Fishery selection and its relevance to stock assessment

and fishery management.

David SampsonProfessor of Fisheries

OSU Hatfield Marine Science CenterCoastal Oregon Marine Experiment Station

• With the European Commission’s Joint Research Center in Ispra, north of Milan.

The JRC provides research based scientific advice to support a wide range of European Union policies.

• Institute for the Protection and Security of the Citizen.

Applied research & development aimed at analyzing, modeling and developing new security applications.

• Maritime Affairs Unit.Shipping container traffic; vessel surveillance & port security; scientific support to fisheries.

• FISHREG Action. ~ 25 fisheries scientists.

Two Years in Northern Italy

At the JRC ...

... while building a bioeconomic simulator, David stumbled upon some surprising behavior related to fishery selectivity.

Resulting publications:• Sampson, D.B. and Scott, R.D. 2011. A spatial model for

fishery age-selection at the population level. Canadian Journal of Fisheries & Aquatic Sciences 68: 1077-1086.

• Scott, R.D. and Sampson, D.B. 2011. The sensitivity of long-term yield targets to changes in fishery age-selectivity. Marine Policy 35: 79-84.

• Sampson, D.B. and Scott, R.D. 2011. An exploration of the shapes and stability of population-selection curves. Fish and Fisheries (available on line).

Talk Outline

1. What is fishery selectivity?

2. Issues related to gear-selectivity.

3. Selection curve shapes and stability.

4. A spatial model for fishery age-selectivity.

5. Conditions that generate domed population-selectivity.

6. Selectivity and MSY reference points.

Arona

Part 1.

What is fishery selectivity ?

? What is Selectivity ?

Fish abundance and catch-at-age

Fishing mortality-at-age

Young fish escape the gear or live elsewhere.

Selection is F-at-age scaled so the maximum value is

100%.

0

200

400

600

800

1000

1 3 5 7 9 11 13 15

Age

Num

ber

of F

ish

N(age) C(age)

0%

5%

10%

15%

20%

25%

30%

35%

1 3 5 7 9 11 13 15

Age

Fra

ctio

n C

augh

t

Factors Influencing Selectivity:

• Gear selection. Fish age / size / behavior affect which fish are caught

and retained by any type of fishing gear.

• The mixture of fishing gears. When there are multiple gear-types with differing gear-

selection traits, the relative catches by each gear-type determine the population-level selectivity.

• Spatial locations of the fish and the fishing. Fishing gear operates at a local scale and can only

catch fish that are near the gear. The population-level Cage depends on the spatial distribution of fishing operations relative to the spatial distribution of the fish.

Selectivity Factors: Gear Selection

Selectivity Factors: Gear Mixtures

Gear 1: 20% Gear 2: 80%Gear 1: 40% Gear 2: 60%Gear 1: 60% Gear 2: 40%Gear 1: 80% Gear 2: 20%

Selectivity Factors: Spatial Effects

Varese

Part 2.

Issues related to gear-selection.

Selection by the Fishing Gear? Age-Based or Length-Based ?

If selection is by age, then no effect on observed length-at-age. Not so if selection is by length.

0%

25%

50%

75%

100%

0

20

40

60

80

100

10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

SelectionN

o. F

ish

0

20

40

60

80

100

10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

No

. F

ish

Length

? What’s Wrong with these Graphs ?

Assessment of Lingcod (Ophiodon elongatus) - 2005

Are such changes in selection plausible?

Another Strange Selection Curve

Assessment of Longspine Thornyhead(Sebastolobus altivelis)- 2005

Selectivity Propositions

1. Fish that are about the same age or size should have the same relative vulnerability (i.e., selection).

2. If estimates of selection by age (or by size) show abrupt changes between adjacent age-classes, there is probably something wrong with the model specifications.

Gelati

Part 3.

Selection Curve Shapes and Stability: An Empirical Analysis.

Selection Curve Shape and Stability

• Virtual Population Analysis (VPA). Complete catch-at-age data to reconstruct abundance-

at-age and F-at-age.

No assumptions about selectivity.

Widely used on both sides of the North Atlantic.

• F-at-age estimates from 15 published, peer-reviewed stock VPA assessments.

• F-at-age converted to smoothed selectivity curves estimates using GAMs.

• Test for Age, Year, and Age x Year effects.

Selection Shape and Stability (cont.)

DATA1

Fig. 1

Age

(yr

)

66

88

1414

1212

1010

19601960 19701970 19801980 19901990 20002000Year

Sel

ectio

n (%

)

Age (yr)

0

25

50

75

100

5 6 7 8 9 10 11 12 13 14 15

19651965

19851985

DATA2

Fig. 2

22

44

1010

88

66

19781978 19881988 19981998

Age

(yr

)

Year

0

25

50

75

100

1 2 3 4 5 6 7 8 9 10

Sel

ectio

n (%

)

Age (yr)

20032003

19831983

Increasing selectivity:

American plaice on the Grand Bank

Asymptotic selectivity:

Atlantic cod on Georges Bank

Selection Shape and Stability (cont.)

DATA3

Fig. 3

22

44

1010

88

66

19781978 19881988 19981998

Age

(yr

)

Year

0

25

50

75

100

2 3 4 5 6 7 8 9 10 11

Sel

ectio

n (%

)

Age (yr)

19831983

20032003

DATA4

Fig. 4

19671967 19871987 1997199719771977

22

44

1010

88

66

Age

(yr

)

Year

0

25

50

75

100

1 2 3 4 5 6 7 8 9 10

Sel

ectio

n (%

)

Age (yr)

19921992

19771977

Domed selectivity:

Atlantic herring (fall spawners) in the southern Gulf of St Lawrence

Saddle selectivity:

Atlantic herring in the Gulf of Maine and Georges Bank

Part 4.

