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Simple Approaches to Data-Poor Stock Assessment
Rainer [email protected]
March 9, 2011, Troutdale, Oregon
Overview• Some background
– Fecundity– Size matters– Recruitment
• Options for Management– Length-only– Semelparous species– Revisiting Schaefer– If biomass is known
NO RELATIONSHIP BETWEEN FECUNDITY AND ANNUAL REPRODUCTIVE RATE IN BONY FISH
Rainer FROESE, Susan LUNAACTA ICHTHYOLOGICA ET PISCATORIA (2004) 34 (1): 11–20
Maximum annual reproductive rate versus mean (solid dots) and minimum (open dots) annual fecundity.
3
Fish and Fisheries, 2004, 5, 86–91
Keep it simple: three indicators to deal with overfishingRainer Froese
4
• Reducing catch to Fmsy is good but insufficient
• Stock size may increase seven-fold if fish are caught after multiple spawning, at around 2/3 of their maximum length
• Large stock size means low cost of fishing5
Age-structure of North Sea Cod, with same catch but different minimum size
For a given catch, the impact on the stock is least if fishare caught at Lopt
Current
Fmsy
Fmsy & Lopt
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Same catch, better age structure
Stock size can increaseseven-fold
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Spawners (N)
Re
cru
its
(N
)
The Hockey-Stick (Barrowman & Myers 2000)
SR 1
max2 RR
Assumptions:a) Constant R/S at low Sb) Constant R at high S
The Smooth Hockey-Stick (Froese 2008)
)1ln(lnS
e A
eAR
)1( maxmax
SReRR
Assumptions:a) Practically constant R at high Sb) Gradually increasing R/S at lower S
where A = ln Rmax
S-R Model comparison for Morone saxatilis (striped bass) n=17 1982 --> 1998[Stock: STRIPEDBASSUSA2]
0
5
10
15
20
25
0 10 20 30 40 50 60
S
R
Froese
Ricker
B&H
observed
Parameters and accounted variance not significantly different
Model α low up Rmax low up r2
B&H 3.67 2.60 4.73 24.9 17.3 36.0 0.834
Froese 3.40 2.64 4.15 17.4 13.5 22.6 0.843
Ricker 3.22 2.64 3.81 19.8 16.5 23.9 0.846
Example Striped bass Morone saxatilis
Extrapolation VERY different
0.01
0.1
1
10
0.01 0.1 1 10
Spawner abundance
Rec
ruit
ab
un
dan
ce
Bold line is Smooth Hockey-Stick with n = 414, α = 4.5, Rmax = 0.85 Dotted line the Ricker model with n = 414, α = 3.1, Rmax = 1.4. Data were normalized by dividing both R and S by Rmax for the respective stock.
Example: 12 stocks of Atlantic cod Gadus morhua
12 Number of replacement spawners versus number of parents for 48 Pacific salmon populations. The fitted smooth hockey stick has a slope of 4.2 (3.6 – 5.2).
Assesment and Management Options
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If nothing is known about the stock
Management:
•Get an estimate of maximum length (interviews; old photos; FishBase)
•Get an estimate of length at first maturity (examine specimens; FishBase)
•Set minimum length in catch and/or start of fishing season such that >90% of the specimens had a chance to reproduce before being caught
•Give incentives to catch only fish with a length of 2/3 of their maximum length
•
Justification:
•Overfishing is theoretically impossible if all fish have a chance to reproduce before capture (Myers and Mertz, 1998). Impact of fishing on cohorts is minimized at about 2/3 of maximum length.
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If L∞ is known
Assessment•Get length at first capture and mean length in catch•Derive reference length where F ~ M from
•Derive reference length where Fmsy ~ ½ M from
Management
•Set minimum length in catch to LF~M, if larger than length where 90% are mature, else use that length
•Set target length in catch to LFmsy 15
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Justification: The mean length Lmean of fishes in the catch is a function of the mean size at first capture Lc and of the fishing mortality F. The fishing mortality associated with Bmsy is typically smaller than the mean natural mortality rate of adult fish (M). If von Bertalanffy growth parameters L∞ and K are known, the mean length in the catch is given by Beverton and Holt 1957, p. 41, assuming that λ = tmax = ∞ and substituting age at first capture tp’ with length at first capture Lc :
))1(1(
L
L
KMF
MFLL c
mean
If no reliable estimates of M and K are available, the M/K ratio can be assumed to be 3/2 (Jensen 1996) and the mean length in the catch where M = F can be obtained from
4
3
LLL c
MF
Inserting F = ½ M mean length equation results in
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49
LLL c
Fmsy
In Baltic cod, legal length at first capture is 38 cm and L∞ is 120 cm. The mean length in the catch resulting from fishing at Fmsy would then be 63 cm, which seems reasonable.
