Estimating Age-Specific Natural Mortality for Sandfish in the Eastern Coastal Waters of Korea

Giphil Cho, Daewook Kim, Sukgeun Jung, Il Hyo Jung and Sangil Kim
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Giphil Cho: Finance∙Fishery∙Manufacture Industrial Mathematics Center on Big Data, Pusan National University, Busan 46241, Korea
Daewook Kim: Department of Mathematics Education, Seowon University, Cheongju, Chungbuk 28674, Korea
Sukgeun Jung: Department of Marine Life Science, Jeju National University, Jeju 63243, Korea
Il Hyo Jung: Department of Mathematics, Pusan National University, Busan 46241, Korea
Sangil Kim: Department of Mathematics, Pusan National University, Busan 46241, Korea

Mathematics, 2020, vol. 8, issue 9, 1-16

Abstract: To estimate age-specific natural mortality, we proposed an age-structured biomass model with an impulsive dynamical system. In the estimation of natural mortality, we considered growth rate and also reproduction rate, growth, and catch of sandfish, Arctoscopus japonicus . Assuming a linear relationship between observed values of the catch per unit effort (CPUE) and total biomass estimated by the age-structured biomass model, we estimated the age-specific natural mortality using the CPUE and catch data, from 1994 to 2009, for varying values of the assumed initial total biomass in 1994, by selecting the largest coefficient of determination ( R 2 ). We suggested the following empirical formula: M i = q K L ∞ ln ( e K ( i + 1 − t 0 ) − 1 e K ( i − t 0 ) − 1 ) , which estimated natural mortality of sandfish, and the derived age-specific natural mortality was significantly related to fecundity and growth. The parameters of von Bertalanffy growth equation and a logistic equation of maturity with total length were derived from the data of otolith and gonad analysis of female sandfish collected from 2005 to 2008 and from 2005 to 2006, respectively. We also conducted sensitivity analysis by varying the exponent in the inverse function of total length.

Keywords: natural and fishing mortality; parameter estimation; age-structured model; sandfish; impulsive differential system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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