Environmental Engineering Reference
In-Depth Information
assume functional relationships between life cycle parameters and environmental
factors (Caswell et al. 1996; Braune et al. 2008). The advantage of this kind of
model is that it results not only in information about the range of the species but also
in life cycle characteristics.
The extended Leslie model for the dragonfly
Gomphus vulgatissimus
(Braune
et al. 2008) was developed in order to study the effects of climate change scenarios
on voltinism (i.e. the number of generations completed within one year) (Corbet
et al. 2006), and on the potential range (i.e. the geographical area within which this
species is able to reproduce and establish a stable population). Knowledge of
voltinism and potential range are needed to understand how species could adapt
or already have adapted to environmental conditions in different regions.
The life cycle was divided into three stages: eggs (
E
), larvae (
L
) and mature
adults (
A
). The projection matrix was constructed from two types of sub-matrices
for each stage: one for survival within that stage (
S
) and one for transition or
development into the next stage (
D
).
0
1
S
E
0
D
A
@
A
L
¼
D
E
S
L
0
0
D
L
S
A
The temporal pattern of the life cycle was determined by the probability distri-
bution function of the random variable development time, which itself depends on
the time course of environmental covariates (S
€
ondgerath and Richter 1990). In the
case of
G. vulgatissimus
the major controlling environmental variables are temper-
ature and day-length (Corbet 1999). The dependency on these variables was
modelled by the accelerated life model (Cox and Oakes 1984) with a multiplicative
approach, leading to the biological time (Schroder and Sondgerath 1996). As
explained above, this item reflects the actual development status of an individual:
the greater the biological time, the more advanced is the development. The devel-
opment is completed when the biological time equals unity. Biological variation
was taken into account by subsequently applying a statistical distribution function
to evaluate the transition probabilities into the next stage. For further details of the
model see Braune et al. (2008). With this model, simulations were done along a
latitudinal gradient from southern (42
N) to northern (62
N) Europe. This latitudi-
nal gradient describes the major distribution limits of the species. Evaluations were
performed for present-day conditions, as well as for three future time points (2020,
2050 and 2080). For the latter, temperature rises according to the scenarios given by
the Intergovernmental Panel of Climate Change (IPCC) were incorporated. The
initial population for each simulation was 5,000 eggs.
The results of two of the four simulations can be seen in Fig.
9.6
. For the present-
day scenario,
G. vulgatissimus
showed a 2-year life cycle, up to about 50
Nin
southern Europe. Between 50
N and 52
N, both 2- and 3-year developments are
shown, suggesting cohort splitting. For latitudes from 52
N to 54.5
N, the larval
life cycle lasted 3 years, followed by a region with 3-4-year development
(54.5
N-56
N). At the northernmost range, the larvae needed 4 years for their
