A Sensitivity Analysis of Deriso's Delay-Difference Equation Using Simulation

The degree to which the delay-difference equation can track biomass changes of fish stocks was examined using a sensitivity analysis technique in conjunction with a simulation model having explicit age-class structure. The simplicity of the delay-difference equation results from the manner in which it subsumes age-class structure by using two parameters, one for mortality and one for growth. The changes in biomass in a simulated stock were followed closely by the equation when error-free determinations of stock parameters were transferred from the simulated stock to the equation, even when a high degree of density dependence was allowed in the growth rate, and in some cases when there were large differences in age-specific mortality in the simulated stock. When error was induced in the stock parameters, the delay-difference equation was fairly robust in estimating biomass with mortality rate and growth rate simultaneously either above the true value or below the true value. Good biomass estimates also resulted when growth rate was at the true value and mortality rate was above the true value. Poor biomass estimates resulted when mortality was overestimated while growth was underestimated, or vice versa.