Appendix C. Equations for the partial derivatives, obtained from the differentiation of the species-specific and total biomasses, and used to evaluate the propagated error.
Partial differentiation of Eq. 3b yields the following three partial derivatives. The derivatives were substituted into Eq. 1 to determine the error in the species-specific biomasses. Note that the partial derivatives themselves are functions of the input variables.
(C.1a)
|
The form of Eq. 4 with the partial derivatives included is shown below in Eq. C2.
(C.2) |
Equation C.2 thus represents the error equation for the species-specific biomass.
Partial differentiation of Eq. 3c shows that the partial derivative of the total biomass with respect to the species-specific biomasses equals 1 (Eq. C.3).
(C.3) |
This result was used to write Eq. 5 in the text.