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survival fraction is determined with the constant m. Using the experimental data,
we solve this equation for
−
m:
−
m
=
LOGN
(
ESF
)
/
T
.
(3.2)
The
model
survival fraction (based on our choice of the time step DT) is derived as
follows:
MSF
=
ESF
(
t
+
DT
)
/
ESF
(
t
)=
EXP
(
−
m
∗
DT
)
.
(3.3)
When the expression for
−
m is substituted into (3.3), we get
MSF
=
EXP
(
LOGN
(
ESF
)
/
T
∗
DT
)
,
(3.4)
which is the basic equation for the model survival fraction. We now have the instan-
taneous survival fraction, and those surviving will mature or hatch at the maturation
or HATCH rate
HATCHING
=
EGGS
/
T
∗
MSF
,
(3.5)
that is, the survivors hatch at the rate, EGGS/T. Remember, eggs do not have to hatch
or die. They may simply wait. When they do die, they are claimed at the model death
rate
DYING
=
EGGS
∗
(
1
−
MSF
)
/
DT
,
(3.6)
the multiplier fraction being the model death rate per egg.
Such life table data can be used to determine the death rate of the adults, a nor-
mal demographic application. If we were to watch 100 new adults, we could calcu-
late the experimental adult survival fraction, EASF, and adult survival time (mean
length of adult life), TA. Let us say that we found these numbers to be 0.8 and 1.0,
respectively. These numbers are used in a parallel way to obtain the equivalent of
equation 3.6 for ADULTS.
The layout for the egg-adult model is shown in Figure 3.1, with an EGG LAY
RATE of 0.5 (eggs per adult per day) and the model results are shown in the graph of
Figure 3.2. We realize that insect egg laying rate is not constant but either declining
with time or pulsed. These concepts could be incorporated in more sophisticated
versions.
Now turn off the BIRTHING and HATCHING flows and put 100 eggs in EGGS.
Run the model to verify that it reproduces the experimental mean maturation rate,
T, and the experimental survival fraction at T. This must be so, since our modeling
process is one of exponential decay for both the DYING and HATCHING flows.
