11 J . Model Structure and Assumptions
217
11.3. Model Structure and Assumptions
The STELLA model is divided into four main modules describing the interrelations between the following compo nents: horseshoe crab eggs, juvenile
horseshoe crabs, adult horseshoe crabs, and bird populations. The model is
run with a time step of DT= 1. A user interface enables easy change of harvesting rates and observations of the effects of harvesting on horseshoe
crab and bird popul ations.
Horseshoe crab spaw ning, bird predation/migration , and harvesting each
take place during two month s of the year in the Delaware Bay. We assume
that harvesting in the Delaware Bay occurs solely within these two months.
Each DT of the model run therefore refers to a single season within a year.
The model is run for 100 seaso ns.
Because of the lack of consistent data, we have applied the following
two-step modeling procedure to specify initial conditions and parameter
values. In the first step, published data are used as much as possible to
specify the model under the assumption that no exploitation takes place.
For example, we estimate the total beach area in Delaware Bay available
for the females to lay eggs. We assume the spaw ning area on the beach extend s 2.5 meters from the shoreline . We assume there are 160,000 meters of
spaw ning beaches (Virtualbirder 2000). Thus, there are 400,000 rrr' of suitable spawning area. Botton et al. (994) state that 44,000 eggs/ m/ are
needed to fully sustain the entire migrating shorebird popul ation (ASMFC
1998). This yields 1.76'10
11 total eggs. If we divide the number of eggs by
the num ber of eggs per female (88 ,000) and assume a sex ratio of 1 : 1, the
corres pon ding combined adult male and female crab pop ulation would be
4,000,000 .
Given a set of initial conditions, the model is run until a steady-state is
reached . Then , in a seco nd step, the steady-state conditions are used to reinitialize the model. The "new" initial conditions and parameter values yield
a cons istent set of conditions that describe the system under investigation .
Table 11.1 lists the initial conditions of the model's state variables. For example, the "new" initial conditions for the numb er of eggs are approximately 1.63'10
11 , compared with 1.76'10
11 from the first step model run . Similarly, the assumed total adult crab populati on is approximately 3,700,000
instead of 4,000,000.
Although the model-gen erated data are close to information published in
the literature , it is difficult to tell how good the actual match is, since all too
often error bars or confidence intervals for empirical and census information are not properly doc umented. Furthermore, the actual horseshoe
crab-shore bird system has for a long time been affected by exploitation
and othe r anthropogenic disturbances, and as a conseque nce it is difficult
to quantify anthropogenic influe nces on the system's dynamics. Yet, by establishing consistent conditions for steady-state population dynamics, we
shall be able to exp lore with the model the impacts of exploitation. In
217
11.3. Model Structure and Assumptions
The STELLA model is divided into four main modules describing the interrelations between the following compo nents: horseshoe crab eggs, juvenile
horseshoe crabs, adult horseshoe crabs, and bird populations. The model is
run with a time step of DT= 1. A user interface enables easy change of harvesting rates and observations of the effects of harvesting on horseshoe
crab and bird popul ations.
Horseshoe crab spaw ning, bird predation/migration , and harvesting each
take place during two month s of the year in the Delaware Bay. We assume
that harvesting in the Delaware Bay occurs solely within these two months.
Each DT of the model run therefore refers to a single season within a year.
The model is run for 100 seaso ns.
Because of the lack of consistent data, we have applied the following
two-step modeling procedure to specify initial conditions and parameter
values. In the first step, published data are used as much as possible to
specify the model under the assumption that no exploitation takes place.
For example, we estimate the total beach area in Delaware Bay available
for the females to lay eggs. We assume the spaw ning area on the beach extend s 2.5 meters from the shoreline . We assume there are 160,000 meters of
spaw ning beaches (Virtualbirder 2000). Thus, there are 400,000 rrr' of suitable spawning area. Botton et al. (994) state that 44,000 eggs/ m/ are
needed to fully sustain the entire migrating shorebird popul ation (ASMFC
1998). This yields 1.76'10
11 total eggs. If we divide the number of eggs by
the num ber of eggs per female (88 ,000) and assume a sex ratio of 1 : 1, the
corres pon ding combined adult male and female crab pop ulation would be
4,000,000 .
Given a set of initial conditions, the model is run until a steady-state is
reached . Then , in a seco nd step, the steady-state conditions are used to reinitialize the model. The "new" initial conditions and parameter values yield
a cons istent set of conditions that describe the system under investigation .
Table 11.1 lists the initial conditions of the model's state variables. For example, the "new" initial conditions for the numb er of eggs are approximately 1.63'10
11 , compared with 1.76'10
11 from the first step model run . Similarly, the assumed total adult crab populati on is approximately 3,700,000
instead of 4,000,000.
Although the model-gen erated data are close to information published in
the literature , it is difficult to tell how good the actual match is, since all too
often error bars or confidence intervals for empirical and census information are not properly doc umented. Furthermore, the actual horseshoe
crab-shore bird system has for a long time been affected by exploitation
and othe r anthropogenic disturbances, and as a conseque nce it is difficult
to quantify anthropogenic influe nces on the system's dynamics. Yet, by establishing consistent conditions for steady-state population dynamics, we
shall be able to exp lore with the model the impacts of exploitation. In