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The aim of this paper is to elucidate the fluctuation mechanism in the catch of pink salmon
Oncorhynchus gorbuscha
harvested in the Maritime Province of Siberia. We used catch data on pink salmon born in odd- and even-numbered years. Monthly indices of the Arctic Oscillation and the Pacific Decadal Oscillation were used as the environmental factors. We assumed that the catch in year
t
,
C_{t}
, and that in year
t
2,
C_{t}
_{ 2}
, could be
used to represent the spawning stock biomass and recruitment, respectively, and
C_{t}
_{ 2}
/
C_{t}
could then be used to represent the recruitment per spawning stock biomass. Under these assumptions, we adopted the equation
C_{t}
_{ 2}
/
C_{t}
=
g
(environmental factors) as the model that forecasted the trajectories of the catch. The results were as follows: 1) the trajectories of the catches of pink salmon born in odd- and even-numbered years can be well reproduced by the model mentioned above. No density-dependent effect was detected in the relationship between
C_{t}
_{ 2}
and
C_{t}
, which corresponds to the stock-recruitment relationship (SRR), for catches in both odd- and even-numbered years. The relationship between
C_{t}
_{ 2}
and
C_{t}
for odd-numbered years showed a clockwise loop; however, that for even-numbered years showed an anticlockwise loop. It is believed that this difference occurs in response to the negative relationship between the catches born in odd- and even-numbered years. Pink salmon is one of the typical fish species to which a density-dependent SRR can be applied; however, this study indicates that the assumption of a density-dependent SRR is not valid.

One of the most important tasks in fisheries resource management is to elucidate the fluctuation mechanism in fish populations. One of the key factors in those mechanisms is the stock-recruitment relationship (SRR). The typical traditional SRR models are the well-known Ricker model [

Recently, however, Sakuramoto proposed a new concept of the mechanism of the SRR which did not assume any density-dependent effect [

The data used in this study are shown below: 1) catch in weight for pink salmon landed in the Maritime Province of Siberia from 1950 to 2010 [

We separated the pink salmon catch data into two groups. One is the catch harvested in the odd-numbered year t, which is denoted with C t O , and another is that harvested in the even-numbered year t, which is denoted with C t E . We calculated the correlation coefficients between C t O and AO and between C t O and PDO in month m (m = 1, 2, …, and 12) of year t − k, (k = 0, 1 and 2), and that between C t E and AO and between C t E and PDO in month m (m = 1, 2, …, and 12) of year t − k, (k = 0, 1 and 2).

The eggs of pink salmon are spawned from September to November in year t, and they hatch from February to March in year t + 1. The fries swim downstream to the ocean from April to May in year t + 1 (

The abundance of pink salmon in the maritime Province of Siberia has not been estimated, and so we cannot use abundance data directly. However, when the abundance is high, the catches in the coastal waters and in rivers would also be high. Further, when the catches in the coastal waters and in rivers are high, the SSB that has escaped the harvest in the coastal waters and rivers would also be high. Therefore, we can assume that the SSB in year t (SSB_{t}) is proportional to the catch in year t (C_{t}). In this study, we assume that C_{t} is proportional to SSB_{t} and the catch in year t + 2 (C_{t+}_{2}), is proportional to the recruitment in year t + 2, (R_{t}_{+}_{2}), which is reproduced by SSB_{t}. Therefore, in this study, we assume SSB_{t} ∝ C_{t} and R_{t+}_{2} ∝ C_{t}_{+2} and we analyze the relationship between C_{t}_{+2} and C_{t} as the SRR, which is the relationship between R_{t}_{+2} and SSB_{t}.

This study used three regression methods in plotting ln(C_{t}_{+2}) against ln(C_{t}), i.e., simple regression analysis, Deming regression analysis [^{ }and Passing and Bablok regression analysis [

Pink salmon born in odd- and even-numbered years are completely separated genetically, because the years when they born are completely separated. Therefore, there may be some competitive relationship between these two stocks in the same way that different species that inhabit the same area sometimes engage in competition. In order to confirm this possibility, we investigated the relationship in the case when ln ( C t + 1 E ) was plotted against ln ( C t O ) , because there might be a possibility that the fries born in the even-numbered year t + 1 are eaten by one-year-old fish born in the odd-numbered year t. The opposite relationship was also checked. That is, ln ( C t O ) was plotted against ln ( C t − 1 E ) .

