78
5. Impact of Fishing Pressure on Mean Length of Fish
Proceed analogously to calculate the totals for the other length classes and
then sum each of those totals to yield the grand total across all age cohorts
of all lengths of fish. Then calculate the fraction of short, medium and long
fishes in the population.
The total number of fish in our system should influence the natural mortality of each age cohort. For simplicity, we assume that the mortalitypopulation size relations are
SHORT MORTALITY 01 =STOTAL POP/20000
MED MORTALITY 01 =STOTAL POP/20000
LONG MORTALITY 0 1 = STOTAL POP/20000
(5)
(6)
(7)
and
SHORTMORTALITY 1 2 = J*TOTAL POP/20000
MED MORTALITY 1 2 = .3*TOTAL POP/20000
LONG MORTALITY 12 =J*TOTALPOP!20000.
(8)
(9)
(0)
With the specifications of equations (5) through (0), mortality rates show
an S-shaped increase with higher total population sizes.
The only major parts of the model still unspecified are births. Assume
only one - to two-year-olds and two- to three-year-olds reproduce at birth
rates of .6 and .8, respectively , and that those rates are the same across the
three length classes. Further assume that it is more likely that short fish produce offspring that are short, and increasingly less likely that they produce
medium and long offspring. Similarly, medium-length fish are more likely
to have offspring that grow to be medium-sized, and a lower likelihood that
their offspring are either short or long. However, the likelihood for an offspring of medium-sized fish to be long or short is assumed to be the same .
Conversely, long fish are most likely to have offspring that grow to be long,
less likely to be medium, and even less likely to be short.
To model the possibility for random outcomes in the determination of
the length of offspring, we make use of STELLA's built-in function RANDOM, which requires us to specify a minimum and maximum between
which the random number should fall. If we specify the minimum and
maximum as 0 and 1, respectively, then on average the random number
will take on a value of .5, but will also equally likely be any number (between 0 and 1) above or below that. Additionally, we can specify a "Seed"
for each random number that will ensure that for subsequent runs the
model will use the same string of random numbers. So, for example:
RAND SHORT 12 = RANDOM(0,1 ,5)
RAND SHORT 23 =RANDOM(0,1,6)
RAND MED 1 2 =RANDOM(0,1,3)
RAND MED 2 3 = RANDOM(O,l,4)
(1)
(2)
(3)
(4)
5. Impact of Fishing Pressure on Mean Length of Fish
Proceed analogously to calculate the totals for the other length classes and
then sum each of those totals to yield the grand total across all age cohorts
of all lengths of fish. Then calculate the fraction of short, medium and long
fishes in the population.
The total number of fish in our system should influence the natural mortality of each age cohort. For simplicity, we assume that the mortalitypopulation size relations are
SHORT MORTALITY 01 =STOTAL POP/20000
MED MORTALITY 01 =STOTAL POP/20000
LONG MORTALITY 0 1 = STOTAL POP/20000
(5)
(6)
(7)
and
SHORTMORTALITY 1 2 = J*TOTAL POP/20000
MED MORTALITY 1 2 = .3*TOTAL POP/20000
LONG MORTALITY 12 =J*TOTALPOP!20000.
(8)
(9)
(0)
With the specifications of equations (5) through (0), mortality rates show
an S-shaped increase with higher total population sizes.
The only major parts of the model still unspecified are births. Assume
only one - to two-year-olds and two- to three-year-olds reproduce at birth
rates of .6 and .8, respectively , and that those rates are the same across the
three length classes. Further assume that it is more likely that short fish produce offspring that are short, and increasingly less likely that they produce
medium and long offspring. Similarly, medium-length fish are more likely
to have offspring that grow to be medium-sized, and a lower likelihood that
their offspring are either short or long. However, the likelihood for an offspring of medium-sized fish to be long or short is assumed to be the same .
Conversely, long fish are most likely to have offspring that grow to be long,
less likely to be medium, and even less likely to be short.
To model the possibility for random outcomes in the determination of
the length of offspring, we make use of STELLA's built-in function RANDOM, which requires us to specify a minimum and maximum between
which the random number should fall. If we specify the minimum and
maximum as 0 and 1, respectively, then on average the random number
will take on a value of .5, but will also equally likely be any number (between 0 and 1) above or below that. Additionally, we can specify a "Seed"
for each random number that will ensure that for subsequent runs the
model will use the same string of random numbers. So, for example:
RAND SHORT 12 = RANDOM(0,1 ,5)
RAND SHORT 23 =RANDOM(0,1,6)
RAND MED 1 2 =RANDOM(0,1,3)
RAND MED 2 3 = RANDOM(O,l,4)
(1)
(2)
(3)
(4)