Ecological Archives M075-023-A3

Ernest Lo. 2005. Gaussian error propagation applied to ecological data: post-ice-storm-downed woody biomass. Ecological Monographs 75:451–466.

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)


(C.1b)


(C.1c)

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.



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