Upload
edwina-pitts
View
215
Download
0
Embed Size (px)
Citation preview
Revisiting Stock-Recruitment Relationships
Rainer Froese24.02.09
Mini-workshop on Fisheries: Ecology, Economics and Policy
CAU, Kiel, Germany
Overview
• A review of S-R models and their properties• Estimating Sdecline
• Estimating unfished biomass S0 and Smsy
• Estimating annual reproductive rate αr
• Estimating rmax • Estimating MSY and Fmsy
• Estimating time to reach Smsy
• MSY and Fmsy from ICES data• Some results
0
500
1000
1500
0 1 2 3 4 5
Rnorm
Fre
quency
(n)
0
500
1000
1500
2000
2500
-5 -3 0 3 5
Rnorm
Fre
quency
(n)
0
500
1000
1500
2000
2500
-5.00 -2.50 0.00 2.50 5.00
LNSnorm
Fre
quency
(n)
Skewed roughly log-normal
Distribution of R
0
500
1000
1500
2000
2500
-5.00 -2.50 0.00 2.50 5.00
LNSnorm
Fre
quency
(n)
0
500
1000
1500
2000
2500
0 1 3 4 5
Snorm
Fre
quency
(n)
Distribution of S
skewed roughly log-normal
The Hump (Ricker, 1954)
S
eSR
max178.2 R
S
SeR
Ae
SSR
178.2lnlnln
178.2max
R
Assumptions: a) negative S-R relationship at high Sb) highest recruitment at intermediate S
where A = ln Rmax
Assumption:Positive S-R relationship at
high S
SS
R
1
maxR
max
1R
SS
R
)1ln(lnlnlnAe
SSR
The Asymptote (Beverton & Holt 1957)
where A = ln Rmax
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 AeAR
)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 Hump 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
Conclusion of detailed comparison(Froese et al. in prep.)
With regard to resilience of stocks to overfishing (α) and the carrying capacity of the environment for recruits (Rmax)
• The Asymptote tends to overestimate both α and Rmax
• The Hump gives conservative estimates of α but tends to overestimate Rmax
• The Piece-wise Hockey-Stick gives the most conservative estimates of α and Rmax
• The Smooth Hockey-Stick tends towards intermediate estimates of α and conservative estimates of Rmax.
Example: North-east Arctic Cod
1,000
10,000
100,000
1,000,000
10,000,000
10,000 100,000 1,000,000 10,000,000 100,000,000
S (tons)
R (
tho
us
an
ds
)
S decline S msy Slim Spa Smax
What is the number of recruits surviving to maturity?
The mean maximum number of recruits surviving to maturity (Rm) can be obtained from Rmax and the age- specific mortality rates of juveniles (Mt)
1
max
tm
rttM
m eRR
where tr is the mean age at recruitment and tm is the mean age at first maturity
What is the unexploited spawner biomass S0?
At S0, recruitment replaces deaths. If the mean mortality rate (M) after mean age at maturity (tm) is known, then the total number of individuals (SN0) can be obtained by summing up annual survival
Multiplying SN0 with mean body weight Wmean gives S0
11
)()(0
M
M
mM
tMMtM
mt
ttMm e
eR
e
eeReRSN
mm
m
m
max1
1
max 1
1
t
t
M
t
t
t
M
tt
mean
r
t
c c
r
t
c c
eP
ePW
WWhere Pt is the proportion of matureindividuals at age t and Mc is the age-specific mortality rate
Example: North-east Arctic Cod
1,000
10,000
100,000
1,000,000
10,000,000
10,000 100,000 1,000,000 10,000,000 100,000,000
S (tons)
R (
tho
us
an
ds
)
S decline S 0Smsy
What is the maximum number of replacement spawners per spawner?
maxR
Sdecline 1. For the hockey-sticks, a simple relationship between maximum recruitment and spawner biomass is given by
2. Dividing Sdecline by mean body weight gives the number of respective (fished) spawners SNdecline
max1
1
max 1
1
)(
)(
t
t
FM
t
t
t
FM
tt
cur
r
t
c cc
r
t
c cc
eP
ePW
W
3. The maximum number of replacement spawners at low spawner densities (αr) is then obtained as
decline
mr SN
R
Multiple spawners
0.0001
0.001
0.01
0.1
1
10
100
0.0001 0.001 0.01 0.1 1 10 100
Spawner abundance (iteroparous)
Rep
lace
men
t sp
awn
er a
bu
nd
ance
α=7α=3
α=1
Standardized replacement spawner abundance over spawner abundance for 56 stocks of 25 iteroparous
species. The curves are smoothed hockey sticks with Rmax = 1 and α as indicated. Median α = 2.1 (1.7 – 2.8).
One-time spawners
Median α = 4.2 (3.6 – 5.2)
0.0001
0.001
0.01
0.1
1
10
100
0.0001 0.001 0.01 0.1 1 10 100
Spawner abundance (semelparous)
Rep
lace
men
t sp
awn
er a
bu
nd
ance
α=4.2
What is the intrinsic rate of population increase rmax?
In semelparous species (one-time spawners )
In iteroparous species(multiple spawners)(Myers & Mertz 1998)
m
r
tr
)ln(max
0)1(maxmax r
Mtrtr mm ee
Time to reach Smsy
)(2
)1ln( 0
curmsy
cur
FF
SS
t
where Scur is the current spawner biomass and Fcur is the current fishing mortality
MSY from ICES data
ICES gives the maximum yield per recruit (Y/R)max and maximum recruitment Rmax can be obtained as geometric mean of recruitment at stock sizes beyond Spa.
Then
MSY = Rmax (Y/R)max
MSY rmax vs MSY (Y/R)max
100
1,000
10,000
100,000
1,000,000
100 1,000 10,000 100,000 1,000,000 10,000,000
M SY (Y/R) (tonnes)
MS
Y r
ma
x (
ton
nes
)
1:1
rmax and Fmsy from ICES data
ICES provides a fishing mortality Fpa that stabilizes the stock at a low size Spa
Fpa must then be smaller than but close to rmax
Fpa thus is a conservative estimate of rmax
Some Results
For 53 ICES stocks with available data• 47 stock sizes are below Smsy
• These will need 0.7 – 22 years to reach Smsy if fishing is halted (median = 6.0 years)
• Current fishing mortality in these stocks is much larger than Fmsy
• Landings from these stocks could be 1 million tonnes higher (+16%) at MSY
Relevance of MSY
• MSY and the related Biomass are goals for overfished stocks and lower limits for healthy stocks
• This is prescribed in the Law of the Sea.
• The Johannesburg Declaration of 2002 set the deadline of 2015 to reach this objective.
• The EC instead aims to reach Fmsy