Artificial Population Regulation

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Artificial Population Regulation

• For regulation of populations
• For commercial harvest
• Maximum Sustained Yield (MSY)
• Based on the logistic equation
• dN/dt rN((K-N)/K)
• Generally found at 1/2 the carrying capacity (K)
• Formula for MSY
• H (Kr)/4

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Frequency of Harvest
The most frequent harvests can be taken at
intermediate population sizes.
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Maximum sustainable yield (MSY)
Anchovy MSY
Krebs Fig. 17.3
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Anchovy Harvest Record
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Optimum yield

• Below MSY because of other interests
• Defined in the U.S. Fishery Conservation and
  Management Act of 1976
• the quantity . . . (1) that will provide the
  greatest overall benefit to the nation, with
  reference to food production and recreation and
• (2) that is prescribed as such on the basis of
  maximum sustained yield as modified by any
  relevant economic, social, or ecological factors.

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Fixed Quota Harvesting
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Reproduction curves replacement
45o line is density independent replacement level
r populations
K type populations
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Whale harvests
Note the lack of whaling during WWII
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Efficiency of whale harvest after WWII
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Haddock Cod fisheries
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Predictions

• Garrod Jones (1974)
• Cod fishery
• Ignored by fisheries managers

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Fixed effort harvesting
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Multiple equilibria in harvesting
Declining harvest efficiency with increased
density
Eo would harvest to extinction U unstable
equilibrium
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IFQs

• Individual fishing quota
• Allowable catch divided into s awarded to or
  purchased by fisherman and companies
• Avoids fishing derby
• Can be sold or traded
• High cost excludes many fishermen
• Can be overcome if community quotas are allowed

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Dynamic pool
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Dynamic pool example

• Plaice (Krebs, Fig. 17.5)
• Best harvest rate would have been about 1/2 of
  actual level

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Interface with economics

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Cycle
Catch

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Effort

Price
Includes political pressure to increase effort
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Biological Conservation

• Population viability analysis (PVA)
• How vulnerable to extinction? Includes minimum
  viable population (MVP)
• Three general methods
• Long term studies - biogeographical patterns
• Subjective expert assessment
• General mathematical model
• Simulation models seem to hold the most promise
• Problems with the analysis
• Changing conditions
• Stochastic forces

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Causes of rarity

• Habitable areas are
• Short-lived
• Small
• Isolated
• Resources sparse
• Predators
• Genetic variation lacking

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Florida panther
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Management decisions
Sumatran Rhino