Stockrecruitment relationships

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Stock-recruitment relationships

• How to interpret a SR curve
• Density independence
• Density dependence
• Ricker vs Beverton-Holt
• Shepherd
• Conclusions/alternatives
• Chapter 4 in textbook

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Stock-recruitment relationships

• Number of offspring vs number of parents

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Stock-recruitment relationships

• Stock
• part of population under consideration for actual
  or potential utilization or

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Stock-recruitment relationships

• Stock
• part of population under consideration for actual
  or potential utilization or
• sample of individuals with similar production
  characteristics

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Stock-recruitment relationships

• Stock
• part of population under consideration for actual
  or potential utilization or
• sample of individuals with similar production
  characteristics
• Recruitment
• of individuals still alive at some specified
  point in time (stage) after the egg stage

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Stock-recruitment relationships
Population is a function of population size at a
previous time First developed for species with
non-overlapping generations
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Stock-recruitment relationships
In more familiar terms
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Stock-recruitment relationships
In more familiar terms
In general
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Stock-recruitment relationships

• What is ??

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Stock-recruitment relationships

• What is ??
• a ratio between generations, or

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Stock-recruitment relationships

• What is ??
• a ratio between generations, or
• net reproductive rate or ,

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Stock-recruitment relationships

• What is ??
• a ratio between generations, or
• net reproductive rate or ,
• net per capita rate of increase

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Stock-recruitment relationships

• What is ??
• a ratio between generations, or
• net reproductive rate or ,
• net per capita rate of increase
• Nk1 recruits (offspring)
• Nk stock (adults)

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Stock-recruitment relationships

• Plot Nk1 vs Nk

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Stock-recruitment relationships

• Plot Nk1 vs Nk
• Simple density-independence
• if ? 1, population is constant

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Stock-recruitment relationships

• Plot Nk1 vs Nk
• Simple density-independence
• if ? 1, population is constant
• if ? lt 1, population is decreasing

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Stock-recruitment relationships

• Plot Nk1 vs Nk
• Simple density-independence
• if ? 1, population is constant
• if ? lt 1, population is decreasing
• if ? gt 1, population is increasing

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? gt 1
Nk1
? 1
Nk
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? gt 1
Nk1
? 1
? lt 1
Nk
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Stock-recruitment relationships

• Principles
• curve must pass through origin

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Stock-recruitment relationships

• Principles
• curve must pass through origin
• no other S level results in 0 recruits

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Stock-recruitment relationships

• Principles
• curve must pass through origin
• no other S level results in 0 recruits
• R must exceed S over some part of the range of S

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Interpreting the shape ofstock-recruitment
relationships

• Straight S-R curve implies density-independence

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Interpreting the shape ofstock-recruitment
relationships

• Straight S-R curve implies density-independence
• Non-linear curve implies density-dependence

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Interpreting the shape ofstock-recruitment
relationships

• Straight S-R curve implies density-independence
• Non-linear curve implies density-dependence
• Decreasing slope compensatory

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Interpreting the shape ofstock-recruitment
relationships

• Straight S-R curve implies density-independence
• Non-linear curve implies density-dependence
• Decreasing slope compensatory
• Increasing slope depensatory

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Compensatory SR
deaths
births
Nk1 Nk
Nk1
Nk
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Compensatory SR
deaths
?
births
Nk1 Nk
?
Nk1
Nk
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What about Nk vs time?
K
Nk
time
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Interpreting the shape ofstock-recruitment
relationships

• Compensatory curves
• rate of recruitment decreases continually (i.e.
  slope is maximum at origin)

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Interpreting the shape ofstock-recruitment
relationships

• Compensatory curves
• rate of recruitment decreases continually (i.e.
  slope is maximum at origin)
• When curve meets replacement line K

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Interpreting the shape ofstock-recruitment
relationships

• Compensatory curves
• rate of recruitment decreases continually (i.e.
  slope is maximum at origin)
• When curve meets replacement line K
• Angle of intersection determines dynamics

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Interpreting the shape ofstock-recruitment
relationships

• Compensatory curves
• rate of recruitment decreases continually (i.e.
  slope is maximum at origin)
• When curve meets replacement line K
• Angle of intersection determines dynamics
• Maximum recruitment max distance

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Another way to look at it...
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What about depensation?
births
Deaths Type II FR
Nk1 Nk
Nk1
Nk
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What about depensation?
births
deaths
Nk1
Nk
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compensation
depensation
Fig 4.13b
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maximum at lowest abundance
compensation
depensation
declines at low abundances
Fig 4.13a
Spawner abundance
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Stock-recruitment relationshipsdepensation

