Crop growth modelling using the generalised logistic function

[2025-12-11]

The generalised logisitic model for crop growth can be defined as:

\[y(t) = {A + {{K-A} \over {C + (Qe^{-Bt})^{1/v}}}}\]

where:

$y(t)$: biomass at time $t$
$A$: lower asymptote (initial or minimum biomass)
$K$: positively affects the upper asymptote. This is the final or maximum biomass if:
- $C = 1.00$, since:
- $y_{max} = A + (K-A)/C^{1/v}$, then
- $y_{max} = A + K - A$, therefore:
- $y_{max} = K$
$C$: negatively affects the final or maximum biomass
$Q$: negatively affects initial or minimum biomass
$e$: Euler’s number (~2.71828)
$B$: growth rate
$v$: asymmetry parameter ($v ≥ 0$; small values: fast growth early; large values: fast growth later)

To solve for $t$ at specific $y$:

\[t(y) = -{{1} \over {B}} \log {\left( { {{1} \over {Q}} \left( \left( {K - A} \over {y - A} \right)^v - C \right) } \right) }\]