12.2. Model Structure
233
12.2. Model Structure
The model consists of three main modules, one each for the kelp , urchin
and otter popul ations. The sample area is representative of one square kilometer of intertidal zone along the California coastline . The time scale of this
mode l is measured in months to capture interannual variation of birth and
death rates of the three species. The model runs for a simulated time frame
of 60 mon ths (5 years).
Initially, otters are abse nt from the model , so the model captures population dynamics only for urchins and kelp . The otter popul ation is introduced
later in the model run so that its effects on kelp and urchin populations
may be better observe d. Twenty otters are introdu ced once into the system,
using a pulse function that yields an inflow of otters in the fifth month of a
model run, and no external additions thereafter.
The otter modul e is composed of two sub-po pulations of otters-male
and female-which can be seen in Figure 12.1. Birth of otters is a function
of the reproductive popul ation, birth rate , and carrying capacity. The carrying capacity is set at 30 otters per square kilometer (cf. Estes et al. 1978).
The reproductive popul ation consists of any males over the age of five and
any females over the age of four (Lubina and Levin 1988).
The birth rate is specified as a graphical relation between potential birth
rate and time of year as shown in Figure 12.2. Otters can give birth at any
time of the year. However, there is a major peak in rep roduction during the
months ofJune and July. The pea k birth rate is given as 16 pups per 100 reproductive adults per year (Ridgeway et al. 1981). The sex of the pup in the
module is determined by a fixed sex ratio, which we set to produce 60%
male and 40% female pu ps.
Otters are separated into different age cohorts and by sex mainly to capture rep resentative feed ing behavior. The model represents three life stages
of the otter: pup, juvenile and adult. Otters are assumed to be pups for one
year, during which time they do not feed on urchins. In contrast, juvenile
otters do feed on urchins. Adult otters feed on urchins and are considered
the sole rep rodu ctive group for the population. The total biomass of
urchins that an otter eats is determ ined by the otter's weight, which differs
by age and sex.
This model assumes that the otter is the top-level pred ator in the ecosystem. Therefore , otters are remove d from the popul ation solely due to natural death. The maximum lifespan of otters is assumed to be 17 years.
The urchin modul e consists of 13 main components, each of which represents a certain range of urchin test (shell) diameter in millimeters. The
first two of these 13 diameter classes are shown in Figure 12.3. The remaining 11 parts of this modul e are, in essence , the same.
Urchins are "recruited" into the population as a function of both the size of
the reproductive population and recruitment rate. Unlike otters, urchins are
assumed to have a constant recruitment rate. No carrying capacity is specified.
233
12.2. Model Structure
The model consists of three main modules, one each for the kelp , urchin
and otter popul ations. The sample area is representative of one square kilometer of intertidal zone along the California coastline . The time scale of this
mode l is measured in months to capture interannual variation of birth and
death rates of the three species. The model runs for a simulated time frame
of 60 mon ths (5 years).
Initially, otters are abse nt from the model , so the model captures population dynamics only for urchins and kelp . The otter popul ation is introduced
later in the model run so that its effects on kelp and urchin populations
may be better observe d. Twenty otters are introdu ced once into the system,
using a pulse function that yields an inflow of otters in the fifth month of a
model run, and no external additions thereafter.
The otter modul e is composed of two sub-po pulations of otters-male
and female-which can be seen in Figure 12.1. Birth of otters is a function
of the reproductive popul ation, birth rate , and carrying capacity. The carrying capacity is set at 30 otters per square kilometer (cf. Estes et al. 1978).
The reproductive popul ation consists of any males over the age of five and
any females over the age of four (Lubina and Levin 1988).
The birth rate is specified as a graphical relation between potential birth
rate and time of year as shown in Figure 12.2. Otters can give birth at any
time of the year. However, there is a major peak in rep roduction during the
months ofJune and July. The pea k birth rate is given as 16 pups per 100 reproductive adults per year (Ridgeway et al. 1981). The sex of the pup in the
module is determined by a fixed sex ratio, which we set to produce 60%
male and 40% female pu ps.
Otters are separated into different age cohorts and by sex mainly to capture rep resentative feed ing behavior. The model represents three life stages
of the otter: pup, juvenile and adult. Otters are assumed to be pups for one
year, during which time they do not feed on urchins. In contrast, juvenile
otters do feed on urchins. Adult otters feed on urchins and are considered
the sole rep rodu ctive group for the population. The total biomass of
urchins that an otter eats is determ ined by the otter's weight, which differs
by age and sex.
This model assumes that the otter is the top-level pred ator in the ecosystem. Therefore , otters are remove d from the popul ation solely due to natural death. The maximum lifespan of otters is assumed to be 17 years.
The urchin modul e consists of 13 main components, each of which represents a certain range of urchin test (shell) diameter in millimeters. The
first two of these 13 diameter classes are shown in Figure 12.3. The remaining 11 parts of this modul e are, in essence , the same.
Urchins are "recruited" into the population as a function of both the size of
the reproductive population and recruitment rate. Unlike otters, urchins are
assumed to have a constant recruitment rate. No carrying capacity is specified.