Table 1 Model variables and biological parameter descriptions.
Symbol/Parameter | Units | Biological interpretation |
|---|---|---|
x | nutrient conc. | nutrient concentration (e.g., mg L\(^{-1}\)) |
y | biomass | phytoplankton biomass (e.g., mg C L\(^{-1}\)) |
z | by-prod. conc. | concentration of inhibitory by-product or toxin |
r | time\(^{-1}\) | intrinsic nutrient replenishment or renewal rate |
k | nutrient conc. | nutrient carrying capacity or inflow saturation level |
\(\mu\) | time\(^{-1}\) | maximum nutrient assimilation rate by phytoplankton |
a | nutrient conc. | baseline half-saturation constant in BD uptake |
b | — | nutrient handling saturation coefficient in uptake |
d | biomass\(^{-1}\) | classical consumer interference strength (crowding) |
e | by-prod.\(^{-1}\) | by-product interference coefficient (allelopathic inhibition) |
c | time\(^{-1}\) | external nutrient forcing rate (de-/eutrophication intensity) |
m | time\(^{-1}\) | baseline phytoplankton mortality rate |
\(\theta\) | by-prod.\(^{-1}\) time\(^{-1}\) | toxin-induced mortality or physiological damage rate |
\(\eta\) | — | strength of by-product-mediated uptake inhibition |
\(\tau\) | time | ecological delay in inhibition or detoxification feedback |
\(\alpha\) | by-prod. (biomass\(^{-1}\) time\(^{-1}\)) | rate of by-product (toxin/exudate) production per biomass |
\(\gamma\) | time\(^{-1}\) | baseline by-product decay or detoxification rate |
\(\omega\) | nutrient\(^{-1}\) time\(^{-1}\) | nutrient-dependent enhancement of detoxification; |
appears in \((\gamma +\omega x)z\) | ||
\(\mathcal {R}_0\) | — | invasion threshold; ratio determining bloom initiation |
\(p_{\textrm{cycle}}\) | — | probability of sustained oscillations under uncertainty |
\(T_d\) | time | damping time of transient oscillations |
