QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

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

Frequency of Harvest

The most frequent harvests can be taken at intermediate population sizes.

Maximum sustainable yield (MSY)

Anchovy MSY

Krebs: Fig. 17.3

Anchovy Harvest Record

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.

Fixed Quota Harvesting

Reproduction curves & replacement

K type populationsr populations

45o line is density independent replacement level

Whale harvests

Note the lack of whaling during WWII

Efficiency of whale harvest after WWII

Haddock & Cod fisheries

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

Predictions

Garrod & Jones (1974)

Cod fishery Ignored by

fisheries managers

Fixed effort harvesting

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

Multiple equilibria in harvesting

Eo would harvest to extinctionU= unstable equilibrium

Declining harvest efficiency with increased density

IFQ’s

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

Dynamic pool

€

Y = FN t

t= tc

∞

∑ W t

Dynamic pool example

Plaice (Krebs, Fig. 17.5)

Best harvest rate would have been about 1/2 of actual level

Interface with economics

?

+

-+

+

+

+

--

+

+

+

+

--

+

+

-

-+ +

+

+

Cycle

Catch

EffortPrice

Includes political pressure to increase effort

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

Causes of rarity

Habitable areas are:– Short-lived– Small– Isolated

Resources sparse Predators Genetic variation lacking

Florida pantherInput demographic patterns Simulation results

Initiation Probability of extinction (years)

Age of reproduction

Adult mortality

Litter size N K 25 50 100 200

Mean time to extinction

3 25 3.0 45 45 0.24 0.77 1.00 1.00 39

3 25 2.5 45 45 0.38 0.94 1.00 1.00 30

3 20 3.0 45 45 0.04 0.28 0.95 0.95 77

3 20 2.5 45 45 0.11 0.57 1.00 1.00 51

2 25 3.0 45 45 0.04 0.45 0.77 0.77 96

2 25 2.5 45 45 0.11 0.91 0.99 0.99 56

2 20 3.0 45 45 0.00 0.04 0.11 0.11 114

2 20 2.5 45 45 0.01 0.27 0.56 0.56 107

Management decisionsSumatran Rhino