5.1 . Three-Age-Cohort Model and Fishing
79
RAND LONG 1 2 = RANDOM(O,l,l)
RAND LONG 23 = RANDOM(0,1,2)
OS)
(6)
will each generate at each time period random numbers between 0 and 1
which are likely different from each other and from other time steps , but
because we specified seeds the same string of random numbers will be
used in subsequent runs . Specifying seeds is advisable if you wish to compare different model runs with each other-if you make a change in a parameter and rerun the model, but have not defined a seed it may be difficult to discern whether a changed result is due to the changed parameter,
or simply that a different set of random numbers was used .
We use these random numbers to calculate the fractions of births from
each subpopulation that add to that and to the other subpopulations:
SHORT BIRTHS =
SHORT BIRTH RATE 1 2 * RAND SHORT 1 2 *SHORT YEAR 1 2
+ SHORT BIRTH RATE 2 3*RAND SHORT 2 3*SHORT YEAR 2 3
+ MED BIRTH RATE 1 2*SO-RAND MED 1 2)*MED YEAR 1 2
+ MED BIRTH RATE 2 3*SO-RAND MED 2 3)*MED YEAR 2 3
+ LONG BIRTH RATE 1 2*(/3)*0-RAND LONG 1 2)*LONG YEAR 1 2
+ LONG BIRTH RATE 2 3*(/3)*(l-RAND LONG 2 3)*LONG YEAR 23. (7)
In equation (7) on average 50% of the births by short fish will yield short
fish. On average 50% of medium fish will yield medium fish and one-half of
the offspring from medium fish that turn out to not be of medium length
will be short fish. Similarly, on average 50% of long fish will have offspring
that grow to be long, and one-third of the remainder will be short. Equations (8) and (9) show the births for the other subpopulations.
MED BIRTHS =
MED BIRTH RATE 1 2 * RAND MED 1 2 * MED YEAR 1 2
+ MED BIRTH RATE 2 3 * RAND MED 2 3 * MED YEAR 2 3
+ SHORT BIRTH RATE 1 2 * (2/3) * O-RAND SHORT 1 2)
* SHORT YEAR 1 2
+ SHORT BIRTH RATE 2 3 * (2/3) * O-RAND SHORT 23)
* SHORT YEAR 2 3
+ LONG BIRTH RATE 1 2 * (2/3)*0-RAND LONG 1 2) * LONG YEAR 1 2
+ LONG BIRTH RATE 2 3 * (2/3) * O-RAND LONG 2 3)
* LONG YEAR 2 3;
(8)
LONG BIRTHS =
LONG BIRTH RATE 1 2 * RAND LONG 1 2 * LONG YEAR 1 2
+ LONG BIRTH RATE 2 3 * RAND LONG 2 3 * LONG YEAR 2 3
+ SHORT BIRTH RATE 1 2 *( /3) * O-RAND SHORT 1 2)
* SHORT YEAR 1 2
79
RAND LONG 1 2 = RANDOM(O,l,l)
RAND LONG 23 = RANDOM(0,1,2)
OS)
(6)
will each generate at each time period random numbers between 0 and 1
which are likely different from each other and from other time steps , but
because we specified seeds the same string of random numbers will be
used in subsequent runs . Specifying seeds is advisable if you wish to compare different model runs with each other-if you make a change in a parameter and rerun the model, but have not defined a seed it may be difficult to discern whether a changed result is due to the changed parameter,
or simply that a different set of random numbers was used .
We use these random numbers to calculate the fractions of births from
each subpopulation that add to that and to the other subpopulations:
SHORT BIRTHS =
SHORT BIRTH RATE 1 2 * RAND SHORT 1 2 *SHORT YEAR 1 2
+ SHORT BIRTH RATE 2 3*RAND SHORT 2 3*SHORT YEAR 2 3
+ MED BIRTH RATE 1 2*SO-RAND MED 1 2)*MED YEAR 1 2
+ MED BIRTH RATE 2 3*SO-RAND MED 2 3)*MED YEAR 2 3
+ LONG BIRTH RATE 1 2*(/3)*0-RAND LONG 1 2)*LONG YEAR 1 2
+ LONG BIRTH RATE 2 3*(/3)*(l-RAND LONG 2 3)*LONG YEAR 23. (7)
In equation (7) on average 50% of the births by short fish will yield short
fish. On average 50% of medium fish will yield medium fish and one-half of
the offspring from medium fish that turn out to not be of medium length
will be short fish. Similarly, on average 50% of long fish will have offspring
that grow to be long, and one-third of the remainder will be short. Equations (8) and (9) show the births for the other subpopulations.
MED BIRTHS =
MED BIRTH RATE 1 2 * RAND MED 1 2 * MED YEAR 1 2
+ MED BIRTH RATE 2 3 * RAND MED 2 3 * MED YEAR 2 3
+ SHORT BIRTH RATE 1 2 * (2/3) * O-RAND SHORT 1 2)
* SHORT YEAR 1 2
+ SHORT BIRTH RATE 2 3 * (2/3) * O-RAND SHORT 23)
* SHORT YEAR 2 3
+ LONG BIRTH RATE 1 2 * (2/3)*0-RAND LONG 1 2) * LONG YEAR 1 2
+ LONG BIRTH RATE 2 3 * (2/3) * O-RAND LONG 2 3)
* LONG YEAR 2 3;
(8)
LONG BIRTHS =
LONG BIRTH RATE 1 2 * RAND LONG 1 2 * LONG YEAR 1 2
+ LONG BIRTH RATE 2 3 * RAND LONG 2 3 * LONG YEAR 2 3
+ SHORT BIRTH RATE 1 2 *( /3) * O-RAND SHORT 1 2)
* SHORT YEAR 1 2