If species die after spawning (salmons, eels, cephalopods)
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Since the probability to die from fishing gets smaller if fishing starts later, and since the impact of a certain catch is smallest near the peak in cohort biomass, it still makes sense to target these species at a large size, shortly before spawning. The question then is how to define a reference point for escapement if no stock-recruitment data are available. The maximum annual reproductive rate for semelparous species equals the slope of the stock-recruitment function at the origin. A mean value across many populations is 4.2 (Froese, unpublished). The intrinsic rate of population increase rmax can then be obtained from
mm tt
r44.1)2.4ln(
max
If we assume that Fmsy = ½ rmax we have
mm
msy ttF
72.0
2
)2.4ln(
Thus, for annual squids Fmsy = 0.7, for Atlantic salmon with average longevity of 5 years, Fmsy = 0.14, and for the European eel with 12 years, Fmsy = 0.06. All values seem reasonable.
If Catch and Effort are Known
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If MSY and Bmsy are known
(Data-rich Management)
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Generic Harvest Control Rules for European FisheriesRainer Froese, Trevor A. Branch, Alexander Proelß, Martin Quaas, Keith Sainsbury & Christopher Zimmermann
• Rules for sustainable and profitable fisheries based on 1) economic optimization of fisheries 2) honoring international agreements 3) true implementation of the precautionary principle 4) learning from international experiences 5) ecosystem-approach to fisheries management 6) recognizing the biology of European fish stocks
• If these rules were applied, catches could increase by 63%
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Harvest Control Rule Schema
0
0.2
0.4
0.6
0.8
1
0 0.5 1 1.5 2
Biomass / B msy
Ca
tch
/ M
SY
B msy0.5 B msy 1.3 B msy
DepletedZone
OverfishingZone
BufferZone
TargetZone
MSY
0.91 MSY
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Fisheries in 2007
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 0.5 1 1.5 2
Biomass / B msy
Cat
ch /
MS
Y
B msy0.5 B msy 1.3 B msy
22
0
200
400
600
800
1,000
1,200
0 500 1,000 1,500 2,000 2,500 3,000 3,500
Spawner Biomass (1000 t)
Lan
din
gs
(100
0 t)
1960
1960
1962
19621967
1967
1977
1978
1978
1.3 B msy
North Sea Herring 1960 - 1978
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North Sea-Herring 1979 - 2008
0
200
400
600
800
1,000
0 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000
Spawner Biomass (1000 t)
Lan
din
gs
(100
0 t)
2008
2008
1985
1985 1987
1983
20032003
1979
1.3 B msy
1987
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ICES F-based Mangement
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Biomass / B msy
F /
Fm
sy o
r C
atch
/ M
SY
B msyB pa
F
Catch
25
North Sea Herring Once More
0
200
400
600
800
0 500 1,000 1,500 2,000 2,500 3,000 3,500
Spawner Biomass (1000 t)
Lan
din
gs
(100
0 t)
19601971 1967
1966
1977
1978
1978
B msy
F -based HCR
Proposed HCR
F-based Management would not have prevented the collapse of herring. 26
Critique of Planned F-based Management
• Fmsy is taken as target, not limit, thus violating UNFSA and the precautionary principle
• Fishing at Fmsy is less profitable than at Fmey • Fishing at Fmsy results in substantially smaller
stocks, violating the ecosystem approach• Fishing at Fmsy results in strongly fluctuating
catches with high uncertainty for the industry• Fishing at Fmsy provides strong incentives for
overcapacity• Fishing at TAC = 0.9 MSY solves these
problems 27
