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Estimation of selectivity in Stock Synthesis : lessons learned from the tuna stock assessment

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Estimation of selectivity in Stock Synthesis: lessons learned from the tuna stock assessment

Shigehide Iwata*1

ToshihdeKitakado*2

Yukio Takeuchi*1

*1 National Research Institute of far seas fisheries

*2 Tokyo University of Marine Science and Technology

Background (1)

Estimation of size selectivity has a large impact on results of stock assessment

However, size composition data are sometimes complex (e.g. bimodal, trimodal…)

As a result, the estimation of size selectivity has difficultyThat was the case in the Pacific Bluefin Tuna assessment

Background (2)

In the case of Pacific Bluefin Tuna (PBFT) assessment, estimation of size selectivity was one of key issuesbecause of some difficulty with many fleets to be considered and complicated size distribution data

By these difficulty, we were not able to get reasonable estimates of selectivity parameters in a normal estimation procedure (i.e. estimation using parametric functional forms, estimation of all the parameters once)

Background (3)For the size composition data in PBFT assessment

Circle size indicate the amount of sample size

Fleet4(Tuna Purse Seine)

There are bimodal distributions

in the observation data at

several year

Purpose of this talk

.

We will introduce some LESSONS learned from the Pacific Bluefin Tuna assessment with focusing on

1. Functional form (non-parametric or parametric)

2. An iterative estimation procedure (an extension of a method used in the IATTC yellow fin stock assessment)

Definitions of parameters

- : Selectivity parameters (nuisance parameters)
- : Other parameters, include parameters of primary interests
- : Number of parameters

Method (1)Functional form

Non-parametric selectivity functional forms are strong tools for estimation of selectivity curve (It is expected to achieve more flexible fit)

Wehope to have a betterfit to size composition data by using non-parametric functional form with same or least number of parameters.

Method (2)Cubic Spline

Number of parameter is AT LEAST4.

We hope the following situation in total likelihood L(θ，φ):

Holds, if

whereindicates parameter for fleet x by using Non-parametric functional form (resp. parametric functional form)

As non-parametric functional form, cubic spline implemented in the Stock Synthesis 3

Parametric.sso：Ｆｌｅｅｔ４：Double normal function

4 parameters

node3.sso, node5.sso and node9.sso ：Ｆｌｅｅｔ４：Cubic Spline (non-parametric)

1+x parameters (x=3,5 and 9)

Survey 1

There is no significant change to the CPUE fit by increasing of # of nodes.

Survey 2

Survey 5

Survey 9

Survey 3

the confidence interval

the observed CPUE

Fleet1 Fleet2 Fleet3

・・・Observed data

Fleet4 Fleet5 Fleet6

The fit to the size composition data except for fleet 4 does not change by using cubic spline.

So the size compositions except for fleet4 are expected to give the big impact on θ

Fleet7 Fleet8 Fleet9

Fleet10 Fleet11 Fleet12

Fleet13 Fleet14

－By using cubic spline curves, the fit to size composition would be improved

－However, there was no significant changein the fit tosize composition data by increasing of # of nodes

・・・Observed data

Fit to the size composition data

Estimated selectivity curve

SSB

Recruitment

There is no significant change in the dynamics of SSB and Recruitment

Results (5)likelihood change

Total Negative Log Likelihood

To be better

In the case of sable fish stock assessment (example in yesterday’s talk), the node numbers are 4 or 5

Summary of non-parametric functional form

By using the non-parametric selectivity functional form

－Total likelihood do not improve even if # of nodes

are 3 or 5.

－Total likelihood will be improved If the # of nodes

are 9.

However the SSB and Recruitment dynamics did not significantly change.

In the case of sable fish stock assessment (example in yesterday’s talk), the number of nodes is 4 or 5. So 9 nodes are too much.

Definitions of parameters

(again)

- : Selectivity parameters (nuisance parameters)
- : Other parameters, include parameters of primary interests
- : Number of parameters

Method (1)

General formation

“Joint likelihood”

“Partial likelihood” contributed by CPUEs

“Residual likelihood” contributed by size comps

Method (2)Procedures

- A two-step method was employed in the Yellow fin stock assessmentin 2012
- HOWEVER, the initially fixed selectivity parameters may not necessarily be the possible best option because those parameters j may be revised by maximizing the residual likelihood (L2) given better estimates of q
- If the further treatment above would produce the better j, thenq should be updated again

An iteratively-fixing method using two separated-likelihood functions

Set initial parameter values (arbitrary)

This time, we used estimates based on the joint likelihood as in YFT tuna stock assessment way,

Then, continue iterative processes as follows

Next, we shows the results after 40 iterative (80 runs, 1 iterative have odd and even run).

The results tend to CONVERGE (especially estimated SSB, recruitment and selectivity) within the odd or even times

To get better parameters

Before iterative run

After 40 iterative run

the confidence interval

the observed CPUE

Before iterative run

After 40 iterative run

the confidence interval

the observed CPUE

Survey 2

Survey 5

Survey 1

Survey 9

Survey 3

Before iterative run

After 40 iterative run

the confidence interval

the observed CPUE

Fleet1 Fleet2 Fleet3

Before iterative run

After 40 iterative run

Fleet4 Fleet5 Fleet6

Fleet7 Fleet8 Fleet9

In the almost fishery, we can get better size selectivity curve.

Fleet10 Fleet11 Fleet12

Fleet13 Fleet14

For the odd iteration run for SPB

For the odd iteration run for Recruitment

/

/

Increasing of iteration

Increasing of iteration

Each line indicates the SSB or REC ratio at same year during stock assessment period

By the Raabe's convergence test, we can conclude the SSB and Recruitment will be converge

After the iterations, series of SSB and recruitment are converged.

However the levels of SSB are different between two runs

Hope this change is “improvement”, but it is necessary to conduct a comprehensive simulation study for more valid conclusion

Before iterative run

After 40 iterative run

Summary

- There was no impact on SSB and Recruitment by increase the number of nodes in PBFT
- The total likelihood dramatically changed only if number of nodes is 9. So, there is no improvement by the introduction of non-parametric functional forms and these were not suitable for the PBF stock assessment.
- The iterative method aimed at providing better estimation of population dynamics. Although the method is not perfect in terms of fitting, but some improvement was observed in the CPUE and size composition(good sign ??)
- Need more practice and investigation on this method