Fishery selection and its
relevance to stock assessment
and fishery management.
David Sampson
Professor of Fisheries
OSU Hatfield Marine Science Center
Coastal Oregon Marine Experiment Station
Two Years in Northern Italy
• 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.
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 ageselectivity. 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 ageselectivity.
5. Conditions that generate domed
population-selectivity.
6. Selectivity and MSY reference points.
Part 1.
What is fishery selectivity ?
Arona
? What is Selectivity ?
Fish abundance and
catch-at-age
N(age)
Fishing mortality-at-age
C(age)
35%
1000
30%
800
Fraction Caught
Number of Fish
25%
600
400
20%
15%
10%
200
5%
0
0%
1
3
5
7
9
11
13
Age
Young fish escape the gear or
live elsewhere.
15
1
3
5
7
9
11
13
Age
Selection is F-at-age scaled so
the maximum value is 100%.
15
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 gearselection 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 populationlevel 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: 60%
20%
40%
80%
Gear 2: 20%
80%
60%
40%
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.
100
100%
75%
60
50%
40
25%
20
0
0%
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
28
30
32
34
36
38
40
Length
100
No. Fish
80
60
40
20
0
10
12
14
16
18
20
22
24
26
40
Selection
No. Fish
80
? 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.
Part 3.
Selection Curve Shapes and
Stability: An Empirical Analysis.
Gelati
Selection Curve Shape and Stability
• Virtual Population Analysis (VPA).

Complete catch-at-age data to reconstruct abundanceat-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, peerreviewed 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.)
Increasing selectivity:
Fig. 1
American plaice on the Grand Bank
Asymptotic selectivity:
Fig. 2
Atlantic cod on Georges Bank
10
14
8
Age (yr)
10
6
4
8
2
6
DATA1
1960
1970
1980
1990
Year
2000
DATA2
1978
1988
100
1998
Year
100
1983
1985
75
Selection (%)
75
Selection (%)
Age (yr)
12
1965
50
25
2003
50
25
0
0
5
6
7
8
9
10
11
Age (yr)
12
13
14
15
1
2
3
4
5
6
Age (yr)
7
8
9
10
Selection Shape and Stability (cont.)
Domed selectivity:
Fig. 3
Saddle selectivity:
Atlantic herring (fall spawners) in the
southern Gulf of St Lawrence
Fig. 4
Atlantic herring in the Gulf of Maine
and Georges Bank
10
10
8
Age (yr)
6
6
4
4
2
2
DATA3
1978
1988
DATA4
1967
1998
Year
1977
1987
1997
Year
100
1977
100
2003
75
75
Selection (%)
Selection (%)
Age (yr)
8
1983
50
25
50
1992
25
0
0
2
3
4
5
6
7
Age (yr)
8
9
10
11
1
2
3
4
5
6
Age (yr)
7
8
9
10
Part 4.
A spatial model for
fishery age-selectivity.
A Mathematical Model for Selectivity
Abundance-at-age (a) by region (i):
N a ,i


 N a 1,i  exp M  Fi  sa 1   1   Pj ,i 
 i j

  N a 1, j  exp M  F j  sa 1  Pi , j
i j
• M is the instantaneous rate of natural mortality.
of fish that
Survival
of fish that
• FiSurvival
is the instantaneous
rate of fishing
mortality
in
stay in region i
migrate into region i
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.
Selectivity Model (continued)
Abundance-at-age:
F-at-age:
Pop. selection-at-age:
N a   N a ,i
i
N a 1


Fa   ln
M
N
a

Sa 
Fa
max Fa 
N.B. This is a cohort (equilibrium) model.
Now we will explore an Excel
version of the populationselectivity model.
Heuristic Explanation for the Dome
Consider a stock in two regions, no movement between regions,
same logistic gear selection curve in both regions.
Fishing morality at age
Higher F 
fewer old fish
Region 1, F = 0.4
0.4
Population selection
Region 2, F = 0.1
0.3
0.2
Lower F 
more old fish
0.1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Age
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.
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.
Sa 


 Z a ,i

N

e
 a ,i
 
i 

 ln
 
 Z a 1,i
   N a 1,i  e
 i 
 


Z a , j
 1   Pj ,i    N a , j  e
 Pi , j  
 
 i j
 i j
M



 Z a 1, j
 1   Pj ,i    N a 1, j  e
 Pi , j  
 
 i j
 i j
maxFa 
The gear-selection coefficients are embedded in the
age- and region-specific total mortality coefficients,
Za,i = M + Fi ∙ sa .
Domed Selectivity (continued)
Condition for domed selection can be written
Fa 1
N a2

M
  ln

N
a 1 

N a 1

M
 Fa   ln

N
a 

Exponentiate and rearrange to get
N a  2  N a  N a 1 2
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
Na   Na, r  N a,1  Na, 2
r 1
2
Na 1   Na 1,r  Na ,1  e
 F1  s  M
r 1
 Na, 2  e
 F2  s  M
2
Na  2   Na  2,r  Na ,1  e 2F1 s  2M  Na, 2  e 2 F2 s  2M
r 1
Decreasing selectivity implies
N a  N a2  N a1   0
2
Domed Selectivity (continued)
N a  N a  2  N a ,1   e 2F1  s  2 M  N a , 2   e 2 F2 s  2M
2
2
 N a ,1  N a , 2  e 2 F1  s  2 M  N a ,1  N a , 2  e 2 F2  s  2 M
Na 1 2  Na,1 2  e 2 F s  2M  Na ,2 2  e 2 F s  2M
1
2
 2  N a ,1  N a , 2  e F1 s  F2 s  2M
Na  N a2  N a,1   Na,1  N a,2  e
2
2M

 e
F2 s
e
F1 s

2
Similar reasoning leads to the solution for any number
of regions. Population-selectivity (given no movement
and constant gear-selection) will be decreasing if
N
i j
a ,i
 N a, j  e
 2M

 e
 Fi s
e
 F j s

2
0
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:
a 1

Y   exp   M  F  S   W  F  Sa 1  exp Z 
i 
a
a

R
Za
a 1
 i 1

A
Spawning biomass-per-recruit:
a 1

SB   exp   M  F  S   W  Mat
i 
a
a

R
a 1
 i 1

A
N.B. No plus-group. All fish are dead by age A+1.
Selectivity and MSY (continued)
B&H stock-recruit relationship:
R    SB 
  4h  R0 5h  1
  SB 

1  h  SB R | F  0

5h  1

SB | F    SB | F  
R
At equilibrium each recruit exactly reproduces
the spawning biomass of its parents.
Equilibrium Yield:
 R  R
Y Y
Selectivity and MSY (continued)
(SSB_MSY/SSB0) vs Sel_a50%
0.50
h=0.7
(FMSY/M) vs Sel_a50%
12
h=0.5
h=0.7
h=0.5
10
0.45
Maturity Age50%
Maturity Age50%
8
0.40
6
0.35
4
0.30
2
0.25
4
6
8
Age
10
12
0
4
M = 0.2; k = 0.15
6
8
10
Age
Fishery selection influences DB-SRA results.
12
Now we will explore an Excel
version of the spatial populationselectivity model, extended to
include the MSY calculation.
Near Como
Summary and Conclusions
Sunrise from my bedroom
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