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C3: Estimation of size-transition matrices with and without molt probability for Alaska golden king crab using tag–recapture data M.S.M. Siddeek, J. Zheng,

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Presentation on theme: "C3: Estimation of size-transition matrices with and without molt probability for Alaska golden king crab using tag–recapture data M.S.M. Siddeek, J. Zheng,"— Presentation transcript:

1 C3: Estimation of size-transition matrices with and without molt probability for Alaska golden king crab using tag–recapture data M.S.M. Siddeek, J. Zheng, D. Pengilly, and Vicki Vanek Alaska Department of Fish and Game Juneau and Kodiak TOPIC C: Specification and estimation: length-structured models November 6, 2014

2 Introduction  Size transition matrices play an important role in modeling growth in the size-structured models.  Crabs grow by molting and then incrementing in size. Therefore, the size transition matrix estimator should contain the molt and the growth increment sub-models.  Unless tag-recaptures are separated by molt and non-molt stages, it will be difficult to estimate the molt probability unequivocally. We have that situation with the Aleutian Islands golden king crab (Lithodes aequispinus) tagging data from the eastern Aleutian Islands region.  We considered a logistic molt probability and a normal growth increment models for the size transition matrix estimator under an integrated stock assessment model setting.  We used a number of diagnostic statistics to investigate the estimator without (Scenario 1) and with the molting probability (Scenario 2) sub- models.

3 Data  Pot fishery retained (1985/86–2012/13) and total catch (1990/91–2012/13), standardized legal size CPUE from observer data (1995/96-2004/05; and 2005/06–2012/13), groundfish fishery bycatch (1995/96–2012/13), and tag release-recapture lengths (from 1991,1997, 2000, 2003, and 2006 tagging experiments).

4 Table 1. Time series of nominal pot fishery retained and observer legal size catch-per-unit-effort (CPUE, number of crabs per pot lift), observer sample size (number of sampled pots), total fishing effort, and GLM estimated CPUE Index for the eastern Aleutian Islands region golden king crab stock. NA = no sampling information. 1990 refers to the 1990/91 fishery. Year Pot Fishery Nominal Retained CPUE Observer Nominal Retained CPUE Observer Sample Size (no.pot lifts) Total Effort (no.pot lifts) CPUE Index 19908.8982.16790 106281 19918.19914.633206 133428 19928.36410.111137 133778 19937.7865.300NA 106890 19945.8922.488NA 191455 19955.8885.2837547 177773 0.734 19966.4515.1676561 113460 0.758 19977.3367.1274676 106403 0.791 19988.8758.9003616 83378 0.954 19998.9649.1413857 79129 0.884 20009.8499.8855047 71551 0.907 200111.65511.0154629 62639 1.184 200212.37211.9453990 52042 1.261 200310.92111.0033970 58883 1.105 200418.29517.5412208 34848 1.802 200525.39727.5361198 24569 1.109 200624.83624.8021103 26195 0.884 200727.95430.7231006 22653 1.019 200827.26029.520613 24466 0.991 200925.85326.669411 26298 0.829 201025.95625.374436 25851 0.849 201137.33340.127361 17915 1.223 201233.01837.735438 20827 1.172

5 Table 2. Tag release and recapture summary (size range: 103 to 183 mm Mid Carapace Length) for the eastern Aleutian Islands region. Total Number of Tagged Crabs (1991,1997, 2000, 2003, and 2006 releases) Time at Large (years) Number of Recoveries by Year at Large 271311936 2491 3214 451 513 612 Overall % recovery6.33

6 Growth Matrix Derivation Formulas Molting probability sub-model: Growth matrix elements: Growth matrix:

7 Tagging data likelihood and recapture prediction formulas (Punt et al., 1997) : Proportion in length-class i of the recaptures which were released in year t that were in length-class j when they were released and were recaptured after y years. Predicted number of recaptures in length-class l: : Target total fishery selectivity vector the number of crabs that were released in year t that were in length- class j when they were released and were recaptured after y years is a vector with at element j and 0 otherwise

8 Population dynamics model and list of likelihoods used in the integrated assessment

9 Stage 2 update of the effective sample size for the length composition likelihoods References: R.I.C.C. Francis, 2011; and McAllister and Ianelli, 1997 Stage 2 update of effective sample size accounts for process errors.

10 Diagnostic Statistics to investigate the growth transition matrix estimator without (scenario 1) and with the molting probability (scenario 2) sub-models.

11 Table 3. Estimate of the growth transition matrix for the golden king crab data from the eastern Aleutian Islands region. Scenario 1 Scenario 2 Statistics?? Biology??

12 Table 4. Correlation matrices of the growth parameters for scenarios 1 and 2. Scenario 1 1 -0.07851 -0.3876-0.09721 Scenario 2 1 0.50761 0.2830.2621 -0.3216-0.2891-0.18131 -0.14840.11420.03560.07541

13 Table 6. Akaike information criterion (AIC) for scenarios 1 and 2. AIC= - 2*ln(MLH) + 2*k, where k=number of parameters Scenario 1Scenario 2Difference Number of estimated parameters 1081102 -ln(MLH) -1072.86-1160.8387.97 AIC -1929.72-2101.66171.94 L 2 metric Base run of scenario1 and scenario 2 models 0.00503 97.5 percentile (upper limit) 0.00669 2.5 percentile (lower limit) 0.00323 Table 5. Evaluating L 2 metrics based on bootstrap confidence limits Note: Likelihood weights are identical for the two scenarios.

