FishSlides - Fisheries Introduction Economic and policy...

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Fisheries
Introduction: Economic and policy issues
Population dynamics
Sustainable catch-effort diagram
Bio-economic equilibria
• Free access.
• Sole owner
Traditional fishery management
• Limited entry
• Season closures
• Gear restrictions

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Fisheries (cont.)
Rights-based management
•I T Q s
• Private harvester agreement, cooperatives
•T U R F s
Protecting marine ecosystems
• Protecting marine habitats
• Controlling bycatch
Aquaculture: Promise and problems

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Fisheries (cont.)
Rights-based management
•I T Q s
• Private harvester agreement, cooperatives
•T U R F s
Protecting marine ecosystems
• Protecting marine habitats
• Controlling bycatch
Aquaculture: Promise and problems

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Components of stock dynamics
Recruitment
during year t
Growth of
individuals
during year t
Catch
during year t
Mortality
during year t
Change in stock
during year t

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Logistic model of population dynamics
Assumes recruitment, growth, and mortality are
determined by S(t) . Natural growth is f(S(t)) .
With catch, Q, equation for popul’n dynamics is
) ( )) ( (
) (
t Q t S f
dt
t dS
 
Specific logistic growth function:
) ( )) ( )( (
) (
t Q t S K t aS
dt
t dS
  
K is carrying capacity; ‘

’ is adjustment speed.

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Numerical example of logistic model
) ( )) ( 100 )( ( 01 .
) (
t Q t S t S
dt
t dS
  

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Natural growth
Stock S(t), tons
tons
per
year
K
Logistic growth model

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Sustainable catch, Q
Stock S, tons
tons
per
year
K
Sustainable yields
Note: dS(t)/dt = f(S(t)) - Q(t), so if Q(t) = f(S(t)), the stock is constant.
MSY

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Sustainable catch, Q
tons
per
year
Sustainable catch-effort curve
Effort E
Stock S
E
C
MSY
Note: With some growth functions and harvest technologies there may be a
critical effort level, E
C
, beyond which positive yields cannot be sustained.

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Deriving Catch-Effort Relationship for Logistic Model
1.
Population Growth, net of catch : ) ( )) ( (
) (
t Q t S f
dt
t dS
 
Example: ) ( )) ( 100 )( ( 01 .
) (
t Q t S t S
dt
t dS
   .
Questions:
 In the absence of any catch, what is the equilibrium level of the stock?
 What level of stock maximizes the sustainable yield?
2. Production Function for Catch: )) ( ), ( ( ) ( t E t S G t Q 
Example: ) ( ) ( 1 . ) ( t E t S t Q 
Problem:
 Express S (unobservable) in terms of Q and E (both observable).

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3. Solve for Steady State Catch as Function of Effort
(i) In a steady state equilibrium, 0
) (

dt
t dS
. Therefore, ) ( )) ( ( t Q t S f  and all
variables are constant over time so we drop t arguments in functions.
Example: Q S S   ) 100 ( 01 . .
(ii) We need to replace S , which is unobserved, by a function of E and Q , which
are observed. To
accomplish this, use the production function
) , ( ) ( E S G t Q 
and solve for S .
Example: Production function SE Q 1 .  implies
E
Q
S 10  .

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3. Solve for Steady State Catch as Function of Effort (cont.)
(iii) Finally, substitute the expression for S from step (ii) into the relationship
between steady state Q and S from step (i). Solve the resulting equation for
steady-state catch, Q , as a function of effort, E .