„ Populační ekologie živočichů "
Stano Pekár
Effect of conditions
► all conditions affect population growth via controlling metabolic processes in ectotherms
► temperature, humidity, day length, pH, etc.
Universal effect of temperatare
► with respect to body temperature: cold-blooded / warm-blooded
► with respect to temperature change: poikilotherms / homoiotherms
► with respect to production of temperature: endotherms /ectotherms
► temperature affects population growth of ectotherms
- rate of metabolism increases approx. by 2.5x for every 10 °C
► physiological time - combination of time and temperature
► rate of metabolism B:   ft ~ g % (T.. temperature)
— ~ M^1
- rate increases with body mass (M): ^ per mass unit ...
1/ P/
- biological time tb:        f ~ Me
Lkear 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 = l/D
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
and S can be estimated from the regression line of v = a + bT
T *
mm *
a + bT = 0
T   = —
nun 7
b
S:
S = D(T-T^) = D
T + -
b
J
D=l- =
1
T + a
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 (T) and T^n
► biofix .. the date when day-degrees begin to be accumulated
time, days
Non-lkear models
► when development rate is a non-linear function of temperature
► ET.. developmental temperature between      and T
max
► at high temperatures organisms die due to overheating
rmax .. upper temperature threshold - temperature at which developmental rate = 0
0.045
0.04 -
Q)
^    0.035 -
C
<D
E
Q.
O
0 >
Q
0.03 -0.025 -
0.02 -0.015 -
0.01 -0.005 -0
0
10
20
—i—
30
40 50
Temperature
time, days
► several different non-linear models (Briere, Lactin, etc.)
► allow to estimate 7^, 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 = axTx (T — T   ) x ~ T —T
V mm '       v max
v .. rate of development (=1/D) T.. experimental temperature
.. low temperature threshold Tmax.. upper temperature threshold a .. unknown parameter
Optimum temperature:
0 Trnin
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 etal. (1995)
v — e    — e
m
T —T
m ^
4>
v .. rate of development
T.. experimental temperature
r , A, p, (j).. unknown parameters
0 Trnin
Tm„„ and      can be estimated from the formula:
0 = e
T —T
(pfTm—^-)
A
0
r t can be estimated from the first derivative:
1  PL, Tm~T
dv(T) pT -= pe--e
dT A