Semidiscrete biomass dynamic modeling: an improved approach for assessing fish stock responses to pulsed harvest events

Continuous harvest over an annual period is a common assumption of continuous biomass dynamics models (CBDMs); however, fish are frequently harvested in a discrete manner. We developed semidiscrete biomass dynamics mod- els (SDBDMs) that allow discrete harvest events and evaluated differences between CBDMs and SDBDMs using an equili- brium yield analysis with varying levels of fishing mortality (F). Equilibrium fishery yields for CBDMs and SDBDMS were similar at low fishing mortalities and diverged as F approached and exceeded maximum sustained yield (FMSY). Dis- crete harvest resulted in lower equilibrium yields at high levels of F relative to continuous harvest. The effect of applying harvest continuously when it was in fact discrete was evaluated by fitting CBDMs and SDBDMs to time series data gener- ated from a hypothetical fish stock undergoing discrete harvest and evaluating parameter estimates bias. Violating the as- sumption of continuous harvest resulted in biased parameter estimates for CBDM while SDBDM parameter estimates were unbiased. Biased parameter estimates resulted in biased biological reference points derived from CBDMs. Semidiscrete BDMs outperformed continuous BDMs and should be used when harvest is discrete, when the time and magnitude of har- vest are known, and when F is greater than FMSY.