Environmental Engineering Reference
In-Depth Information
example (Caswell
2001
; Soetaert and Herman
2009
) is the life cycle of teasel
(
Dipsacus sylvestris
), a European perennial weed with the following six stages:
dormant seeds 1st year, dormant seeds 2nd year, small rosettes, medium rosettes,
large rosettes and flowering plants. Pascarella and Horvitz (1998) also used a stage-
classified matrix model to determine the importance of environmental variation to
the dynamics of a tropical understory shrub caused by hurricanes.
Selhorst et al. (1991) coupled two Leslie models to describe the predator-prey
relationship between two arthropods,
Scolothrips longicornis
and
Tetranychus
cinnabarinus
. The difficulty in dealing with insect populations is that the develop-
ment of insects strongly depends on environmental factors (e.g. temperature), so
that the age of an individual is not a good indicator for its development status.
Several studies dealing with insect populations therefore used an approach combin-
ing age and stage by coupling several Leslie processes (Sondgerath and Muller-
Pietralla 1996; Braune et al. 2008).
Size-dependent classes are widely used when dealing with fish populations.
In these cases fecundity is a function of the size of the individuals and not of
their age. Jung et al. (2009) used a Leslie size-dependent approach to simulate the
dynamics of the Pacific cod in order to improve the reliability of stock assessments
for fisheries management. Size-dependent vital rates were also regarded by Ang and
De Wreede (1990) for the simulation of algal life histories.
In order to control an African pest rodent, Stenseth et al. (2001) used a Leslie
model with three stages of females and three stages of males. In this study they
formulated the vital rates as functions of density and rainfall. Bieber and Ruf (2005)
set up a Leslie model for the wild boar with three stages: juveniles, yearlings and
adults. They found that reducing juvenile survival will have the largest effect on the
population growth in good years, whereas strong hunting pressure on adult females
will lead to the most effective population control in bad years. Heppel et al. (2000)
did a meta-analysis of 50 mammal populations based on Leslie models. They
examined the impacts of small changes in fertility, juvenile and adult survival on
the population growth. On this base they were able to discriminate between
carnivores, rodents, grazers, marine species and primates.
9.2 Model Description
The dynamics of age-structured populations is usually described with matrix
models, which can be traced back to the papers of Leslie (1945, 1948). The main
assumption of these models is that time and age are measured in the same units. For
example, if the age classes consist of individuals from 0 to 1 year old, from 1 to
2 years old and so on, then the time step of the model must be one year. If the age
classes denote 1-week old individuals and so on, then the time step of the simulation
model has to be one week. Hence, during one time step, individuals from one age
class pass into the next class according to the age-specific survival rate. The first age
class consists of the offspring from all reproductive age classes.
