Data on the number of sardines and RPS for the Pacific stock of Japanese sardine after 1976 were provided by the Fisheries Agency and Fisheries Research Agency of Japan [3]. Data prior to 1975 were obtained from Wada and Jacobson [4]. The asymptotic standard length (Hereafter, we call this “length”) of sardine from 1976 to 1982, except 1979, and from 2011 to 2018 were obtained from Table 1 of Paper 1 [1]. The number of sardines in the waters off the southeastern coast of Hokkaido (Doto region) during 1976-1986 was obtained from Table 1 in Paper 2 [2]. The individual growth of sardine from 1976 to 1986 was obtained from Figure 4 of Paper 2 [2].

First, we compared the results of the two studies. Next, we compared the trajectories of population abundance (number of fish), length, and three-year moving average of the RPS. Further, we compared the trajectories of length in year t with the three-year moving average of year t − k (k = 0, 1, …, 4). We then estimate the parameter of the regression line for the length in year t against the three-year moving average in year t − 3. The data on the individual growth of sardines obtained from Paper 2 were also examined in the same manner.

Figure 1 shows the data periods used in Papers 1 and 2. In Figure 1, N denotes the average number of fish per period. The red circle indicates 374 hundred million

fish. In Paper 1, two data periods were used from 1976 to 1982, except for 1979 and 2011 to 2018. The authors of Paper 1 noted that density-dependent growth was observed in both periods, and stronger density-dependent growth was observed in the 2011 to 2018 period. We did not use the length data used in Paper 1. Then, instead of length, we used the asymptotic standard length listed in Table 1 of Paper 1.

Figure 2 shows the relationship between the asymptotic standard length and the population abundance of sardines. The closed circles indicate data from 1976 to 1982, except for 1979, and the open circles indicate data from 2011 to 2018. Both slopes of the regression lines were significantly negative; that is, the 1976 to 1982 period was −0.512 (p = 0.034), and the 1976 to 1982 period was −0.406 (p = 0.012). The pattern shown in Figure 2 is similar to that in Figure 6 of Paper 1 [1]. Therefore, we can discuss density-dependent growth using the asymptotic standard length.

Why was the density dependency for the 2011 to 2018 period much stronger than that for the 1976 to 1982 period? The authors of Paper 1 noted that in the 2011 to 2018 period, the zooplankton biomass in July in the summer feeding grounds was lower than that in the 1976 to 1982 period. However, Figure 7b of Paper 1 shows that the wet weight of zooplankton did not drastically differ between the two periods. Further, as shown in Figure 1, the average number of fish in the 2011 to 2018 period was one-seventh of that of the 1976 to 1982 period. Therefore, if zooplankton biomass was the cause of the difference in density-dependent growth, a much greater difference in zooplankton biomass should exist between the two periods.

Figure 3 shows the relationship between the asymptotic standard length and the sardine population abundance in the Doto region. In this case, the slope of

the regression lines for the former period was −0.0375 and with a significant probability of p = 0.274; that is, the slope was not significantly negative, and density-dependent growth was not detected.

Even in the case of Figure 2, the length from 1978 to 1982 appears to be density-independent. The slope of the regression line for the data from 1978 to 1982 and the 95% confidence intervals were −0.0162 (p = 0.505) and (−0.123, 0.0704); that is, the lengths from 1978 to 1982, shown in Figure 2, were also considered as density-independent growth.

The middle part of Figure 1 shows a summary of Paper 2. In Paper 2, data from 1976 to 1986 were used. The data were divided into two periods: 1976-1979 and 1980-1986. They noted that density-dependent growth was observed in the former period; however, density-independent growth was observed in the latter period. Exploring the reasons for these differences, the authors of Paper 2 considered that the feeding ground was enlarged in the latter period to maintain a high abundance of food resources. It is well known that the distribution of sardines changes significantly according to population size. However, as they noted themselves, there is no evidence that the distribution of sardines was quite different before and after 1980.

Both papers used the same 7-year data from 1976 to 1982, and the year of use in Paper 2 was only 4 years longer. However, these results were varied. In Paper 1, density-dependent growth was detected for 1976-1982. However, in Paper 2, density-dependent growth was detected from 1976 to 1979, and density-independent growth was detected from 1980 to 1986.

When we used the abundance data in the Doto region, the length of the 1978 to 1982 period showed density-independent growth. Therefore, there is a possibility that density-independent growth continued for a relatively long period from 1976 to 1986, although the population size had historically been large (Figure 1, bottom). Therefore, a new question has arisen. If the sardine population succeeded in avoiding density-dependent effects and maintaining density-independent growth by expanding its feeding grounds, why did it collapse in 1988? Therefore, it is considered that both conclusions; that is, the weaker or stronger density-dependent growth occurred owing to the different abundance of zooplankton (Paper 1), and the density-dependent growth and density-independent growth occurred because of the different sizes of feeding grounds (Paper 2), seemed questionable.

