time-varying vs. non-time- varying growth in the gulf of mexico king mackerel stock assessment: a...

Time-Varying vs. Non-Time-Varying Growth in the Gulf

of Mexico King Mackerel Stock Assessment:

a Case StudySoutheast Fisheries

Science Center

Jeff Isely, Michael Schirripa, John Walter and Matt LaurettaSEFSC

J.J. Isely et al. | CAPAM Workshop | La Jolla, CA | November 3-7, 2014 Growth: theory, estimation, and application in fishery stock assessment models |


Landings


Investigative Model Configures• KMK_GOM_1: uses CPUE only with no length or age-at-length(AAL);

Two length bins (i.e. one big plus group) Allows recruitment deviations; Fixed sex-specific growth at Data Workshop values

• KMK_GOM_2: start with #1

Add only lengths and selectivity • KMK_GOM_3: starts with #2

Adds Age at Length Freely estimated constant (time invariant) growth (i.e. no informed priors)


Females seems to be getting smaller over time


Additive random walk deviations in the growth parameters


Approaches to Model Selection

• use numerical methods quantify the performance of the model fit to the data for each model

• use more of a “deductive reasoning” approach: utilizing “if / then” logic to arrive at a “common sense” decision

• Some combination of the two methods


• Model_3: Ignore the observed changes in size-at-age and fits model to the data “as is” (null model).

• Model_4: Use time varying growth to address the changes in observed size-at-age. Fixes the growth parameters at those estimated in in #3. Allows for annual deviations in male and female L∞ and k.

• Model_5: Use time varying selectivity to address the changes in observed size-at-age. Fixes the growth parameters at those estimated in in #3. Allows for annual deviations in fleet-specific selectivites.

Three Models for Consideration


IF Model_3 is “more” correct THEN:

• No pattern to the size-at-age over time• We would expect no significant improvement

in the fit statistics if we vary growth• We would expect no significant improvement

in the fit statistics if we vary selectivity


IF Model_4 is correct THEN:

• we would expect to see a similar decrease in size-at-age for both male and females


Both sexes show similar patterns


Resulting Growth Curves


IF Model_5 is correct THEN we would need to believe that all gears changed selectivity at the same rate

J.J. Isely | CAPAM Workshop | La Jolla, CA | November 3-7, 2014 Growth: theory, estimation, and application in fishery stock assessment models |


There IS a significant improvement in the model fit statistics for Models_4 & 5

COMPONENT Model_3 Model_4 Model_5 Model_6No. Parameters 503 600 800 509Total Likelihood 16,467 15,902 16,224 17,471 Catch 14.89 11.52 11.11 31.70Survey -101.56 -145.19 -106.20 -123.93Discard 41.42 39.94 89.76 334.43Length_comp 3013.39 2943.67 2794.71 3591.72Age_comp 13498.50 13002.00 13423.70 13640.70Size_at_age* 3896 3814 3915 3860Recruitment -0.79 -3.71 0.17 -3.63Parm_priors 0.10 0.15 0.45 -0.01Parm_devs 0.64 52.76 9.32 0.08

** Although the LL maybe lower, it does not mean that the model is the most parsimonious


Both Model_4 and _5 fit better than _3


SSB for the four model configurations


SSB trends are similar, certainty is not

Model_1 Model_2

Model_3 Model_4


• Both of the alternative models (Model_4 & Model_5) explain the data better than the null model (Model_3) but requires the belief of unbiased length/age sampling. Cannot identify underlying ecological or environmental causes.

• Model_4 accounted for the most variation in the data while using the fewest number of parameters to do so, but requires the belief that growth has decreased consistently and substantially in the past 25 years.

• Model_5, while not requiring a change in growth, requires the belief that the selectivity for all gears changed in synchrony without a change in fishing methods.

Conclusions (Assessment Scientist)


• Model_4: A 25-year decreasing trend in growth is unlikely.-Reject

• Model_5: It is highly unlikely that selectivity for all gears changed simultaneously. -Reject

• Model_3, Although not the best fit, requires the fewest assumptions and is consistent with our perception of the fishery. -Accept

Conclusions (review workshop)


• Weaknesses: The GOM KMK assessment model is not very stable. The data streams are lacking contrast and thus any real definitive signal related to stock status or stock productivity was not captured in the analysis.

• Strengths: Despite the weaknesses, nearly every model configuration suggests that the stock size has been increasing since 1990 with no indication that the stock is currently being overfished or experiencing overfishing.

• Recommendation: The current management strategy seems to be very effective at achieving stated goals and there is no evidence to suggest changes in the current quota would be beneficial.

