Estimation Of Fish Natural Mortality Coefficient Using Virtual Population Analysis

Fish natural mortality coefficient (M), also instantaneous natural mortality rate, is an important parameter in fishery resource assessment. Many mathematical models of fish population dynamics include M directly or indirectly. However, M is the least known among the four factors affecting fish stock variation: recruitment, growth, natural death and fishing death. For a long time, fishery scientists have explored different methods to estimate M accurately, expecting to better understand fish stocks, and further to achieve rational management and sustainable exploitation of fishery resources.Using both simulation data and real fishery data, this thesis has attempted to estimate fish M based on Virtual Population Analysis (VPA).Firstly, the method of estimating M using'standard'statistical catch-at-age (SCAA) model was proposed. Results show that the quality of the annual recruitment data greatly affected the estimated Ms. When white noise (Coefficient of variation, CV) of the recruitment data reached 10%, the estimated Ms were biased, even when the CVs of catch data (C) and effort data (E) were low. CVs in C and E were also important factors to affect the estimated M, and CVC made more impacts than CVE on the estimated M. For the four simulated fishery scenarios (good contrast, one-way trip, recovery and status quo) the results indicated that the one-way trip fishery outperformed the other three, since it obtained the most viable estimated M for all the supposed conditions. In contrast, the recovery fishery had the worst performance. When M varied through ages, von-Bertalanffy growth function (VBGF) was introduced into the SCAA model to estimate the age dependent M, and the one-way trip and good contrast fisheries obtained better estimated Ms than the recovery and status quo fisheries.Subsequently, using Monte Carlo simulation analyses, M was estimated from the'standard'VPA, when fish abundance (N) and catch (C) data were available. Results show that the method performed better for cases of low fishing mortality coefficient (F). When CVs in the simulated data were less than about 10%, reliable estimates for M were obtained. Normally distributed errors produced the most viable estimates for M.Then, M was estimated using the approximate model of VPA—Pope (1972)'s Cohort Analysis (CA) model. Simulation analyses show that the method performed better for species with short longevity and high Ms. When CV of stock size was less than about 10%, the estimated M were mostly reliable. Compared with the CV in the simulated data, the variation of F made less impact on the estimation of M. Error structure of lognormal distribution in model was appropriate for Pope's CA model than normal and gamma distributions. Based on Pope's CA model, a seasonal cohort analysis (SCA) model was presented. Simulation analyses show that when CVs of N and C were low, the SCA model could closely reflect the real seasonal fisheries and obtain better estimated M than those from Pope's CA model.Afterwards, simulation analyses were used to compare the four methods of M estimation, including'standard'VPA, quadratic equation for Pope's approximation (QE-Pope), least sum of square for Pope's approximation (LSS-Pope) and least sum of square for MacCall's approximation model (LSS-MacCall). When M increased or F decreased, the quality of the estimated M could be improved, and the value of M gave more impacts on the estimates. Outliers in the abundance data would greatly impact the estimated results of the'standard'VPA, but made relatively less impacts on the method of LSS. Generally speaking, the QE-Pope obtained stable results both when simulated data have and have no outliers.Finally, the estimation of fish M using extended survivors method based on C and abundance index (catch per unit effort, CPUE) data was analyzed. Monte Carlo simulation analyses show that the estimated M was more sensitive to the CV of C than that of CPUE data; smaller F could improve the quality of estimated M, and the value of M itself did not make much impact on the estimation.For the real fishery data, the'standard'VPA method, Pope CA model,'standard'statistical VPA method and extended survivor method were applied to the Yellow Sea anchovy (Engraulis japonicus), North Atlantic albacore (Thunnus alalunga) and Flack lake trout (Salvelinus namaycush), respectively. Except for the larger errors in the estimated M of the older age that caused by the greater uncertainties in the observed N of anchovy, viable estimates of M were obtained for younger age groups of anchovy, and fisheries of North Atlantic albacore and Flack lake trout. Therefore, they may show that the estimation methods of fish M analyzed in this thesis are applicable in real fisheries.