Canary rockfish (Sebastes pinniger) COSEWIC assessment and status report: chapter 20

Appendix 1: Reconciling catch and surveys for Canary rockfish

Please note: Technical appendices on derivation of landings and abundance indices are available on demand.

The two most reliable survey indices come from the west coast of Vancouver Island (WCVI) shrimp survey and the USA triennial survey. Analysed separately with a log-linear model, the WCVI shrimp survey indicates a decline rate of -0.051 yr-1 and the triennial survey has a decline rate of -0.15 yr-1 (Table 1). If one does an analysis of covariance survey as a categorical variable, the interaction term is not significant (i.e. different slopes between surveys) and the intercept term is significant. The common slope estimate for the analysis of covariance is -0.064 yr-1, close to the WCVI survey index which has many more data points than the triennial.

If we accept the slope of the combined analysis is representative of the long term trend in canary rockfish biomass on the coast, how do we reconcile the historic catches with the stock productivity?

A very simple production model would be

Bt+1 = gBt - Ct

where Bt is biomass in year t, Ct is catch in year t, and g is the surplus production rate, in this case assumed to be time invariant and density independent. In the absence of fishing

g = Bt+1 / Bt

 

Given guesses of g and the biomass at the beginning of the time series (B0 ), it is possible to estimate Bt. The slope of the log linear regression over the time period can then be estimated. The question can be addressed by examination of the set of g and B0 that gives a log linear slope equal to that observed in the combined survey analysis. The question then becomes; Are these consistent with what we know about canary rockfish?

The set of feasible g and B0 values are negatively correlated, as g increases, B0 declines (Table 2). A harvest rate of about 5% is considered sustainable, approximately equivalent to stating that a surplus production rate of 5% would be reasonable for this species if its biomass was in the region of maximum total production (i.e. MSY). The results indicate that with this growth rate and B0 = 18 000 t, the required slope value can be obtained. The results for this scenario indicate a surviving biomass of close to 4000 t in 2004 (Table 3). This is within the range of survey estimates of minimum biomass (actual biomass estimates depend on trawl catchability).

That the biomass appears to have declined throughout most if not all of this period indicates that the harvest rates experienced were not sustainable. The estimated harvest rates from the scenario in Table 3 are increasing in the most recent years. If we had some confidence in these estimates this could be a cause for concern. However, as indicated above, a constant surplus production rate and no density dependence were assumed for this model, which was done as a test of ranges, not as a population assessment.

The overall conclusion is that reported catches are consistent with plausible biomass estimates and the combined trend of the two more reliable indices. Thus, fishing can explain the observed decline.

 

Table A1 (a. Separate analyses): Results of log-linear analysis of long term trend in BC canary rockfish from the WCVI shrimp and USA triennial surveys
Survey N slope p val
WCVI 29 -0.051 0.0406
TRI 7 -0.15 0.0200

 

Table A1 (b. Combined analysis, separate slopes and intercepts): Results of log-linear analysis of long term trend in BC canary rockfish from the WCVI shrimp and USA triennial surveys
Term estimate p val
intercept 206.5 0.0028
year -0.10 0.0037
survey(TRI) 0.71 0.0055
year*survey -0.049 0.1354

 

Table A1 (c. Combined analysis, common slope, separate intercept): Results of log-linear analysis of long term trend in BC canary rockfish from the WCVI shrimp and USA triennial surveys
Term estimate p val
intercept 133.7 0.0041
year -0.064 0.0062
survey(TRI) 0.68 0.0082

 

Table A2: The set of g and B0 values that give a slope of -0.064 between ln biomass and year for BC Canary rockfish
Bo g
10 000 1.115
11 000 1.103
12 000 1.092
13 000 1.083
14 000 1.074
15 000 1.067
16 000 1.061
17 000 1.055
18 000 1.050
19 000 1.045
20 000 1.040
21 000 1.036
22 000 1.033
23 000 1.029
24 000 1.026

 

Table A3: Input data (catch) and estimated biomass for g = 1.05 and B 0 = 18 000 t for B.C. canary rockfish
Year Catch (t) Biomass ln Biomass H Rate
1980 1 173.3 17 726.7 9.78 0.07
1981 626.4 17 986.6 9.80 0.03
1982 826.6 18 059.4 9.80 0.05
1983 1 335.5 17 626.8 9.78 0.08
1984 1 789.8 16 718.4 9.72 0.11
1985 1 498.9 16 055.4 9.68 0.09
1986 1 156.8 15 701.3 9.66 0.07
1987 1 411.9 15 074.5 9.62 0.09
1988 1 814.3 14 014.0 9.55 0.13
1989 1 816.7 12 897.9 9.46 0.14
1990 1 590.9 11 951.9 9.39 0.13
1991 1 352.6 11 197.0 9.32 0.12
1992 1 401.8 10 355.0 9.25 0.14
1993 1 113.9 9 758.8 9.19 0.11
1994 1 198.9 9 047.9 9.11 0.13
1995 924.2 8 576.0 9.06 0.11
1996 761.6 8 243.3 9.02 0.09
1997 746.7 7 908.8 8.98 0.09
1998 832.7 7 471.5 8.92 0.11
1999 975.8 6 869.2 8.83 0.14
2000 821.2 6 391.5 8.76 0.13
2001 852.0 5 859.0 8.68 0.15
2002 896.4 5 255.6 8.57 0.17
2003 864.7 4 653.7 8.45 0.19
2004 809.2 4 077.2 8.31 0.20


Figure A1: Log linear regression of biomass vs. year for the B.C. canary rockfish catch series and g = 1.05 and B0 = 18 000 t

Figure A1. Log linear regression of biomass vs. year for the B.C. canary rockfish catch series and g = 1.05 and B0 = 18 000 t.

Page details

Date modified: