j}\), where \(i\) and \(j\) are the two species targeted by antibiotics |
\({D}_{N}\) | Magnitude of the difference between \({\hat{R}}_{i}\) and \(\hat{s}\), where \(i\) is the non-targeted species |
\({d}_{{{min }}}\) | Minimum value of \({d}_{i}\) among all nonzero species-specific death rates \({d}_{i}\) during antibiotic perturbation |
Coexistence region size or size of convex hull | Fraction of supply rates that lead to coexistence |
Specialist/generalist consumer | Species that consumes one/all resources at nonzero rates |
More specialist/generalist consumer | Species that has a more/less even distribution of consumption rates |
