estimation of selectivity in stock synthesis: lessons learned from the tuna stock assessment...

Estimation of selectivity in Stock Synthesis: lessons learned from

the tuna stock assessment

Shigehide Iwata*1

Toshihde Kitakado*2

Yukio Takeuchi*1

*1 National Research Institute of far seas fisheries

*2 Tokyo University of Marine Science and Technology

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 (1)

In the case of Pacific Bluefin Tuna (PBFT) assessment, estimation of size selectivity was one of key issues because 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 (2)

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

.

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)

Purpose of this talk

Non-parametric selectivity functional

form

Definitions of parameters

: Selectivity parameters (nuisance parameters)

: Other parameters, include parameters of primary interests

: Number of parameters

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

We hope to have a better fit to size composition data by using non-parametric functional form with same or least number of parameters.

Method (1)Functional form

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

Method (2)Cubic Spline

Number of parameter is AT LEAST 4. We hope the following situation in total likelihood L(θ， φ): Holds, if

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

Runs explanationParametric.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)

Results (1)CPUE fit

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

Survey 2

Survey 3

Survey 5 Survey 9

Survey 1

the confidence intervalthe observed CPUE

Results (2)fit to size composition data

Fleet1 Fleet2 Fleet3




Fleet13 Fleet14

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

　　　・・・ Observed data

Results (3)fit to the size composition data

－ By using cubic spline curves, the fit to size composition would be improved－ However, there was no significant change in the fit to size composition data by increasing of # of nodes

Estimated selectivity curve

Fit to the size composition data

　　　・・・ Observed data

Results (4)The dynamics of SSB and Recruitment

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

SSB

Recruitment

Results (5)likelihood change

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

To be better

Total Negative Log Likelihood

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.

An iteratively-fixing method

Definitions of parameters(again)

: Selectivity parameters (nuisance parameters)

: Other parameters, include parameters of primary interests

: Number of parameters

1 2

1

2

( , ) ( , ) ( , )

( , )

( , )

TL L L

L

L

“Joint likelihood”

“Partial likelihood” contributed by CPUEs

“Residual likelihood” contributed by size comps

Method (1)General formation

A two-step method was employed in the Yellow fin stock assessment in 2012

HOWEVER, the initially fixed selectivity parameters may not necessarily be the possible best option because those parameters may be revised by maximizing the residual likelihood (L2) given better estimates of

If the further treatment above would produce the better , then should be updated again

Method (2)Procedures

1 2

1

1) ( , ) ( , ) ( , ) maxˆ2) ( , ) max

TL L LL

An iteratively-fixing method using two separated-likelihood functions

1 1 0ˆ ˆargmax ( , )L

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

0 0 1 2, ,

ˆ ˆ( , ) argmax ( , ) argmax ( , ) ( , )TL L L

1 2 1̂ˆ argmax ( , )L

2 1 1ˆ ˆargmax ( , )L

2 2 2̂ˆ argmax ( , )L

3̂

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

To get better parameters

The points to accept this method or not are…

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

Results (1)Fleet 1

Before iterative runAfter 40 iterative run


Results (2)Fleet 11



Results (3)CPUE fit all


Survey 5

Survey 9


Survey 2

Survey 3

Survey 1

Results (4)size selectivity fit


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





Fleet13 Fleet14

Results (6)Convergence

For the odd iteration run for SPB

1 4 7 10 13 16 19 22 25 28 31 34 37 400

0.20.40.60.8

11.21.41.61.8

2

Increasing of iteration

For the odd iteration run for Recruitment

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

1 4 7 10 13 16 19 22 25 28 31 34 37 400

0.5

1

1.5

2

2.5

Results (7)SSB and recruitment

Before iterative runAfter 40 iterative runAfter the

iterations, series of SSB and recruitment are converged.

However the levels of SSB are different between two runsHope this change is “improvement”, but it is necessary to

conduct a comprehensive simulation study for more valid conclusion

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

Summary

estimation of selectivity in stock synthesis: lessons learned from the tuna stock assessment...

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