Simple Approaches to Data-Poor
Stock Assessment
Rainer Froese
rfroese@ifm-geomar.de
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 LUNA
ACTA ICHTHYOLOGICA ET PISCATORIA (2004) 34 (1): 11–20
Maximum annual reproductive rate versus mean (solid dots) and minimum
(open dots) annual fecundity.
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Fish and Fisheries, 2004, 5, 86–91
Keep it simple: three indicators to deal with overfishing
Rainer 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 fishing
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Age-structure of North Sea
Cod, with same catch but
different minimum size
Fmsy & Lopt
Fmsy
Current
For a given catch, the impact
on the stock is least if fish
are caught at Lopt
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Same catch, better
age structure
Stock size can increase
seven-fold
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The Hockey-Stick
(Barrowman & Myers 2000)
Recruits (N)
R2  Rmax
R1    S
Spawners (N)
Assumptions:
a) Constant R/S at low S
b) Constant R at high S
The Smooth Hockey-Stick
(Froese 2008)
R  Rmax (1  e


Rmax
ln R  A  ln(1  e
where A = ln Rmax
Assumptions:
a) Practically constant R at high S
b) Gradually increasing R/S at lower S

S
)

e
A
S
)
Example Striped bass Morone saxatilis
S-R Model comparison for Morone saxatilis (striped bass) n=17 1982 --> 1998
[Stock: STRIPEDBASSUSA2]
25
20
15
Froese
Ricker
R
B&H
10
observed
5
0
0
10
20
30
40
50
60
S
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
Parameters and accounted variance not significantly different
Extrapolation VERY different
Example: 12 stocks of Atlantic cod Gadus morhua
Recruit abundance
10
1
0.1
0.01
0.01
0.1
1
10
Spawner abundance
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.
Number of replacement spawners versus number of parents for 48 Pacific
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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
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• Set target length in catch to LFmsy
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
:
L
FM
Lmean  L (1 
(1  c ))
FM K
L
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
LF  M 
3Lc  L
4
Inserting F = ½ M mean length equation results in
LFmsy 
9 Lc  4 L
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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.
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If species die after spawning (salmons, eels,
cephalopods)
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 stockrecruitment 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
rmax 
ln(4.2) 1.44

tm
tm
If we assume that Fmsy = ½ rmax we have
Fmsy 
ln(4.2) 0.72

2tm
tm
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. 17
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 Fisheries
Rainer 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
0.5 B msy
B msy
1.3 B msy
MSY
1
0.91 MSY
Depleted
Zone
Catch / MSY
0.8
Buffer
Zone
Overfishing
Zone
Target
Zone
0.6
0.4
0.2
0
0
0.5
1
Biomass / B msy
1.5
2
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Fisheries in 2007
0.5 B msy
B msy
0.5
1
1.3 B msy
1.6
1.4
Catch / MSY
1.2
1
0.8
0.6
0.4
0.2
0
0
Biomass / B msy
1.5
2
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North Sea Herring 1960 - 1978
1,200
1.3 B msy
Landings (1000 t)
1,000
800
1960
1967
600
1962
1960
1962
400
1967
1977
1978
200
1978
0
0
500
1,000
1,500
2,000
2,500
3,000
3,500
Spawner Biomass (1000 t)
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North Sea-Herring 1979 - 2008
1,000
1.3 B msy
1987
Landings (1000 t)
800
1985
600
2003
1985
2003
1987
2008
400
2008
200
1979
0
0
1983
500
1,000
1,500
2,000
2,500
3,000
3,500
4,000
Spawner Biomass (1000 t)
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ICES F-based Mangement
B pa
2
Catch
B msy
1.8
F / Fmsy or Catch / MSY
1.6
1.4
1.2
F
1
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
1.2
Biomass / B msy
1.4
1.6
1.8
2
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North Sea Herring Once More
B msy
800
Landings (1000 t)
1966
600
F -based HCR
1971
1960
1967
1977
400
1978
Proposed HCR
200
1978
0
0
500
1,000
1,500
2,000
2,500
3,000
3,500
Spawner Biomass (1000 t)
F-based Management would not have prevented the collapse of herring.
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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
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Thank You
Rainer Froese
IFM-GEOMAR, Kiel, Germany
rfroese@ifm-geomar.de
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