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Table 1 Frequently used functions of absolute and relative plant growth rate. a , b , c are model parameters and the symbol t denotes time or age

From: Methods of modelling relative growth rate

Function name/source Growth function Absolute growth rate Relative growth rate
Chapman-Richards
(Richards 1959)
a(1 − e − bt)c abce bt(1 − e − bt)c −1 bc (1 − e − bt)− 1
Gompertz (1825) \( a{e}^{-b{e}^{-ct}} \) \( abc{e}^{-ct}{e}^{-b{e}^{-ct}} \) bce − ct
Kangas (1968) - - \( a{e}^{b{t}^{-c}} \)
Korf
(Zeide 1993)
\( a{e}^{-b{t}^{-c}} \) \( abc{t}^{-c-1}{e}^{-b{t}^{-c}} \) bct − (1 + c)
Logistic
(Verhulst 1838)
a(1 + ce − bt)−1 abce bt(1 + ce − bt)−2 bc (c + e bt)− 1
Monomolecular
(Weber 1891)
a(1 − ce − bt) abce bt bc (e bt − c)− 1
Weibull
(Zeide 1993)
\( a\left(1,-,, {e}^{-b{t}^c}\right) \) \( abc{t}^{c-1}{e}^{-b{t}^c} \) \( bc{t}^{\left(c-1\right)}\kern0.5em {\left({e}^{b{t}^c}-1\right)}^{-1} \)