Colvin, M.E., C.L. Pierce, and T.W. Stewart. 2012. Semi-discrete biomass dynamic modeling: an improved approach for assessing fish stock responses to pulsed harvest events. Canadian Journal of Fisheries and Aquatic Sciences. 69(10): 1710-1721 PDF

Overview.— 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 simulated a commercial fishery for common carp to develop semi-discrete biomass dynamics models (SDBDMs) that allow discrete harvest events. We evaluated differences between CBDMs and SDBDMs using an equilibrium yield analysis to evaluate sustained yield at varying levels of fishing mortality (F). The effect of applying harvest continuously when it was in fact discrete was evaluated by fitting CBDMs and SDBDMs to a hypothetical stock of common carp (Cyprinus carpio) undergoing discrete harvest and evaluating bias in parameter estimates. Equilibrium fishery yields for CBDMs and SDBDMS were similar at low levels of F and became increasingly different as F approached and exceeded F at maximum sustained yield (FMSY). Discrete harvest resulted in lower equilibrium yields at high levels of F relative to continuous harvest. Biological reference points were reduced when harvest was discrete, providing a biological basis for the use of F0.1, where reducing FMSY compensates for violating the assumption of continuous harvest. Parameters estimated from SDBDMs were unbiased regardless of F. Parameters were negatively biased in the exponential CBDM. Intrinsic growth rate was relatively robust to violating the assumption of continuous harvest in CBDMs containing Bmax. The parameter, Bmax was negatively biased with increasing harvest for CBDMs. Effects of parameter bias on biological reference points were generally negative for BMSY and MSY, while FMSY was relatively unbiased. Semi-discrete BDMs outperformed continuous BDMs and should be used when harvest structure (i.e., date, amount) are known and F is greater than FMSY for models containing Bmax. Discrete harvest dynamics should be accounted for using regardless of level of harvest in exponential BDMs.