We analyze the asymptotic standard length. The top panel of Figure 4 shows the trajectory of the number of fish from 1976 to 2018. The blue open circles indicate the data corresponding to the closed circles in Figure 2, and the red open circles indicate the data corresponding to the open circles in Figure 2. Closed red circles indicate the trajectory of the number of fish in the Doto region. The middle part of Figure 4 shows its length. The bottom of Figure 4 shows the RPS (black points) and the three-year moving average of the RPS (purple line). In the

first two years, 1976 and 1977, the length was high; however, in the next four years, 1978, 1980, 1981, and 1982, it was low. The reason why the length in the latter period decreased is generally explained by a density-dependent effect due to the increase in sardine abundance. However, this may not be valid because the abundances in the Doto region in 1977 and 1980 seem almost the same, although the lengths are quite different, and the abundance in the Doto region in 1982 is 3.4 times larger than in 1980; however, the lengths in 1982 and 1980 seem almost the same.

The top of Figure 5 is the same as that in the middle of Figure 4; that is, the trajectory of length is shown again to compare the fluctuations easily between the length and RPS. The middle and bottom of Figure 5 show the trajectory of the RPS and the three-year moving average in year t − 3, which are plotted at year t on the x-axis, in order to compare the fluctuations easily between the length in year t and the RPS three years ago. The scale of the y-axis in the middle of Figure 5 is almost 10 times larger than that at the bottom of Figure 5. The middle and bottom of Figure 5 show that the up and down of the length and that of the RPS coincide well. For instance, the high lengths in 1976 and 1977 coincide with the high three-year moving average of the RSP in 1973 and 1974, which is plotted on the x-axis in 1976 and 1977. The low length in 1978, 1980,

1981, and 1982 coincided well with the low three-year moving average of the RSP in 1975, 1977, 1978, and 1979, respectively. The high lengths in 2011, 2012, 2013, and 2014 coincided well with the high three-year moving average of RSP in 2008, 2009, 2010, and 2011, respectively. The low lengths in 2015, 2016, 2017, and 2018 coincided with the low three-year moving average of RSP in 2012, 2013, 2014, and 2015, respectively. It is considered that the length becomes high or low depending on the environmental conditions in the years when the fish were born.

Figure 6 shows the relationship between the length in year t and the three-year moving average in year t − 3. The slope of the regression line was 0.0327, which was not significant (p = 0.131). However, the RPS in 1976 and 1977 was extremely high, so we excluded the data from 1976 and 1977 and recalculated the regression line between the length in year t and the three-year moving average in year t − 3 (Figure 7). Figure 7 shows a clear positive relationship between the length in year t and the three-year moving average in year t − 3. The slope of the regression line was 0.625, which was statistically positive (p = 0.00834).

We adopted the same approach as the individual growth data in Paper 2 [2]. The top part of Figure 8 is the same as that in Figure 4. The top of Figure 8 shows the trajectories of the population abundance of sardines from 1976 to 2018. The blue open circles indicate the years in which individual growth data were used. Closed red circles indicate the trajectory of the number of fish in the Doto region.

The middle part of Figure 8 shows the individual growth obtained from Paper 2 [2]. The bottom of Figure 8 is the same as that in Figure 4. Individual growth in the first four years seems to decrease with an increase in the population. However, when we used the abundances in the Doto region, the interpretation changed. The abundance from 1980 to 1986 largely fluctuated, even though individual growth for those years seemed to be constant. Therefore, it is difficult to explain the difference in individual growth between these two periods by the difference in the feeding area, as the authors of Paper 2 noted, without showing any evidence.

The top of Figure 9 is the same as that in the middle of Figure 8; that is, the trajectory of the individual growth is shown again to compare the fluctuations easily between individual growth and RPS. The middle and bottom parts of Figure 9 are the same as those in the middle and bottom parts of Figure 5. Figure 9 shows that the pattern of individual growth is similar to that of the three-year moving average of RPS. For instance, the high individual growth in 1976-1977 coincided well with the high three-year moving average of RSP from 1973 to 1974, which was plotted on the x-axis from 1976 to 1977. The low individual growth from 1980 to 1986 coincided well with the low three-year moving average of the RSP from 1977 to 1983. It is considered that individual growth becomes high or low is also determined by environmental conditions in the years when the fish were born.

