Multispecies Analysis

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Multispecies Analysis

• Goals
• Explain the modification of single species
  fisheries models for multispecies analysis
• stock-recruitment
• biomass dynamics
• Describe and discuss MSVPA
• Explain multispecies Yield-Per-Recruit
• Discuss the basic problem of managing
  multispecies fisheries
• Distinguish between biological and
  technological interactions in multispecies
  fisheries

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Aquatic Ecosystems
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Multispecies Stock and Recruitment The Ricker
Model

• two interacting species
• one is of interest
• the second negatively affects the recruitment
  of the first
• competition
• predation
• new
• variable X stock of 2nd
• parameter c effect

R S e a-bS-cX
log(R/S) a - bS - cX error
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Cod and Herring Recruitment

• suggests instantaneous mortality of herring
  due to cod 0.75
• several 100s of juvenile herring per year
• however, high Mcould be spurious
• NEED CONTRAST (S X)
• here, estimate agrees with cod gut content
  analysis

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General Multispecies Ricker
R S e a-bS- ? ci Xi
for i 1 to n additional species
Similar derivations possible withother
Stock-Recruitment models.
What is a potential problem with this
approach? What was needed to provide meaningful
results with one additional species (X) ?
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Multispecies Biomass Dynamics

• Two approaches
• model complexity
• simplification (data aggregation)

Model Complexity
Bt1 Bt r Bt ( 1 - Bt / k - c Xt) - Ct
X as biomass, c as effect parameter
Ct Bt Et q, as previously
(Ut1/Ut) - 1 r - (r / kq)Ut - r c Xt - qEt
NEED good contrast between U, X,and E
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General Multispecies Biomass Dynamics Model
Bi,t1 Bi,t r Bi,t ( 1 - ? bi,jBj,t) - Ct
bi,j the interaction coefficient between
species i and j (community matrix)

• Problems with Parameter Estimation?
• available data (indices only)
• thus need to estimate q
• number of parameters
• contrast

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Multispecies VPA

• Extension of VPA to include
• Natural mortality due to predation among
  fished species

• Require
• usual catch-at-age data
• several species
• predation relationships
• from gut analysis?
• proportion total diet from VPA species
• preferences
• estimate (or assumption) on non-predatory M

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Equations of MSVPA
Uj NjRjPj
j cohort N number R annual ration /
individual (wt.) P proportion of ration from
species in MSVPA U amount consumed by
cohort (wt.)
Eij (Uj Aij) / Wi
Eij i-th cohort eaten by j-th Aij
preference matrix, defined as proportion of
i-th in j-ths diet Wi weight of individual in
i-th
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Cohort Equations
Ni,t Ni1,t1 eM (Ci,t Ei,t)eM/2
M non-predatory natural mortality C
catch E sum of all i individuals eaten by
other cohorts
If M0
Ni,t Ni1,t1 Ci,t Ei,t

• Must solve iteratively due to E
• solution of many cohorts is linked

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From the North Sea

• Some considerations
• High data requirements
• A matrix must be either
• independent of abundance
• or
• measured each year
• What if M dominated by abiotic factors?

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Aggregated Production Models

• Aggregated Biomass Dynamics
• Simplify Problem By Assuming
• Biomass is Biomass
• at least for some group of spp.
• Especially in tropical fisheries
• biomass dynamics unclear for single species
  data
• better fit with aggregated data

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Multispecies Yield-Per-Recruit

• Extension of Original Yield-Per-Recruit
• single species model
• integrated several models
• recruitment, growth, M, F
• dynamic pool
• age-structured
• avoid growth overfishing
• maximize Yield/Recruit
• specific tr and F
• Yield/Recruit Number Dying
• X Proportion of Death
• From Fishing X Weight
• Summed Across All Ages
• Beyond Recruitment

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Multispecies Equations
i species t age, t gt tr D Number
Dying F M as usual p fraction
recruited W weight at age
Remember (by species i) Fi E qi so ...
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• Also need
• numbers dying
• initial cohort size

Ni,t1 Nit e - ( Eqipit Mit )
Dit Ni,t1 - Ni,t Nit (1 - e - ( Eqipit
Mit ) )

• Initial Ns from other sources
• surveys?
• Aggregated Yield is Yield

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The Aggregative Approach

• as in Biomass, MSYPR
• assume
• biomass is biomass
• size tropic relationships remain in
  balance
• seems to work sometimes
• Why do it?
• fishery occurs that way
• esp. tropical trawls
• technological interactions
• impossible to separate harvest by species
• lack of species specific data
• may reflect some biological truth (wishful,
  but interesting)

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• BUT there are problems even if true
• common harvest rate
• based on strong and weak stocks
• weaker stocks may go extinct
• always get greater return from individual
  harvests
• not always possible

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Management Options for Multispecies Fisheries

• Detailed model of interactions
• many parameters
• very expensive, if possible
• Manage weakest stock
• forgo production
• Manage for average stock
• constant escapement
• constant harvest
• possible local extinctions
• All strategies questionable
• due to complexity
• Direct Empiricism
• try it out, adapt
• set clear criteria for success/failure
• harvest, extinctions, etc.