fishery selection and its relevance to stock assessment and fishery management
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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