Dynamic Pool models

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Dynamic Pool models

• Yield-per-recruit
• Beverton-Holt vs
• Ricker
• SSB-per-recruit
• eggs-per-recruit
• Chapter 7 in text

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Dynamic pool models

• Consider explicitly how growth and mortality
  affect stock biomass and reproductive potential
• Do this by separating stock biomass into
  age-specific components,
• dealing with effects of growth and mortality on
  each component, and then
• combining component effects to obtain overrall
  picture

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Yield-per-recruit models

• Allow you to examine trade-off between capturing
  a large of fish early in their life vs a
  smaller of larger fish later in life
• If F is set too high, growth overfishing will
  occur
• If F is set too low, large fish will be captured
  but total yield will be low
• Age at harvest is a trade-off between growth and
  mortality

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7.11
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A optimal capture age
7.11
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Yield-per-recruit models

• Yield assumed to depend on growth, age at first
  capture and fishing mortality,
• effects of recruitment added later

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Yield-per-recruit models

• Consider the standing crop of a stock, i.e.
  biomass ( aver wt) present at any time,
• The yield from that stock at given time is the
  biomass the inst. fishing mortality rate

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Yield-per-recruit models

• over the course of a time period,
• where tc and tmax are ages at first capture and
  maximum age respectively

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Yield-per-recruit models

• Weight (Wt) can be expressed as a von Bert
  equation

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Yield-per-recruit models

• Nt is expressed in terms of what happens to the
  individuals once they are recruited and enter the
  fishery.

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Yield-per-recruit models

• Nt is expressed in terms of what happens to the
  individuals once they are recruited and enter the
  fishery.
• In the simplest case, if recruitment R to an area
  of a fishery occurs at time tr, then the number
  surviving before they are at an age where they
  can be captured is
• where tr is the age of recruitment and assuming
  that tlttc or age at first capture

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Yield-per-recruit models

• With further refinement this leads to the
  Beverton-Holt yield equation.

Rnumber of recruits Usummation constant in the
cubic expansion of the growth equation
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Yield-per-recruit models

• Beverton-Holt yield equation can be used to
  calculate YPR for a single cohort of fish (see
  Box 7.6) and plotted to find the F that maximizes
  YPR

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Yield-per-recruit modelsF0.6, M 0.2
T B7.6.1
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Yield-per-recruit modelsF0.0-0.9
T B7.6.2
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Yield-per-recruit models
7.12
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Yield-per-recruit models

• The Beverton-Holt yield equation has 2 parameters
  that can be adjusted to manage the fishery yield
• F
• tc age at first capture

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Yield-per-recruit models

• Managers can vary one or more to obtain the
  maximum yield using isopleths
• What value of F leads to highest YPR?
• What value of tc leads to highest YPR?
• What combination of tc and F leads to highest
  YPR?

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Yield-per-recruit modelsAtlantic croaker example

• Commercial landings have fluctuated dramatically
  in last 60 yrs (from 1000-20000 tons)
• Steady decline since 1987
• Recreational catches peaked in 1991
• Barbieri et al. use a YPR model to assess whether
  F was too high in 2 fisheries

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Yield-per-recruit models
Croaker in lower Chesapeake Bay (Z0.6)
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Yield-per-recruit models

• Croaker in lower Chesapeake Bay (Z0.6)
• Conclusions
• No indication of growth overfishing
• Harvest at status quo
• Obtain better current mortality rates

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Yield-per-recruit models
Croaker in lower Chesapeake Bay (Z0.6)
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Yield-per-recruit models
Croaker in North Carolina (Z1.3)
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Yield-per-recruit models

• Croaker in North Carolina (Z1.3)
• Conclusions
• Indication of growth overfishing
• Increase age at first capture
• Lower fishing mortality rates

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Yield-per-recruit models
Croaker in North Carolina (Z1.3)
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Yield-per-recruit models

• Croaker in North Carolina vs Chesapeake Bay
• Differences may be due to
• NC data 1979-1981
• CB data 1988-1991
• Temporal or spatial patterns?

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Yield-per-recruit models

• Varying 2 parameters can also allow
  generalizations
• e.g. spotted whiting (vary growth rate, K)

Fishing mortality (F)
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Yield-per-recruit models

• Varying 2 parameters can also allow
  generalizations
• e.g. spotted whiting (vary M)

Fishing mortality (F)
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Yield-per-recruit models

• Varying 2 parameters can also allow
  generalizations
• e.g. spotted whiting (vary tc)

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Yield-per-recruit models

• Conclusions of whiting analysis
• A stock with high K will generally require a high
  F to maximize yield
• A stock suffering high M will need a greater F to
  produce a maximum yield and yield will always be
  lower
• Delaying age at first capture allows an increased
  yield maximized at a higher F

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Yield-per-recruit modelsassumptions

