| Summary: | 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, <i>Arctoscopus japonicus</i>. 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 (<inline-formula><math display="inline"><semantics><mrow><msup><mi>R</mi><mn>2</mn></msup></mrow></semantics></math></inline-formula>). We suggested the following empirical formula: <inline-formula><math display="inline"><semantics><mrow><msub><mi>M</mi><mi>i</mi></msub><mo>=</mo><mfrac><mi>q</mi><mrow><mi>K</mi><msub><mi>L</mi><mo>∞</mo></msub></mrow></mfrac><mi>ln</mi><mrow><mo>(</mo><mrow><mfrac><mrow><msup><mi>e</mi><mrow><mi>K</mi><mrow><mo>(</mo><mrow><mi>i</mi><mo>+</mo><mn>1</mn><mo>−</mo><msub><mi>t</mi><mn>0</mn></msub></mrow><mo>)</mo></mrow></mrow></msup><mtext> </mtext><mo>−</mo><mtext> </mtext><mn>1</mn></mrow><mrow><msup><mi>e</mi><mrow><mi>K</mi><mrow><mo>(</mo><mrow><mi>i</mi><mo>−</mo><msub><mi>t</mi><mn>0</mn></msub></mrow><mo>)</mo></mrow></mrow></msup><mtext> </mtext><mo>−</mo><mtext> </mtext><mn>1</mn></mrow></mfrac></mrow><mo>)</mo></mrow><mo>,</mo></mrow></semantics></math></inline-formula> 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.
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