Further Analysis of Clockwise Loops and Anticlockwise Loops Observed in a Stock-Recruitment Relationship

Loop-shaped trajectories are commonly observed in the stock-recruitment relationship (SRR). A mechanism that explains why the loops emerge in SRR has been proposed, and the aim of this study was to validate this mechanism using 62 stocks that live in the waters around Japan, the Northwest Atlantic Fisheries Organization area, and elsewhere. We discuss the relationship between the age at maturity and the slope of the regression line adapted for the SRR data. Further, we discuss whether or not the age at maturity determines whether clockwise or anticlockwise loops are dominant. The results were as follows: 1) The slopes of the regression line adapted for the SRR had positive values when the age at maturity was low. As the age at maturity increased, the slopes decreased to zero and then became negative values. As the age at maturity increased even further, the slopes again changed from negative values to zero and then from zero to positive values. 2) Clockwise loops were dominant when the age at maturity was low, and anticlockwise loops were dominant when the age at maturity was high. As the age at maturity increased even more, clockwise loops again became dominant. These findings coincide well with the results presented by Tanaka et al. In the past, a density-dependent effect has been considered to be the main factor driving the fluctuations, but the present results indicated that a different mechanism may control the SRR and the fluctuations in the population.