Dynamic Pool Models: Integrating Models for Resource Management

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Dynamic Pool Models Integrating Models for
Resource Management
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Lecture Goals

• List the four components of a typical dynamic
  pool model
• Explain additional population structure in
  dynamic pool models
• Define and explain the rational behind F0.1

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Population Structure

• Different Ages or Stages
• remember life tables
• larvae, juvenile, adult (reproductive)
• and now Recruits - caught by fishery
• Varying rates for each stage or age
• reproduction
• growth
• natural mortality
• harvest

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We want to include age/stage structure in an
explicit model of the population under harvest.
QUESTION When to harvest (what age/stage) to
obtain maximum biomass or 'yield' ?
Observed total biomass is a product of individual
growth and mortality (opposite effects)
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Processes Modeled

• Also environmental influences on
• growth, recruits, natural mortality
• Predation included in Natural Mortality
• Fishing impact on growth through alteration of
  age structure
• Management alters Fishing Mortality

A Fishery System Model
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Recruitment Model

• Represent process as
• Random or single constant value
• Beverton-Holt (Constant over range)
• others (e.g. Ricker)

Pacific Halibut, IPHC Data
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Growth Model

• Length as an asymptotic function (of time)
• Parameters (L0 , L? , k) estimated from field
  data of size-at-age

When L0 0 Lt L? (1 - e -kt)
Von Bertalanffy Growth
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Fishing Mortality

• F Fishing Mortality Rate
• Exponential decay function
• Translate to per unit of time by
• mortality 1 - e -F

F is a function of effort (f) catchability (by
age) qa Fa qaf
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Natural Mortality

• Modelled mathematically like F (exponential)
• Magnitude is often unknown or poorly known
• Biotic components
• competitors, predators, prey
• Abiotic components
• temperature, humidity, mechanical disturbance
• usually related to meteorology

• Estimated as
• constant all ages
• constant by age
• age specific
• stage specific
• Estimated by
• mark-recapture experiments
• empirical relationships
• body size, temperature

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Combine Submodels into a Single Model (based upon
data assumptions)
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Complete dynamic pool model allows potential
impact of management decisions to be evaluated.

• Management can act on
• Age of Entry to fishery
• via gear
• mesh/hook size
• Fishing mortality
• via effort
• time fished
• vessels/nets/etc.
• both?

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below age 2 not caught
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3-D perspective
Age-at-selectivity Age of Entry YPR yield per
recruit
Figure 10.3 Isopleths describing the response of
Macrodon ancylodon (King Weakfish)
yield-per-recruit to different combinations of
fishing mortality and age-at-50-selectivity.
Analysis was conducted using a single-gear model
with the base case scenario where M 1.2
www.fao.org/docrep/003/Y1715E/y1715e06.htm
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Interpreting The Yield Per Recruit Contours
Yield / Recruit
Fishing Mortality
Yield / Recruit
Fishing Mortality
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F0.1 - a cautious approach

• Yield per recruit approach may ignore
• stock size - recruitment (but pre-recruit
  surveys)
• variability in parameters

Always have uncertainty! (unquantified
variability)
Alternative is F0.1 which is always LESS than the
predicted optimum.