Figure 10 shows the relationship between individual growth in year t and the three-year moving average in year t − 3. Figure 10 shows a clear positive relationship between individual growth in year t and the three-year moving average in year t − 3. The slope of the regression line was 0.0125, which was significantly positive (p = 0.00784). When the data for 1976 and 1977 are excluded, as shown in Figure 7, a significant positive slope is also obtained; that is, the slope of the line was 0.126, which was statistically positive (p = 0.00688).

Next, we discuss the mechanism that produces an apparent density dependency using the long trajectories of recruitment (top), spawning stock biomass, SSB (middle), and RPS (bottom) of the sardine (Figure 11). All the data were transformed on a natural logarithmic scale. The horizontal line in each figure represents the average value. The fluctuation pattern of recruitment coincided well with that of the RPS. The RPS in the 1960s was below average, and recruitment was also below average. However, the RPS suddenly began to increase in 1969 and continuously increased to an extremely high level in 1970, 1971, and 1973 (red open circles). According to this extremely high RPS, recruitment began to increase considerably from far below the average to above the average (red open circles).

According to the increase in recruitment, SSB also began to increase with a couple of years of delay (red open circles). The extremely large RPS finished in 1974, and the large RPS, which exceeded the average, continued for more than

10 years (red broken circle). According to the continuously high SRP from 1974 to 1985, recruitment increased further from 1980 to 1987. The SSB also continued to increase and reached its maximum value in 1988, with a 2 years delay from the high recruitment in 1986.

However, good environmental conditions never persist, and poorer environmental conditions are necessary. The years from 1988 to 1991 indicate the years when an abrupt change from good to poor environmental conditions occurred. The RPS values from 1988 to 1991 were extremely low (blue open circles). This change in the RPS directory affected recruitment, which dropped abruptly in 1988. The extremely low RPS was completed in 1991; however, poor environmental conditions continued until 2004 (blue broken circle). In other words, the RPSs during this period were below the average. Recruitment continued to decrease until 2004, and SSB reached its lowest level over the years. The environmental condition changed again; that is, the RPS suddenly changed from bad to good in 2008 and 2010 (green open circles). The level was not as extreme as at the beginning of the 1970s; however, the successive huge RPS made the extremely low recruitment jump to the average (green open circles). The high RPS continued after 2010. Therefore, recruitment and SSB increased after 2010. As explained above, the fluctuation of recruitment and SSB was controlled by the RPS, which was considered to be an indicator of environmental conditions.

Figure 12 schematically illustrates the mechanism described above. The upper

figure shows the trajectory of the environmental condition; that is, the trajectory of the RPS. In Phase 1, the environmental conditions were poor for the species, and the strength of recruitment and population abundance was also low, as shown in the lower figure of Figure 12. However, Phase 1 suddenly changed to Phase 2 because of the sudden change from poor to extremely good environmental conditions. The strength of recruitment also increased from low to extremely high, corresponding to the period from 1969 to 1973, as shown at the bottom of Figure 11. The SSB also increased because of this jump in recruitment. As shown at the bottom of Figure 11, after the extremely good condition of the RPS had finished, the good condition continued for more than 10 years. Recruitment then increased continuously (Phase 3). According to the increase in recruitment, SSB also increased with a 2- or 3-year time lag. The SSB further increased and reached an extremely high level (Phase 4).

However, Phase 4 suddenly dropped into Phase 5 due to a sudden change from good to extremely bad environmental conditions. The recruitment strength also dropped to an extremely low level (Phase 5). This implies that an abrupt change from Phase 4 to Phase 5 occurred at a high population size. As shown at the bottom of Figure 11, the extremely poor conditions of the RPS had finished, and the bad conditions continued for more than 10 years. Recruitment subsequently decreased continuously. According to the decrease in recruitment, SSB also decreased with a two- or three-year time lag. Finally, the SSB further decreased and reached an extremely low level (Phase 1).

Notable increases in recruitment always occur when the population abundance is extremely low, and a decrease in recruitment always occurs when the population abundance is extremely high. This is the mechanism by which apparent density dependency is commonly detected. In other words, environmental conditions are the true trigger to change the phase and not a density-dependent effect.

This mechanism can also be applied to the density dependence of the growth. In other words, when environmental conditions were poor, growth was also low. However, the environmental conditions suddenly changed from bad to good, and the growth also changed from low to high. Good environmental conditions continued for several years, SSB reached a high level, and growth was maintained at a high level. However, the environmental conditions suddenly changed from good to poor at high population levels. In response to this environmental change, growth also changed from high to low. Therefore, when we focus on the relationship between growth and population size, higher growth occurs when the population size is small, and lower growth occurs when the population size is large. This is the mechanism by which the apparent density dependency in growth is commonly detected. In other words, environmental conditions, and not the density-dependent effect, are the true trigger to change growth.