14 Figure 1. Observed tag recaptures (open circle) vs. predicted tag recaptures (solid line) by length-class for scenarios 1 to 2 fits to eastern Aleutian Islands region golden king crab data.

15 Figure 2. Predicted (line) vs. observed (bar) retained catch relative length frequency distributions for scenarios1 (no molting probability sub-model) and 2 (with molting probability sub-model) for 1985/86 to 2012/13 in the eastern Aleutian Islands region. Length group 1 is 103 mm CL. Figure 3. Predicted (line) vs. observed (bar) total catch relative length frequency distributions for scenarios1 (non molting) and 2 (with molting) for 1985/86 to 2012/13 in the eastern Aleutian Islands region. Length group 1 is 103 mm CL.

16 Figure 4. Comparison of input observer CPUE indices (open circles with two standard errors) with predicted CPUE indices (colored solid lines) for scenarios 1 (red) and 2 (green) for eastern Aleutian Islands region golden king crab, 1995-2012.

17 Figure 5. Predicted effective sample size vs. input 2 nd stage effective sample size for retained, total, and groundfish discard catch length compositions for scenarios 1 and 2 fits to golden king crab data in the eastern Aleutian Islands region, 1985/96 to 2012/13. The red line is the 45 0 line passing through the origin.

18 Figure 6. Estimated total selectivity and retention curve for pre- (Pre2005) and post- (Post2005) rationalization periods under scenarios 1 (solid black line) and 2 (dotted red line) fits to eastern Aleutian Islands region golden king crab data.

19 Figure 7. Trends in golden king crab mature male biomass for scenarios 1 and 2 in the eastern Aleutian Islands region, 1985/86–2012/13. Mature male crabs are ≥ 121 mm CL. Scenario 2 estimates have two- standard error confidence limits.

20 Conclusions  Scenarios 1 (without molting probability sub-model) and 2 (with molting probability sub-model) produced mixed results: - significant difference in total negative log likelihood values between the two scenarios - significant difference in overall fit between the two scenarios discounting for additional number of parameters -AIC ; - non significant L 2 metrics by bootstrap (limited number of samples); - similar trends in observed vs. predicted number of recaptures and CPUE; - similar trends in mature male biomass, total selectivity, and retention; and - slightly different length composition fits.

21 Discussion  The impact of the difference in the two growth transition matrices was not fully reflected on a number of plots. We should not solely rely on the plots to detect the matrix difference. The parameter confounding under the integrated model setting may produce closer results of derived variables.  Should the growth transition matrix be estimated outside or inside the model?  Should biology (or common sense) override statistics?

22 Thank you Acknowledgement Heather Fitch, William Gaeuman, Lee Hulbert, Robert Foy, Andre Punt, Steve Martel, Paul Starr, Johnoel Ancheta, Mark Maunder, and Dave Fournier.

23 Figure 1. Historical commercial harvest (from fish ticket and in metric tons) and catch-per-unit effort (CPUE, number of crabs per pot lift) of golden king crab in the eastern Aleutian Islands region, 1985/86–2012/13 fisheries (note: 1985 refers to the 1985/86 fishery). Figure 2. Historical commercial harvest (from fish ticket and in metric tons) and catch-per-unit effort (CPUE, number of crabs per pot lift) of golden king crab in the Adak region, 1985/86–2012/13 fisheries (note: 1985 refers to the 1985/86 fishery).

24 Table 3. Estimate of the growth transition matrix for the golden king crab data from the eastern Aleutian Islands region. Scenario 1 Scenario 2 Mid CL 103108113118123128133138143148153158163168+ 103 0.02740.08990.20660.28450.23470.11590.03430.00610.00060.0000 108 0.04130.11650.23510.28440.20610.08940.02320.00360.00030.0000 113 0.06050.14600.25890.27510.17520.06680.01520.00210.00020.0000 118 0.08610.17710.27600.25760.14410.04820.00970.00120.00010.0000 123 0.11890.20800.28470.23350.11470.03370.00590.00060.0000 128 0.15980.23630.28420.20470.08830.02280.00350.00030.0000 133 0.20890.25990.27450.17380.06580.01490.00200.0002 138 0.26590.27660.25670.14270.04750.00950.0011 143 0.33010.28500.23240.11350.03320.0058 148 0.40080.28500.20410.08760.0225 153 0.48010.27860.17530.0660 158 0.57890.27120.1499 163 0.72790.2721 168+ 1.0000 Mid CL 103108113118123128133138143148153158163168+ 103 0.03620.01630.20280.48780.23470.02190.00040.0000 108 0.05440.01940.21940.47930.20950.01770.00030.0000 113 0.08100.02290.23380.46400.18420.01410.00020.0000 118 0.11880.02640.24430.44050.15880.01100.00010.0000 123 0.17110.02970.24910.40810.13360.00830.00010.0000 128 0.24020.03240.24610.36630.10880.00610.00010.0000 133 0.32620.03400.23380.31630.08530.00440.0000 138 0.42580.03400.21230.26100.06390.00290.0000 143 0.53190.03240.18340.20490.04550.0019 148 0.63520.02950.15110.15340.0309 153 0.72750.02740.12750.1177 158 0.80430.03750.1582 163 0.86820.1318 168+ 1.0000

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