Use of multiple selectivity patterns as a proxy for spatial structure

Felipe Hurtado-Ferro1, André E. Punt1 & Kevin T. Hill2

1 University of Washington, School of Aquatic and Fishery Sciences2 NOAA, National Marine Fisheries Service

Outline

• What is the ‘fleets-as-areas’ concept• A case study: Effect of spatial structure on Pacific

sardine assessment

Description of the problem

Deeper look at selectivity estimates

Some conclusions

Which spatial factors have the largest effect

Sardines have stage-dependent seasonal migrations

-134 -130 -125 -120 -115 -110 -105

20

25

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Point Conception

Cape Mendocino

Assessment assumes a single mixed stock with different

selectivity in different areasPNW

CA

Ensenada

-134 -130 -125 -120 -115 -110 -105

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Point Conception

Cape Mendocino

Spatial structure of stocks matters, but it can be difficult to deal with

Histogram of lcomp1

De

nsi

ty

0 1 2 3 4 5 6 7

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0.1

0.2

0.3

Histogram of lcomp2

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nsi

ty

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00

.10

0.2

0

One possible way out: Represent the areas using selectivity curves

• Assume that the stock is homogeneously distributed (i.e. fully mixed)

• Define fleets geographically• Assign a different selectivity curve to each fleet

How well does the fleet-as-areas approach perform when applied

to a spatially-heterogeneous stock?

??

A case study: Pacific sardine

1985 1990 1995 2000 2005 2010

0

70

Ensenada0

50Southern California

0

30Central California

0

50Oregon and Washington

0

20 British Columbia

Ca

tch

(x1

00

0 to

ns)

The recovery of the Pacific sardine

-134 -130 -125 -120 -115 -110 -105

25

30

35

40

45

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55

Ensenada

Monterrey

San Diego

Astoria

ENSSCACCAORWABC

10

California f ishery opens againQuota expanded

Spaw ning biomass above 20000 tons detected

Mainly bycatch Directed f ishery

Adapted from Wolf, 1992

Some issues suggest that the fully-mixed stock assumption may be violated

Source: Lo et al., 2010

Large animals migrate north during summer and return during winter

Commercial catchesFishery independent surveys

1985 1990 1995 2000 2005 2010

0

70Ensenada

Ca

tch

es

(x1

00

0 to

ns)

PFMC, 2007

Some issues suggest that the fully-mixed stock assumption may be violated

Demer et al. 2012

A few questions arise

- What is the effect on the performance of Stock Synthesis 3 (SS3) of:• occasional persistence in the PNW• movement between CA and PNW• Presence of southern

subpopulation

- Can the fleets-as-areas approach deal with these issues?

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Point Conception

Cape Mendocino

The analysis is based on a stock assessment evaluation framework

Movementhypotheses

Assessment data

Spatially-structured operating model

Data set 1 Data set 2 Data set n

Assessment results

Performance measures

…

Assessment model

The operating model is spatially explicit, with different fleets and movement.

Divided in 10 areasof 2 degrees of lattitude

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Point Conception

Cape Mendocino

ENSSCACCAPNW

Divided in 20 areasof 1 degree of lattitude

-134 -130 -125 -120 -115 -110 -105

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Point Conception

Cape Mendocino

ENSSCACCAPNW

Spatially explicit model Seasonal movement

Weekly time steps

Two types of movement: Advection and diffusion

How do you define ‘fleets’? Fishery composed by six “fleets” with different selectivities

5 10 15 20 250.0

0.5

1.0ENSSCA1SCA2CCA1CCA2PNW

Length (cm)

Sele

ctivi

ty

SCA and CCA are also divided by season. That is, catches in the first semester are assumed

to be taken by a different ‘fleet’ than those in the second semester.