A spatial model for

fishery age-selectivity.

•M is the instantaneous rate of natural mortality.

• Fi is the instantaneous rate of fishing mortality in

region i.• Coefficient sa is the gear selectivity for age-a fish.

• Coefficient Pi,j is the proportion of fish that move into

region i from region j at the end of each year.

A Mathematical Model for Selectivity

Abundance-at-age (a) by region (i):

jiajji

ja

jiijaiiaia

PsFMN

PsFMNN

,1,1

,1,1,

exp

1exp

Survival of fish that stay in region i

Survival of fish that migrate into region i

Selectivity Model (continued)

F-at-age:

MNNF

aa

a

1ln

Pop. selection-at-age:

aa

a FFS max

Abundance-at-age:

iiaa NN ,

N.B. This is a cohort (equilibrium) model.

Now we will explore an Excel version of the population-

selectivity model.

Heuristic Explanation for the Dome

Consider a stock in two regions, no movement between regions, same logistic gear selection curve in both regions.

The population selection curve is the average of the two Fage curves. The Region 1 curve (F = 0.4) dominates at young ages; the Region 2 curve (F = 0.1) dominates at old ages.

0

0.1

0.2

0.3

0.4

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Age

Fis

hin

g m

ora

lity

at

ag

e

Region 1, F = 0.4

Population selection

Region 2, F = 0.1

Higher F fewer old fish

Lower F more old fish

Part 5.

Conditions that generate domed population-selectivity.

Conditions for Domed Selectivity

Domed selection if Sa+1 < Sa. Under what conditions?

The general conditions are difficult to discern because the equation for population selection is complicated.

ai

jiZ

jija

jiij

Zia

iji

Z

jija

jiij

Zia

a F

M

PeNPeN

PeNPeN

S

jaia

jaia

max

1

1

ln

,,1,,1

,,,,

,1,1

,,

The gear-selection coefficients are embedded in the age- and region-specific total mortality coefficients,

Za,i = M + Fi ∙ sa .

Domed Selectivity (continued)

MN

NFMNNF

a

aa

a

aa

1

1

21 lnln

212 aaa NNN

Condition for domed selection can be written

Exponentiate and rearrange to get

Direct substitution of the general equations for Na , Na+1 and Na+2 into this inequality produces a mess.

But, useful results can be obtained from the simpler problem of no movement and constant gear-selection.

Domed Selectivity (continued)

Consider the case of two regions.

2,1,

2

1, aa

rraa NNNN

MsF

aMsF

ar

raa eNeNNN

21

2,1,

2

1,11

MsF

aMsF

ar

raa eNeNNN

22

2,22

1,

2

1,22

21

Decreasing selectivity implies 0212 aaa NNN

Domed Selectivity (continued)

MsF

aaMsF

aa

MsFa

MsFaaa

eNNeNN

eNeNNN

22

2,1,22

2,1,

2222,

2221,2

21

21

MsFsF

aa

MsFa

MsFaa

eNN

eNeNN

2

2,1,

2222,

2221,

21

21

21

2

222,1,

21,2

12 sFsFMaaaaa eeeNNNNN

Similar reasoning leads to the solution for any number of regions. Population-selectivity (given no movement and constant gear-selection) will be decreasing if

022

,,

sFsFM

jijaia

ji eeeNN

Venizia

Genoa

Part 6.

Selectivity & MSY reference points.

Selectivity and MSY

Equilibrium yield is derived from standard equations for yield-per-recruit, spawning biomass-per-recruit, and a Beverton & Holt stock-recruit relationship.

Yield-per-recruit:

Spawning biomass-per-recruit:

N.B. No plus-group. All fish are dead by age A+1.

A

aa

a

aa

a

ii Z

Z

SFWSFMR

Y1

1

1

exp1exp

A

aaa

a

ii MatWSFMR

SB1

1

1

exp

Selectivity and MSY (continued)

B&H stock-recruit relationship:

SB

SBR

FRSBFSB ||

Equilibrium Yield: RR

YY

At equilibrium each recruit exactly reproduces the spawning biomass of its parents.

15

04

hRh

15

0|1

h

FRSBh

Selectivity and MSY (continued)

0

2

4

6

8

10

12

4 6 8 10 12

Age

(FMSY/M) vs Sel_a50%h=0.7 h=0.5

0.25

0.30

0.35

0.40

0.45

0.50

4 6 8 10 12

Age

(SSB_MSY/SSB0) vs Sel_a50%h=0.7 h=0.5

Fishery selection influences DB-SRA results.

Maturity Age50% Maturity Age50%

M = 0.2; k = 0.15

Now we will explore an Excel version of the spatial population-

selectivity model, extended to include the MSY calculation.

Near Como

Sunrise from my bedroom

Summary and Conclusions

Summary of the Lessons Learned

• VPA results indicate considerable variation in population-selection.

• We should not be surprised to find that population-selectivity varies through time. (Constant selection is unusual.)

• We should not be surprised to find that population-selectivity is dome-shaped.

• MSY and related biological reference points are functions of selectivity and also the spatial distribution of fishing.

Grazie per l’Attenzione