Database Reference
In-Depth Information
Table 3.1
Time
Died
Survived
Hatched
Time*Survived
Time*Hatched
0
1
99
0
0
0
1
3
96
0
96
0
2
3
93
2
186
4
3
4
89
3
267
9
4
5
84
21
336
84
5
5
79
9
395
45
6
6
73
7
438
42
7
6
67
5
469
35
8
7
60
3
480
24
9
8
52
2
468
18
Col. Sum = 45
52
3135
261
3135/45/100 =
261/52 =
0.697 = ESF
5.02 = T
Time is measured in days in this case, with data displayed for the beginning
of the next day (the result of the previous day). This table yields two important
averaged numbers, the experimental survival fraction, ESF (0.699, say 0.7), and the
experimental maturation time, T, (5.019, say 5 days). How can we use such data to
parameterize a model, when the model time step is dramatically different from this
experimentally found maturation time?
We must develop a new concept: the model survival fraction, MSF. In ecological
experiments, the instantaneous survival rate cannot be measured. But the survival
rate can be measured over some real time period, the maturation time, by counting
the number of eggs surviving to maturation. A problem arises when we wish to
model the system at a shorter time step than the real one. We need to model at these
shorter times because the characteristic time of the system may be shorter than the
shortest feasible measurement time of some particular part of the system. So we
have the experimental time step (the maturation time) and the model time step (DT)
and we must devise a conversion from experiment to model.
That conversion is based on the assumption that the survival fraction is a declin-
ing exponential, with ESF and T as its mean point.
1
ESF
(
t
)=
N
(
t
+
DT
)
/
N
(
t
)=
EXP
(
−
m
∗
t
)
(3.1)
=
the dimensionless experimental survival fraction
as a function of time.
N is the population size. Later, when we attempt to confirm the experimental data
with our model, we will shut off the birth and hatch rate and observe the (necessarily
exponential) decline in egg population due to death. The resulting instantaneous
1
We are constrained here to the assumption of exponential decline since both the DEATH and
HATCH flows in the model are arranged as exponential decays.