• Mechanisms
• Constant predation

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Stock-recruitment relationshipsdepensation

• Mechanisms
• Constant predation
• Allee effect

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Stock-recruitment relationshipsassumptions

• Linear and curvilinear relationships possible
• Average S-R curve does not change
• All individuals are alike
• S and R measured without error
• Unit stock exists

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Stock-recruitment relationshipsRicker vs B-H

• Beverton-Holt

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Stock-recruitment relationships Ricker vs B-H

• Beverton-Holt

a recruit/spawner b slope
a
a dens-indep b dens-dep
b
Max recr a/b
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Stock-recruitment relationships Ricker vs B-H
parameters

• Beverton-Holt
• a increases the height of the asymptote and
  reduces curvature
• b increases rate of approach to the asymptote

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Fig 4.5a
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Fig 4.5b
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Stock-recruitment relationships Ricker vs B-H

• Beverton-Holt
• Recruitment asymptotic

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Stock-recruitment relationships Ricker vs B-H

• Beverton-Holt
• Recruitment asymptotic
• Intra-year feedback

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Stock-recruitment relationships Ricker vs B-H

• Beverton-Holt
• Recruitment asymptotic
• Intra-year feedback
• Recruits limited by food/habitat

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Stock-recruitment relationships Ricker vs B-H

• Beverton-Holt
• Recruitment asymptotic
• Intra-year feedback
• Recruits limited by food/habitat
• Marine species

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Stock-recruitment relationships Ricker vs B-H

• Ricker

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Stock-recruitment relationships Ricker vs B-H

• Ricker

a slope b peak
a dens-indep b dens-dep
a
b
Max recruit Occurs when S 1/b
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Stock-recruitment relationships Ricker vs B-H
parameters

• Ricker
• a leads to a higher steeper peak in recruitment
  at a fixed level of spawner abundance
• b decreases the height of the peak and reduces
  the level of spawner abundance at which the peak
  occurs

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Fig 4.6a
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Fig 4.6b
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Stock-recruitment relationships Ricker vs B-H

• Ricker
• Recruitment declines at high stock sizes
• (greater den-dep)

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Stock-recruitment relationships Ricker vs B-H

• Ricker
• Recruitment declines at high stock sizes
• Inter-year feedback

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Stock-recruitment relationships Ricker vs B-H

• Ricker
• Recruitment declines at high stock sizes
• Inter-year feedback
• Recruits limited more by predation

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Stock-recruitment relationships Ricker vs B-H

• Ricker
• Recruitment declines at high stock sizes
• Inter-year feedback
• Recruits limited more by predation
• Anadromous species
• e.g. Atlantic salmon

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Stock-recruitment relationships Ricker vs B-H

• Summary
• Both models contain dens-dep and -indep terms

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Stock-recruitment relationships Ricker vs B-H

• Summary
• Both models contain dens-dep and -indep terms
• Compensatory mortality reduces recruitment at hi
  stock levels

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Stock-recruitment relationships Ricker vs B-H

• Summary
• Both models contain dens-dep and -indep terms
• Compensatory mortality reduces recruitment at hi
  stock levels
• Mechanism of compensation differs

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Stock-recruitment relationships Ricker vs B-H

• Summary
• Both models contain dens-dep and -indep terms
• Compensatory mortaltiy reduces recruitment at hi
  stock levels
• Mechanism of compensation differs predation vs
  starvation

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Stock-recruitment relationships Shepherd curve

• 1 additional parameter (c)

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Stock-recruitment relationships Shepherd curve

• 1 additional parameter (c)
• can take Ricker or B-H form

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Stock-recruitment relationships Shepherd curve

• 1 additional parameter (c)
• can take Ricker or B-H form
• a slope at low stock sizes

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Stock-recruitment relationships Shepherd curve

• 1 additional parameter (c)
• Can take Ricker or B-H form
• a slope a low stock sizes
• b height of recruitment peak

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Stock-recruitment relationships Shepherd curve

• c determines shape of the curve

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Stock-recruitment relationships Shepherd curve

• c determines shape of the curve
• clt1 curve rises indefinitely (dens indep)

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Stock-recruitment relationships Shepherd curve

• C determines shape of the curve
• clt1 curve rises indefinitely (dens indep)
• c1 B-H form (dens dep)

