6.2. Basic Model with Spatial Movement
103
INFLOWS :
E_DOT = ALPHA* (P*V*E*N-J *E)
Ni [Reg ion] (t) = Ni[ Regi on] ( t - dt) + (Ni_DOT[ Re g i on ]) *
dt
I NIT Ni[Re g ion] = 5000
INFLOWS:
Ni _DOT [Re g ion] = Ri[Re gi on]*Ni[ Re gion ]*(l -
Ni [Re g i on ] /Ki[Re gion ]) -V* Ei[ Re gi on]*Ni[ Regi on]
ALPHA = .6
Di[Region] = Ni[Region] / N
Ei[Regi on] = Di[Regi on] *E
J = . 22
Ki[Region] = 2 0000
N = ARRAYSUM(Ni[ *])
P = 2.9
Ri[Region] = .60
V = .00006
6.2. Basic Model with Spatial Movement
Now let us allow the fish of the previo us section to freely move from one
region to any of the other regions. That movement may, to some extent, be
rando m. To capture randomn ess, introduce a new converter RAND, and
define it as a new, one-dimensional array with 12 elements. Use the Array
Editor to do so . Each of these elements should be a rando m number betwee n 0 and 1, to capture the probability of fish moving, for example , from
region 1 to region 2, from region 1 to region 3, from region 1 to region 4,
and so on. Use 12 different see ds in the specification of the random numbers, so each of them may be different , but can be repl icated from model
run to model run .
Since each of these rand om numbers for the spec ification of movement
rates is defined indep endently, we need to ensure that we don 't allow more
fish to move out from anyone region than there are fish in that region . One
convenient method to guarantee that this condition is fulfilled is to normalize the rand om numbers generated for the emigration of fish from each of
the regions. We first sum all the random numbers generated for movement
from each region :
RAND N1 =RAND[P12]+RAND[P13l+RAND[P14]
RAND N2 = RAND[P21]+RAND[P23]+RAND[P24]
RAND N3 = RAND[P31]+RAND[P32]+RAND[P34]
RAND N4 =RAND[P41]+RAND[P42]+RAND[P43l.
(7)
(8)
(9)
(0)
103
INFLOWS :
E_DOT = ALPHA* (P*V*E*N-J *E)
Ni [Reg ion] (t) = Ni[ Regi on] ( t - dt) + (Ni_DOT[ Re g i on ]) *
dt
I NIT Ni[Re g ion] = 5000
INFLOWS:
Ni _DOT [Re g ion] = Ri[Re gi on]*Ni[ Re gion ]*(l -
Ni [Re g i on ] /Ki[Re gion ]) -V* Ei[ Re gi on]*Ni[ Regi on]
ALPHA = .6
Di[Region] = Ni[Region] / N
Ei[Regi on] = Di[Regi on] *E
J = . 22
Ki[Region] = 2 0000
N = ARRAYSUM(Ni[ *])
P = 2.9
Ri[Region] = .60
V = .00006
6.2. Basic Model with Spatial Movement
Now let us allow the fish of the previo us section to freely move from one
region to any of the other regions. That movement may, to some extent, be
rando m. To capture randomn ess, introduce a new converter RAND, and
define it as a new, one-dimensional array with 12 elements. Use the Array
Editor to do so . Each of these elements should be a rando m number betwee n 0 and 1, to capture the probability of fish moving, for example , from
region 1 to region 2, from region 1 to region 3, from region 1 to region 4,
and so on. Use 12 different see ds in the specification of the random numbers, so each of them may be different , but can be repl icated from model
run to model run .
Since each of these rand om numbers for the spec ification of movement
rates is defined indep endently, we need to ensure that we don 't allow more
fish to move out from anyone region than there are fish in that region . One
convenient method to guarantee that this condition is fulfilled is to normalize the rand om numbers generated for the emigration of fish from each of
the regions. We first sum all the random numbers generated for movement
from each region :
RAND N1 =RAND[P12]+RAND[P13l+RAND[P14]
RAND N2 = RAND[P21]+RAND[P23]+RAND[P24]
RAND N3 = RAND[P31]+RAND[P32]+RAND[P34]
RAND N4 =RAND[P41]+RAND[P42]+RAND[P43l.
(7)
(8)
(9)
(0)