► all conditions affect population growth via controlling metabolic processes in ectotherms
► temperature, humidity, day length, pH, etc.
Lepidoglyphus sp.
Universal effect of temperature
► temperature affects population growth of ectotherms
- rate of metabolism increases approx. by 2.5x for every 10 °C
fio =2-5
► physiological time - combination of time and temperature
► universal temperature dependence:
-P/
- rate of metabolism B:   B ~ e (T.. temperature)
- rate increases with body mass (M): per mass unit...
- biological time tb:
M
1/ P/ tb~MAe/T
0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0
10
A A. siro n C. malaccensis
15 20
Temperature [°C]
25
30
Linear model
► model is based on the assumption that developmental rate is a linear function of temperature T
► valid for the region of moderate temperatures (15-25°)
► at low temperatures organisms die due to coldness
D .. development time (days)
v .. rate of development = IAD
Tmin .. lower temperature limit - temperature at which
developmental rate = 0
0.045
0.04 ■
0)
"pg    0.035 -
0)
E
Q.
O
0)
>
0)
Q
0.03 -0.025 -
0.02 -0.015 ■
0.01 -0.005 ■ 0
0
10
15       20       25 30
35
Temperature
ET.. effective temperature .. developmental temperature between Tand Tmin S .. sum of effective temperature .. number of day-degrees [°D] required to complete development
.. does not depend on temperature = D*ET
Tmin and S can be estimated from the regression line of v = a + bT
T •
min *
a+bT=0
T.
nun 7
b
S:
S = D{T-Tmn) = D
f a" T + -
b
J
D=l- =
1
v   a + bT
S =
a + bT
► sum of effective temperature (S) [°D] is equal to area under temperature curve restricted to the interval between current temperature (7) and Tmin
► biofix .. the date when day-degrees begin to be accumulated
time, days
1=1
<l o
11 /Q
► when development rate is a non-linear function of temperature
► ET.. developmental temperature between Tmin and r,
max
► at high temperatures organisms die due to overheating
rmax .. upper temperature threshold - temperature at which developmental rate = 0
	0.045 -I
	0.04 -
Q)	
CO	0.035 -
	
nt	0.03 -
	
E	0.025 -
Q.	0.02 -
O	
vel	0.015 -
0	
Q	0.01 -
	0.005 -
	0 -
Temperature
1899
time, days
► several different non-linear models (Briere, Lactin, etc.)
► allow to estimate Tmin, Tmax and Topt (optimum temperature)
► easy to interpret for experiments with constant temperature
► instead of using average day temperature, use actual temperature
Briere et al. (1999)
v
= cixT x (T — T   ) x A/y —T
V mm '       v max
v .. rate of development {-\ID) T.. experimental temperature Tmin.. low temperature threshold Tmax.. upper temperature threshold a .. unknown parameter
Optimum temperature:
0 Tmin
T     Topt Tmax
^opt
AT   +3T. +Jl6T2 +9T2 -16T T
max mm      V max mm mm max
10
► parameters are estimated using non-linear regression
Lactin et al. (1995)
v = epT - e
(pTr
m
T —T
m ^
4>
v .. rate of development
T.. experimental temperature
Tm, A, p, (j).. unknown parameters
0 Tmin
rmax and Tmin can be estimated from the formula:
0 = e
T —T
A
0
Topt can be estimated from the first derivative:
T —T 1    pTm m
-= pe--e
dT A