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Stock-recruitment relationships Shepherd curve

• C determines shape of the curve
• clt1 curve rises indefinitely (dens indep)
• c1 B-H form
• cgt1 Ricker form (more dens dep)

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Fig 4.7a
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Fig 4.7b
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B-H to Ricker
Fig 4.7c
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Variation In peak recruitment
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sparse data
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Lack of data at low and hi stock sizes
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R
S
B-H
Fig 4.8a
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S
B-H
R
Fig 4.8b
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Stock-recruitment relationships Conclusions

• Generally do not fit data well

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Stock-recruitment relationships Conclusions

• Generally do not fit data well, but fit is only
  as good as data used.

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Stock-recruitment relationships Conclusions

• Generally do not fit data well, but fit is only
  as good as data used.
• Error can obscure fits

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original fit
B-H
Ricker
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Stock-recruitment relationships Conclusions

• Generally do not fit data well, but fit is only
  as good as data used.
• Error can obscure fits
• Some generalizations can be made

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Stock-recruitment relationships Conclusions

• Do not incorporate environmental factors.

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Incorporating environmental variability
unfav envir hi F collapse
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Stock-recruitment relationships Conclusions

• Do not incorporate environmental factors
• S-R relationship easiest to detect at very low or
  very high stock sizes?

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Stock-recruitment relationships Conclusions

• Do not incorporate environmental factors
• S-R relationship easiest to detect at very low or
  very high stock sizes,when compensatory and
  depensatory mechanism are most evident

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Stock-recruitment relationships Conclusions

• Do not incorporate environmental factors
• S-R relationship easiest to detect at very low or
  very high stock sizes,when compensatory and
  depensatory mechanism are most evident
• Effects of fishing

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Environmental Sources of Mortality

• Fluctuations in environmental conditions can
  strongly influence survival of eggs and larvae
• Point of No Return
• Ocean Stability Hypothesis
• Match-Mismatch Hypothesis
• Member-Vagrant hypothesis
• Bigger is Better Hypothesis

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Environmental Sources of Mortality

• Point of No Return
• The time at which starving larvae become too weak
  to feed and recover
• Ocean stability hypothesis
• Calm ocean conditions increase high density
  patches of larval food and larvae can feed better
  under calm conditions
• Match-Mismatch Hypothesis
• Larval food production and larval hatching must
  match in space and time or larval mortality will
  be high. (Spawning must be synchronized with
  production).

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Environmental Sources of Mortality

• Member-Vagrant Hypothesis (Sinclair, 1988)
• Physical ocean conditions that retain larvae in
  favorable patches are more important than
  biological factors in determining year-class
  success
• Bigger is Better Hypothesis
• Because mortality rates decline with size,
  growing big quickly will minimize mortality rates
• Not necessarily true. Counter gradient variation
  (Conover and Present, 1990)
• Cost to feeding

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Stock-recruitment relationships alternatives

• Spawner-recruit probability transition matrix
  (see Table 4.1)

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Stock-recruitment relationships alternatives

• Spawner-recruit probability transition matrix
  (see Table 4.1)
• Divide potential S R into intervals, and

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Stock-recruitment relationships alternatives

• Spawner-recruit probability transition matrix
  (see Table 4.1)
• Divide potential S R into intervals, and assess
  probability of a given S producing a given R

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Stock-recruitment relationships alternatives

• Spawner-recruit probability transition matrix
  (see Table 4.1)
• Divide potential S R into intervals, and assess
  probability of a given S producing a given R
• advantages incorporates variation, is not
  constrained by a specific SR relationship

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Stock-recruitment relationships alternatives

• Spawner-recruit probability transition matrix
  (see Table 4.1)
• Potential S R into intervals, and assess
  probability of a given S producing a given R
• advantages incorporates variation, is not
  constrained by a specific SR relationship
• disadvantages long data series over a range of
  stock sizes needed

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Stock-recruitment relationships alternatives

• Paulik diagrams
• Multistage models with a series of SR curves over
  various life history stages

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Irish Sea plaice, Pleuronectes platessa real
data 1963-1994
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Irish Sea plaice, Pleuronectes platessa
temperature variation
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Irish Sea plaice, Pleuronectes platessa fitting
Ricker curves
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Irish Sea plaice, Pleuronectes platessa Paulik
diagram
cold
warm
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Irish Sea plaice, Pleuronectes platessa
conceptual Paulik diagram
cold
warm