Divided in 10 areasof 2 degrees of lattitude

-134 -130 -125 -120 -115 -110 -105

20

25

30

35

40

45

50

55

Point Conception

Cape Mendocino

ENSSCACCAPNW

Divided in 20 areasof 1 degree of lattitude

-134 -130 -125 -120 -115 -110 -105

20

25

30

35

40

45

50

55

Point Conception

Cape Mendocino

ENSSCACCAPNW

How do you define ‘fleets’? Fishery composed by six “fleets” with different selectivities

However, in the OM, SCA and CCA selectivity curves were averaged to avoid confounding

effects

5 10 15 20 250

0.5

1ENSSCA-CCAPNW

Length (cm)

Sele

ctivi

ty

Divided in 10 areasof 2 degrees of lattitude

-134 -130 -125 -120 -115 -110 -105

20

25

30

35

40

45

50

55

Point Conception

Cape Mendocino

ENSSCACCAPNW

Divided in 20 areasof 1 degree of lattitude

-134 -130 -125 -120 -115 -110 -105

20

25

30

35

40

45

50

55

Point Conception

Cape Mendocino

ENSSCACCAPNW

Survey coverage

Hill et al. 2011

My model (that is, 2010) Stock assessment (2011)

1980 1985 1990 1995 2000 2005 2010

DEPM

Aerial

TEP

Sampling of age- and length-comps was designed to generate overdispersed samples

c=1 c=2 c=3 i=3 l=Lmax a=Ac

m=2

… i=3 … …

m=1 w=2 i=1 l=2 a=2

w=1 i=2 l=1 a=1

33in

5in 3, 3i l

ab

4in

3in 3, 3

3i lb

3, 32i lb

1in

For a given fleet, pick which months (m) have non-zero

catches

In m, pick which weeks (w) and areas

(c) have non-zero catches (i)

From each i, sample n fish from the

catches according to length comp

Age comp samples (b) are conditioned on

length

Note this step can be catch-weighted or uniform

Scenarios on four non-exclusive processes were explored

Movement (M)• No migration (Ma)• ‘Constant’ seasonal

migrations (Mb)• Migration is a function of SST

(Mc)

Southern subpop. influx (S)• No influx (Sa)• Periodic influx (Sb)

Persistence in the PNW (P)• No recruitment in the PNW

(Pa)• Uniform recruitment along

the entire west coast (Pb)

Data availability (L)• Full length- and age-

composition data (La)• Data availability equal to

that of the assessment (Lb)

biom.years

c(re

al.b

iom

s[, 1

]/1e+

05, 0

, 0)

02

46

810

12

Bes

tx1

05 to

ns

a'Real'Estimated

biom.years

c(re

al.b

iom

s[, 2

]/1e+

05, 0

, 0)

b

biom.years

c(re

al.b

iom

s[, 3

]/1e+

05, 0

, 0)

c

1980 1985 1990 1995 2000 2005 2010

0.6

0.8

1.0

1.2

1.4

Year

rel.q

uant

s[1,

, 1]

d

Bes

tB

true

Year

rel.q

uant

s[1,

, 2]

1980 1985 1990 1995 2000 2005 2010

e

Year

rel.q

uant

s[1,

, 3]

1980 1985 1990 1995 2000 2005 2010

f

Year

Results with only diffusion show negative bias not related to spatial factors

Large sample sizeUniform sampling

Actual sample sizeUniform sampling

Actual sample sizeWeighed sampling

Scenarios MaSaPa

Migration, recruitment and sampling affect estimates of SSB in the last year (2010)

0.0

0.5

1.0

1.4

Ma Mb Mc

Sb

Sa

PaL

aU

PaL

bU

PaL

bW

PbL

aU

PbL

bU

PbL

bW

0.0

0.5

1.0

1.4

PaL

aU

PaL

bU

PaL

bW

PbL

aU

PbL

bU

PbL

bW

PaL

aU

PaL

bU

PaL

bW

PbL

aU

PbL

bU

PbL

bW

Ma – Only diffusionMb – Seasonal migrationMc – Migration following SST

Sa – No influx from the S. subpopSb – Influx of the S. subpop in summer

Pa – Uniform recruitmentPb – Recruitment only in SCA

La – Large composition sample sizesLb – Comp. sample sizes same as assessment

U – Uniform samplingW – Weighed sampling

Migration, recruitment and sampling affect estimates of SSB in the last year (2010)

