Revisiting StockRecruitment Relationships

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Revisiting Stock-Recruitment Relationships

• Rainer Froese
• 24.02.09
• Mini-workshop on
• Fisheries Ecology, Economics and Policy
• CAU, Kiel, Germany

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Overview

• A review of S-R models and their properties
• Estimating Sdecline
• Estimating unfished biomass S0 and Smsy
• Estimating annual reproductive rate ar
• Estimating rmax
• Estimating MSY and Fmsy
• Estimating time to reach Smsy
• MSY and Fmsy from ICES data
• Some results

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Typical S-R Data
(N)
(tonnes)
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Distribution of R
roughly log-normal
Skewed
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Distribution of S
skewed
roughly log-normal
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The Hump (Ricker, 1954)
where A ln Rmax
Assumptions a) negative S-R relationship at
high S b) highest recruitment at intermediate S
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The Asymptote (Beverton Holt 1957)
where A ln Rmax
Assumption Positive S-R relationship at high S
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The Hockey-Stick (Barrowman Myers 2000)

• Assumptions
• Constant R/S at low S
• Constant R at high S

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The Smooth Hockey-Stick (Froese 2008)


where A ln Rmax

• Assumptions
• Practically constant R at high S
• Gradually increasing R/S at lower S

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Example Striped bass Morone saxatilis
Parameters and accounted variance not
significantly different
Extrapolation VERY different
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Example 12 stocks of Atlantic cod Gadus morhua
Bold line is Smooth Hockey-Stick with n 414, a
4.5, Rmax 0.85 Dotted line the Hump with n
414, a 3.1, Rmax 1.4. Data were normalized by
dividing both R and S by Rmax for the respective
stock.
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Conclusion of detailed comparison(Froese et al.
in prep.)

• With regard to resilience of stocks to
  overfishing (a) and the carrying capacity of the
  environment for recruits (Rmax)
• The Asymptote tends to overestimate both a and
  Rmax
• The Hump gives conservative estimates of a but
  tends to overestimate Rmax
• The Piece-wise Hockey-Stick gives the most
  conservative estimates of a and Rmax
• The Smooth Hockey-Stick tends towards
  intermediate estimates of a and conservative
  estimates of Rmax.

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When does R decline?
For the hockey-sticks
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Example North-east Arctic Cod
Slim Spa
Smax
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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)

where tr is the mean age at recruitment and tm is
the mean age at first maturity
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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
Where Pt is the proportion of mature individuals
at age t and Mc is the age-specific mortality
rate
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Example North-east Arctic Cod
Smsy
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What is the maximum number of replacement
spawners per spawner?
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
3. The maximum number of replacement spawners
at low spawner densities (ar) is then obtained as
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Multiple spawners
Standardized replacement spawner abundance over
spawner abundance for 56 stocks of 25 iteroparous
species. The curves are smoothed hockey sticks
with Rmax 1 and a as indicated. Median a 2.1
(1.7 2.8).
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One-time spawners
Median a 4.2 (3.6 5.2)
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What is the intrinsic rate of population
increase rmax?
In semelparous species (one-time spawners )
In iteroparous species (multiple spawners) (Myers
Mertz 1998)
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Estimating MSY and Fmsy
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Time to reach Smsy
where Scur is the current spawner biomass and
Fcur is the current fishing mortality
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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

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MSY rmax vs MSY (Y/R)max
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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

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rmax vs Fpa
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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

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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

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Thank You