102
6. Spatial Fisheries Model
values for ALPHA can move the system from damped oscillations to explosive oscillations-oscillations whose amplitude increases .
There must be an intermediate value for ALPHA at which the oscillations
are neither damped nor explosive. Such oscillatory system behavior is
known as a stable limit cycle. Can you find the value for ALPHA that yields
a stable limit cycle? Do you need to change that value if you change R/
There are several important conclusions that we can draw from the observation of high model sensitivity to the choice of ALPHA. If our model accurately reflects the decision-making rules that the fishermen apply to their
choice of effort, and if values of ALPHA-estimated from empirical dataare in the vicinity of the value that yields stable limit cycles, then it is virtually impossible to know in which direction the system will move because it
is unlikely that the data gathered from the real system will be sufficiently
precise to make an accurate prediction. Even the smallest deviation from
those values for ALPHA that lead to stable limit cycles will result either in
damped or explosive oscillations.
In contrast, if estimates of ALPHA are sufficientlysmall in comparison with
the value that yields stable limit cycles, then we know that the oscillations
must be damped and a steady-state will ultimately be achieved. We can
then use the model (or analytical techniques) to identify the steady-state effort and corresponding population sizes. Those could then be used to set effort levels in the fishery through policy interventions or management plans.
If ALPHA is relatively large, so that we can expect explosive oscillations,
and if we perceive such oscillations as detrimental to the fishery, then we
may want to implement policies to reduce ALPHA. One simple yet effective
approach would be to introduce a profit tax. Since changes in ALPHA are
proportional to profit,
dE = E= ALPHA • PROFIT = ALPHA • (P • V • E • N - ] • E)
dt
(4)
then if PROFIT gets taxed at a rate q, for O
dt
OS)
such a tax would in effect lower ALPHA, and possibly induce damped oscillations leading ultimately to a steady-state .
BASIC SPATIAL FISHERIES MODEL
E(t) = E(t-dt) + (E_DOT) * dt
INIT E = 20000
6. Spatial Fisheries Model
values for ALPHA can move the system from damped oscillations to explosive oscillations-oscillations whose amplitude increases .
There must be an intermediate value for ALPHA at which the oscillations
are neither damped nor explosive. Such oscillatory system behavior is
known as a stable limit cycle. Can you find the value for ALPHA that yields
a stable limit cycle? Do you need to change that value if you change R/
There are several important conclusions that we can draw from the observation of high model sensitivity to the choice of ALPHA. If our model accurately reflects the decision-making rules that the fishermen apply to their
choice of effort, and if values of ALPHA-estimated from empirical dataare in the vicinity of the value that yields stable limit cycles, then it is virtually impossible to know in which direction the system will move because it
is unlikely that the data gathered from the real system will be sufficiently
precise to make an accurate prediction. Even the smallest deviation from
those values for ALPHA that lead to stable limit cycles will result either in
damped or explosive oscillations.
In contrast, if estimates of ALPHA are sufficientlysmall in comparison with
the value that yields stable limit cycles, then we know that the oscillations
must be damped and a steady-state will ultimately be achieved. We can
then use the model (or analytical techniques) to identify the steady-state effort and corresponding population sizes. Those could then be used to set effort levels in the fishery through policy interventions or management plans.
If ALPHA is relatively large, so that we can expect explosive oscillations,
and if we perceive such oscillations as detrimental to the fishery, then we
may want to implement policies to reduce ALPHA. One simple yet effective
approach would be to introduce a profit tax. Since changes in ALPHA are
proportional to profit,
dE = E= ALPHA • PROFIT = ALPHA • (P • V • E • N - ] • E)
dt
(4)
then if PROFIT gets taxed at a rate q, for O
dt
OS)
such a tax would in effect lower ALPHA, and possibly induce damped oscillations leading ultimately to a steady-state .
BASIC SPATIAL FISHERIES MODEL
E(t) = E(t-dt) + (E_DOT) * dt
INIT E = 20000