• recruitment curve is a knife edge rather than
  ogive
• natural mortality is constant after the age of
  recruitment and fishing mortality is constant
  after the age at first capture
• weight is predicted by the von Bert equation
• Steady-state stock structure
• i.e. total yield in any one year from all age
  classes is the same as that from a single cohort
  over its whole life span

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Yield-per-recruit modelsassumptions
Knife-edge recruitment
M is constant after tr, F is constant after tc
vonBert weight
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Yield-per-recruit modelsRicker method

• Same basic equation

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Yield-per-recruit modelsRicker method

• Same basic equation
• Growth follows this model

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Yield-per-recruit modelsRicker method

• And numbers alive at time t

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Yield-per-recruit modelsRicker method

• And numbers alive at time t
• And biomass for the next time interval is

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Yield-per-recruit modelsadvantages

• exploited and non-exploited segments
• more biological realism
• no need to address variability in YCS
• showing the pattern of ages and sizes in the
  catch

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Yield-per-recruit modelslimitations

• No underlying SR relationship
• stable environment
• equal probability of capture for similarly-aged
  individuals
• difficult to estimate recruitment overfishing
• best for species with low M

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Yield-per-recruit modelslimitations

• If M is high, YPR may not reach a maximum at a
  reasonable F

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Yield-per-recruit modelslimitations

• In short-lived species with high M, predicted
  Fmax may be extremely high
• Fmax obtained from a YPR analysis does not
  necessarily equal Fmsy produced from surplus
  yield analysis

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FmcyF giving maximum consistent yield, e.g.
(2/3)MSY
7.20
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Yield-per-recruit modelslimitations

• Where a YPR curve approaches an asymptote, Fopt
  is often taken to be the value at which an
  increase in one unit of F increases the catch by
  one tenth (0.1) of the amount caught by the first
  unit of F,
• or the point where the slope of the yield curve
  is 0.1 of the value of the slope at low levels of
  fishing mortality.
• This value is known as F0.1

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tangent to curve
slope at origin
10 slope
7.20
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Yield-per-recruit modelsF0.1 vs Fmax reference
points

• F0.1 will always be less than Fmax, ensuring a
  safer harvest
• F0.1 more precise target than Fmax when the YPR
  curve has a flat top
• No theoretical reason was selecting 0.1

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Dynamic pool modelsalternative approaches

• Basic YPR model assumes that recruitment is
  constant,
• thus ignoring the impact of F on future
  recruitment
• age structure of the population is similar to
  that of a aging cohort

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Dynamic pool modelsalternative approaches

• YPR models can detect growth overfishing but
  not recruitment overfishing
• Reduction in spawning stock biomass to the point
  where recruitment is impaired
• When SR curve falls below replacement level

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7.14
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Dynamic pool modelsSSB/R

• A method to detect recruitment overfishing is
  examining changes is SSB/R,
• Spawning stock biomass per recruit
• SSB/R is an extension of YPR that evaluates
  effects of F and tc on the spawning potential of
  a stock

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Dynamic pool modelsSSB/R

• Maximum SSB/R exists when F0, or a virgin
  population
• Combinations of F and tc reduce SSB/R and are
  expressed as of maximum

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Dynamic pool modelsSSB/R

• To evaluate SSB/R, plot SSB vs R
• of max SSB/R under current F and tc can be
  plotted as a replacement line (R/SSB)
• If data lie above line, enough SSB for population
  to replace itself
• If points lie below line, SSB is not adequate

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North Sea cod
Fcrash0.91
Fcurrent0.91
Overfishing early Stock high
7.16
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Dynamic pool modelsSSB/R

• Management scenarios involve different slopes
• Rule of thumb if SSB/R lt 20, recruitment
  overfishing is likely

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SSB/R0.67 kg R/SSB1.5
SSB/R2.0 R/SSB0.5
B lower F or higher tc, higher SSB/R and SSB
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Dynamic pool modelsEPR

• Eggs-per recruit (EPR) deals with lifetime
  fecundity of females (rather than SSB)
• Used to assess how much changes in age-0
  mortality induced by habitat degradation can be
  offset by altering F on older fish
• Or, to determine how much additional F is
  possible if age 0 survival is improved by habitat
  clean-up
• Evaluate EPR under different Fs and tc as max
  lifetime EPR

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Dynamic pool modelsEPR

• Can also be used to test sensitivity to
  additional sources of mortality
• which will depend on reproductive characteristics
  and current mortality rate
• Comparison across species show that sturgeon
  tend to be more sensitive than other species,
  why?
• Later age at maturity, lower fecundity, longer
  time between spawnings (see Boreman 1997)

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Dynamic pool modelsEPR and SSB/R

• present only a simple approximation for examining
  the potential for recruitment overfishing
• do not help to determine if the population under
  study is increasing, decreasing, or in
  equilibrium
• assume that mortality mechanisms only act on the
  population in a density-independent fashion
• can incorporate density-dependent mortality
  functions once the functional forms are defined