Environmental Engineering Reference
In-Depth Information
a
b
35
0.008
30
25
0.006
20
0.004
15
10
0.002
5
0.000
0
0
5
10 15
Temperature [°C]
20
25
30
35
0
100 200
Time [days]
300
c
d
1.0
1.5
0.8
0.6
1.0
0.4
0.5
0.2
0.0
0.0
0
100 200
Time [days]
300
0
100 200
Time [days]
300
Fig. 9.4 Relation between temperature, development rate, biological time and transition probability:
(a) Temperature-dependent development rate described by an O'Neill function with
r
max
¼
0.0085
and
T
opt
¼
25. (b) Artificial time course of temperature described by a sine function. (c) Resulting
biological time calculated by integrating the O'Neill function over time. (d) Weibull distributions with
scale parameter 1 and different shape parameters (2 for the
solid
line and 12 for the
dashed
one) applied
to the biological time shown in panel c lead to the transition probabilities of the extended Leslie model
the increase of the development rate as a consequence of increasing the temperature
by 10
C. An example for an O'Neill function can be seen in Fig.
9.4a
. Combining this
function with a real temperature course yields a time dependent development rate.
Finally, integrating this time-dependent rate over time will give the biological time:
ð
t
biol
ð
t
Þ¼
rate temp
ð
ðÞ
Þ
d
t
0
For simplicity, one can regard the biological time as the sum of the development
rates. This is because an integral can be approximated by an infinite sum of
