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

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)

\( a\left(1,-,, {e}^{-b{t}^c}\right) \)

\( abc{t}^{c-1}{e}^{-b{t}^c} \)

\( bc{t}^{\left(c-1\right)}\kern0.5em {\left({e}^{b{t}^c}-1\right)}^{-1} \)