Errors in Coefficient or Expected Value? Effects of Different Methods on Simulated Values for a Linear Model and the Nonlinear Von Bertalanffy Growth Model

Abstract

Monte Carlo simulation is widely applied to incorporate the uncertainties in fisheries assessment models. However, even modeling the same kind of uncertainty, different practices often occur among studies, which may lead to erroneous results. We demonstrate how simulation results differed among methods of incorporating uncertainty into simulation in different ways: adding random errors to model either coefficients or expected values. Using life history parameter data from sailfish (Istiophorus platypterus), natural mortality from Pauly's empirical equation, and lengths-at-age from the von Bertalanffy growth model (VBGM) were simulated using different methods. Different simulation methods did not affect the averages of simulated values from Pauly's empirical equation and had only slight effects on the simulated lengths-at-age from the VBGM. For both linear Pauly's equation and nonlinear VBGM, the variances of the simulated values from the errors-in-coefficients methods were under-estimated, being approximately 1 to 7% or 40 to 95% of those from errors-in-expected-values methods, depending on whether the correlation among coefficients was included or not. Therefore, adding random errors with either an additive or multiplicative error structure to the expected values is preferred over the errors-incoefficient methods for fully representing uncertainty in the data.