According to Sakuramoto [

C t + 2 / C t = g ( x 1 , x 2 , … , x n ) (1)

where x_{1}, x_{2}, …, x_{n} denote the environmental factors that control C_{t}_{+2}/C_{t}, which corresponds to the R per SSB (RPS). In this model, n denotes the number of environmental factors and g(•) denotes the function that determines how environmental factors affect the ratio C_{t+}_{2}/C_{t}. We applied stepwise regression analysis using R software, “stepwlm”, to select the optimal model shown in Equation (1). Using the estimated values of C_{t}_{+2}/C_{t}, we calculated C_{t+2} using the following equation;

C t + 2 = exp [ { ln ( C t + 2 / C t ) } estimated ] { C t } observed (2)

We calculated the correlation coefficients between C t O and AO and between C t O and PDO in month m of year t − k (k = 0, 1 and 2), and those between C t E and AO and C t E and PDO in month m of year t − k (k = 0, 1 and 2). The AOs and PDOs that showed high correlation coefficients with p-values less than 0.10 are shown in

_{t}_{+2}) against ln(SSB_{t}) for odd-numbered years. The parameters of regression lines estimated by the simple, Deming and

Odd numbered years | ||||||
---|---|---|---|---|---|---|

AO | PDO | |||||

Variable | r | p-value | Variable | r | p-value | |

t | a_{4}* | 0.429 | 0.020 | - | - | |

a_{11}* | −0.322 | 0.089 | ||||

t − 1 | a_{9} | 0.327 | 0.083 | - | - | |

t − 2 | a_{2}* | −0.410 | 0.027 | p_{11} | −0.324 | 0.087 |

a_{5}* | 0.408 | 0.028 | ||||

a_{10} | 0.370 | 0.048 | ||||

Even-numbered years | ||||||

AO | PDO | |||||

Variable | r | p-value | Variable | r | p-value | |

t | a_{4} | −0.315 | 0.096 | p_{1}* | −0.334 | 0.076 |

a_{9} | −0.329 | 0.081 | ||||

t − 1 | a_{4} | 0.513 | 0.004 | - | - | |

a_{12} | 0.351 | 0.062 | ||||

t − 2 | a_{2}* | −0.410 | 0.027 | p_{11}* | −0.324 | 0.087 |

a_{5}* | 0.408 | 0.028 | ||||

a_{10} | 0.370 | 0.048 |

Passing-Bablok regression methods are shown in

_{t}_{+2}) against ln(SSB_{t}) for even-numbered years. The parameters of the regression line estimated by the simple, Deming and Passing- Bablok regression methods are shown in

Odd-numbered years | |||||
---|---|---|---|---|---|

a | b | 95% C.L. | Detection of density effect | ||

Simple | 0.738 | 0.528 | (0.204, 0.852) | b < 1 | Detected |

Deming | −0.0669 | 0.918 | (0.689, 1.208) | b = 1 | Not detected |

P-B | −0.0418 | 1.021 | (0.733, 1.470) | b = 1 | Not detected |

Even-numbered years | |||||

a | b | 95% C.L. | |||

Simple | 0.87 | 0.52 | (0.164, 0.876) | b < 1 | Detected |

Deming | 0.0518 | 1.015 | (0.578, 1.592) | b = 1 | Not detected |

P-B | −0.153 | 1.117 | (0.430, 1.571) | b = 1 | Not detected |

the slopes were not statistically different from unity, and it was judged that no density-dependent effect was detected. In

ln(C_{t}_{ +1}) born in even year t + 1 against ln(C_{t}) born in odd year t. | ||||||
---|---|---|---|---|---|---|

a | b | 95% C.L. | p-value | r | ||

Simple | 2.122 | −0.216 | (−0.448, 0.0115) | b = 0 | 0.0663 | −0.340 |

Deming | 2.304 | −0.325 | (−0.476, −0.088) | b < 0 | ||

ln(C_{t}_{+1}) born in odd year t + 1 against ln(C_{t}) born in even year t | ||||||

a | b | 95% C.L. | p-value | r | ||

Simple | 2.530 | −0.500 | (−1.113, 0.113) | b = 0 | 0.106 | -0.301 |

Deming | 8.139 | −3.776 | (−18.452, −1.792) | b < 0 |

The slope was significantly negative with a 10% significance level (p = 0.0663) when the simple regression analysis was applied, and the slope was significantly negative with a 5% significance level when the Deming regression analysis was applied. That is, we can conclude that ln ( C t + 1 E ) has a negative relationship with ln ( C t O ) . The result of the oppositional relationship, that is, ln ( C t O ) plotted against ln ( C t − 1 O ) is also shown in

In Equation (1), the candidates for the environmental factors are shown in _{t} were less than 0.10. Using these monthly AOs and PDOs, we estimated the optimal model using the stepwise regression analysis in R software. Here, we assume that ln (C_{t}_{+2}/C_{t}) corresponds to ln(RPS_{t}).