Ma – Only diffusionMb – Seasonal migrationMc – Migration following SST

Sa – No influx from the S. subpopSb – Influx of the S. subpop in summer

Pa – Uniform recruitmentPb – Recruitment only in SCA

La – Large composition sample sizesLb – Comp. sample sizes same as assessment

U – Uniform samplingW – Weighed sampling

Last year of assessment

Average over the last 20 years

Factor Df Sum Sq / Total Sum Sq

Sum Sq / Total Sum Sq

Seasonal movement 2 0.248 0.096Southern subpopulation 1 0.000 0.001Persistence in the PNW 1 0.027 0.062Length-composition data 1 0.033 0.002Sampling method 1 0.059 0.012Residuals 3593 0.632 0.828

Last year of assessment

Average over the last 20 years

Seasonal movementMb-Ma 0.097 0.011Mc-Ma -0.242 -0.137Mc-Mb -0.338 -0.147

Southern subpopulationSb-Sa -0.017 0.000

Persistence in the PNWPb-Pa -0.055 -0.049

Uncertainty in spatial structure can be captured by multiple fleets with different selectivity

biom.years

c(re

al.b

iom

s2[,

1]/1

e+05

, 0, 0

)

02

46

810

12

Bes

tx1

06 ton

s

'Real'Estimated

biom.years

c(re

al.b

iom

s2[,

2]/1

e+05

, 0, 0

)

biom.years

c(re

al.b

iom

s2[,

3]/1

e+05

, 0, 0

)

1980 1985 1990 1995 2000 2005 2010

0.4

0.6

0.8

1.0

1.2

1.4

Year

rel.q

uant

s[1,

, 1]

Bes

tB

true

Year

rel.q

uant

s[1,

, 2]

1980 1985 1990 1995 2000 2005 2010

Year

rel.q

uant

s[1,

, 3]

1980 1985 1990 1995 2000 2005 2010

Year

seq(8, 26, 0.5)

sel.f

un(a

pply

(sel

xpar

s[, ,

adv

r, 2

], 1,

mea

n), s

eq(8

, 26,

0.5

),

0

.5)

Adv. = 0.25

0.0

0.2

0.4

0.6

0.8

1.0

10 15 20 25

seq(8, 26, 0.5)

sel.f

un(a

pply

(sel

xpar

s[, ,

adv

r, 2

], 1,

mea

n), s

eq(8

, 26,

0.5

),

0

.5)

Adv. = 0.5

10 15 20 25

seq(8, 26, 0.5)

sel.f

un(a

pply

(sel

xpar

s[, ,

adv

r, 2

], 1,

mea

n), s

eq(8

, 26,

0.5

),

0

.5)

Adv. = 0.75 SCA1SCA2CCA1CCA2

10 15 20 25

Length (cm)

Sel

ectiv

ity

As migration rate increases, selectivity curves diverge, capturing this uncertainty.

Adv. = 0.25 Adv. = 0.50 Adv. = 0.75

Selectivity estimates also change for the Pacific Northwest and the aerial survey

22

24

26

0.25 0.5 0.75

SizeSel_12P_1_Aerial_N

Advection rate

19

20

21

0.25 0.5 0.75

SizeSel_6P_1_PNW_BLK2repl_2004

Advection rate

These are the estimates for the peak of double normal selectivity, i.e. the length at which selectivity is 1

Leng

th

So, does the “fleets-as-areas” approach work?

• Selectivity captures some of the variance from the spatial structure, but not all of it.

• Some biases due to spatial uncertainty were not solved by allowing multiple fleets.

• Furthermore, having more parameters can make models unstable.

• A spatially-explicit model might perform better.

The spoiler slide: An actual spatial model is better than a fleet-as-areas approximation

0.0

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Bes

tB

true

Last year

0.0

0.5

1.0

1.5

Bes

tB

true

Mean over 20 y.

MaPa MaPb MbPa MbPb McPa McPb MaPa MaPb MbPa MbPb McPa McPb

2010-like 2011-like

0.0

0.5

1.0

1.5

Bes

tB

true

Last year

0.0

0.5

1.0

1.5

Bes

tB

true

Mean over 20 y.

MaPa MaPb MbPa MbPb McPa McPb

Spatial - estimate all

THANK YOU

Acknowledgements:The organizers of this Workshop, Nancy Lo, Roberto Felix-Urraga , Richard Parrish

Washington