Performance of Deming and Passing-Bablok Regression Analysis in Detecting Proportionality in the Stock-recruitment Relationship

Simulation studies were conducted to investigate whether a simple, Deming, or Passing-Bablok regression analysis can detect proportionality in the stock-recruitment relationship (SRR) when the data contain process and/or observation errors. The results indicated that the Deming and Passing-Bablok regressions were much more able to detect proportionality between recruitment (R) and spawning stock biomass (SSB) than was simple regression analysis. With simple regression analysis, when the number of samples was large and the observation errors in the SSB were large, the detection of proportionality decreased greatly. When the true slope of the regression line of ln(R) against ln(SSB) was less than unity, and the coefficient of variation in the observation error in R was large and that in SSB was small, the probability that Deming and Passing-Bablok regressions erroneously detected proportionality was extremely high. However, simple regression analysis seldom erroneously detected proportionality because it tended to underestimate the slope in response to process and/or observation errors. When the Deming and Passing-Bablok regressions were applied to data for the Japanese sardine Sardinops melanostictus (Temminck Schlegel 1846), Pacific sardine Sardinops sagax (Jenyns 1842) , and chub mackerel Scomber japonicas Houttuyn 1782, the slopes were not statistically different from unity and no density-dependent effect could be detected.