The results are also shown in

ln ( R P S t ) = − 0.128 − 0.173 a 2 , t − 2 + 0.504 a 5 , t − 2 + 0.404 a 4 , t − 0.356 a 11 , t (3)

Here a_{m}_{,t}_{−k} denotes the AO in month m of year t − k. The result is shown in

The AOs in February and May in year t − 2 and the PDO in January in year t and the PDO in November in year t − 2 were chosen as the environmental factors for the model forecasting the catch ratio in even-numbered years. That is,

ln ( R P S t ) = 0.0810 + 0.116 a 2 , t − 1 + 0.475 a 7 , t − 2 − 0.132 a 1 , t − 0.218 a 12 , t − 2 (4)

Here p_{m}_{,t}_{-k} denotes the PDO in month m of year t − k. The result is shown in

are also shown at the bottom of _{t}), which is defined by the ratio of the catch, ln(C_{t}_{+2}/C_{t}), in both odd- and even-numbered years, was well reproduced only by these environmental factors, and no density-dependent effect seems to exist in the RPS in both sets of years.

The relationships of the catches between C_{t}_{+2} and C_{t}, which corresponds to the SRR, for the populations born in odd- and even-numbered years were similar, and no density-dependent effect was detected. That is, when the simple regression analysis was applied, the slopes of the regression lines were statistically less than unity; however, when Deming and Passing and Bablok regression analyses were applied, the slopes of the regression lines were not statistically different from unity. That is, SRR can be expressed by a simple proportional model, and the differences from the line can be explained by environmental factors, as Sakuramoto insisted [

The ratio of the catch, C_{t}_{+2}/C_{t}, which corresponds to the RPS, was well reproduced using only environmental factors for both odd- and even-numbered years. This means that the RPS can be reproduced using only the environmental factors, and no density-dependent effect operates in either odd- or even-numbered years. The results coincided well with those for the Pacific stock of Japanese sardines [

AO was selected as the only environmental factor when the model was applied to the odd-numbered years. In contrast, AO in year t was not selected and PDO in years t and t − 2 was selected when the model was applied to the even-num- bered years. AO in February in year t − 2 was selected for both the models; however, the signs in the partial coefficients were opposite, i.e., the value was negative for odd-numbered years and positive for even-numbered years.

In _{t}_{+2}) against ln(SSB_{t}), were opposite for odd- and even-numbered years. According to Sakuramoto [

The mechanism is illustrated in

In term 2, the direction of R is opposite that for species A, and the resultant direction of the combined vectors of R and SSB is northeast. In terms 3 and 4, the mechanisms are the same, and the resultant directions of the combined vectors of R and SSB are northwest and southwest, respectively. That is, when time passes from term 1 to term 4, the resultant trajectory of the SSR forms an anticlockwise loop. The opposite case can also occur. That is, the true trajectory of SRR for fish species C shows an anticlockwise loop, and the R for fish species D has a strong negative correlation with that for species C; thus, the trajectory of SRR for species D forms a clockwise loop. However, according to the theory proposed by Sakuramoto [

The catches born in odd- and even-numbered years have a negative relationship with each other. There might be cannibalism between the pink salmon born in odd-numbered years and those born in even-numbered years. That is, the fries born in even-numbered year t + 1 may be eaten by one-year old fish born in odd-numbered year t, and fries born in odd-numbered year t might be eaten by the one-year old fish born in even-numbered year t − 1. Whether it is true or not has not been investigated at this stage; therefore, further investigation is necessary to elucidate this possibility. However, it must be true that the negative relationship between the catches born in odd- and even-numbered years would be a key factor in understanding the fluctuation mechanism in the pink salmon population.

In this study, we did not discuss the effect of fries that have been artificially released. However, this effect is considered to be negligible, because Morita et al. [

1) We discussed the SRR under the assumption that C_{t} and C_{t}_{+2} were proportional to SSB_{t} and R_{t}_{+}_{2}, and analyzed the relationship between the catches as the SRR. The results indicate that no density-dependent effects were detected in SRR for the pink salmon born in both odd- and even-numbered years.

2) The fluctuation of the catch ratio of the pink salmon born in odd- and even-numbered years can be well reproduced by the model that is described by the following equation:

C t + 2 / C t = g ( environmentalfactors )

Here we assumed that C_{t}_{+2}/C_{t} represents RPS. That is, RPS can be reproduced only by environmental factors. This result coincides well with those obtained and analyzed by Sakuramoto [

3) The relationships between the catches of pink salmon born in odd- and even-numbered years were negative, which is a key factor in understanding the fluctuation mechanism in the pink salmon population.

We thank Dr. Rikio Sato for their useful comments, which improved this manuscript.

Hasegawa, S., Suzuki, N. and Sakuramoto, K. (2017) On a Catch-Forecasting Model for the Pink Salmon Oncorhynchus gorbuscha in the Maritime Province of Siberia. Open Access Library Journal, 4: e3406. https://doi.org/10.4236/oalib.1103406