Additional Conclusions (review workshop)


• Ageing method improvement: Has a change in ageing methods resulted in an increase in age at size?

• Institutional Memory: Were historical tournament/quota samples included in the general recreational catch samples?

• Coding/Identification issues: Are the small king mackerel in the historic Headboat samples really king mackerel? Were confiscated illegal catches included in the recreational samples?

• Regulations: Has there been a change in gear configuration in the Rec and HL fisheries that would eliminate larger fish (e.g. circle hooks)?

• Ecosystem-based assessment: Continue to investigate possible environmental and food-web changes in the GOM (FATE project).

Remaining issues to be resolved




• Coding/Identification issues: Are the small king mackerel in the historic Headboat samples really king mackerel? Or were theyconfiscated illegal catches included in the recreational samples?





Questions?


Approaches to Model Selection

• Can use numerical methods quantify the performance of the model fit to the data for each model?

• Can use more of a deductive reasoning approach: utilizing “if / then” logic to arrive at a “common sense decision”?

• Some combination of the two methods• (It’s critical to keep in mind that the data are likely

biased to some degree (not perfect); one can favor the “right” model for the wrong reasons)


Figure 3.2.9. Observed and predicted length compositions of landings of GOM king mackerel in the recreational charter-private fleet (top). Observed (N) sample sizes and effective sample sizes (effN) estimated by SS are also reported. Pearson residuals for the length composition fit (bottom). Solid circles are positive residuals (i.e., observed greater than predicted) and open circles are negative residuals (i.e., predicted greater than observed).


Figure 3.2.6. Observed and predicted length compositions of landings of GOM king mackerel in the commercial handline line fleet (top). Observed (N) sample sizes and effective sample sizes (effN) estimated by SS are also reported. Pearson residuals for the length composition fit (bottom). Solid circles are positive residuals (i.e., observed greater than predicted) and open circles are negative residuals (i.e., predicted greater than observed).


Profile on Steepness


Fit to Lengths was improved with each successive model

Model_2 Model_3 Model_4


Fit to Observations


Model Configurations

• The total fishery was parsed into 5 fleets• Commercial fisheries included handline (H&L),

gillnet, and shrimp-fishery bycatch• Recreational fisheries included Headboat and

Charter/Private • Surveys included Commercial H&L CPUE, Shrimp

Effort, Headboat CPUE, SEAMAP Trawl Survey (age_1), and SEAMAP Larval Survey (SSB)


Landings


Label Value Active_CntPhase Min Max Init Status Parm_StDevL_at_Amin_Fem_GP_1 21.00 _ -3 10 80 21.00 NA _L_at_Amax_Fem_GP_1 112.15 1 3 100 150 112.03 OK 0.491VonBert_K_Fem_GP_1 0.36 2 4 0.1 0.5 0.37 OK 0.005CV_young_Fem_GP_1 0.27 3 6 0.01 0.3 0.27 OK 0.005CV_old_Fem_GP_1 0.10 4 6 0.01 0.3 0.10 OK 0.002L_at_Amin_Mal_GP_1 21.00 _ -3 10 80 21.00 NA _L_at_Amax_Mal_GP_1 93.06 5 3 70 120 93.11 OK 0.292VonBert_K_Mal_GP_1 0.38 6 4 0.1 0.7 0.38 OK 0.006CV_young_Mal_GP_1 0.34 7 6 0.01 0.5 0.35 OK 0.007CV_old_Mal_GP_1 0.06 8 6 0.01 0.3 0.06 OK 0.001


Life History Functions


• Try constant growth with time varying selctivities

Next Steps


Additive random walk deviations in the growth parametersparm’ (y) = parm (y-1) + dev(y)


Time varying growth adds 92 parameters but reduces LL by 769 units

TOTAL 16,659.00 15,890.30 (768.70)Catch 16.49 11.58 (4.91)Equil_catch - - Survey (104.84) (148.40) (43.56)Discard 44.83 40.33 (4.50)Length_comp 3,196.99 2,933.44 (263.55)Age_comp 13,504.90 12,999.90 (505.00)Recruitment (0.14) (2.72) (2.57)Forecast_Recruitment - - Parm_priors 0.18 0.21 0.03Parm_softbounds 0.01 0.01 0.00Parm_devs 0.63 56.02 55.39Crash_Pen - -

Model_3 Model_4


Fits to HL CPUE

Model_1 Model_2

Model_3 Model_4

time-varying vs. non-time- varying growth in the gulf of mexico king mackerel stock assessment: a...

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