212
~ (jill! Based Modelling
will be overgrown by Mytilus and thus also change to state "M" in the next time
step, irrespective of the current state of the cell.
The parameter quantifying the dispersal probability of Mytilus, p8, is the probability that a cell which is not in state "M" but whose eight neighbouring cells are
in state "M" will itself change to "M" in the next time step. Accordingly, the probability that a cell with n neighbours, n= 1 .. 7, in the state "M", will itself change to
"M", is pl1= 1-( l_p8)"m
Disturbance events
Storms and ice winters are taken into account in the model. As far as storms are
concerned, we distinguish between years without storm, with one storm, and those
with two storms. Irrespective of the occurrence of storms, ice winters may also
occur. The corresponding probabilities of these extreme disturbance events are
listed in Table 8.2.1.
The simulation programme determines the occurrence of storms by drawing a
uniformly distributed random number each year. If this number is smaller than
pISt, one storm will occur. If it is greater than pISt but smaller than pISt+p2St,
two storms occur. Otherwise, there is no storm. The occurrence of ice winters is
determined in the same way using another random number.
Storms and ice winters affect individual grid cells, i.e. whether the cell will
change to state "0" is determined randomly for each grid cell in accordance with
the transition probabilities specified in Table 8.2.1. In the case of two storms, the
cell is disturbed twice with the corresponding transition probability. This way of
modelling the effects of a disturbance event means that we do not take into account
the fact that disturbance events might alter entire areas, i.e. clusters of grid cells, at
the same time.
Simulation
At the beginning of a simulation, the grid is randomly initialized, i.e. each grid is
assigned to one of the four possible states with a probability of I in 4. The simulation is run for fifty years.
8.2.1
Results of the First Model
Fig. 8.2.1 presents the typical results of the first model for four different parameter
combinations. It shows time series of the abundances of the three species (quantified by the number of occupied grid cells), time series of the disturbance events,
and snapshots of the spatial distribution of the species on the grid. Note that within
each year, the abundance of grid cells may take four different values, depending on
the processes settlement, succession, dispersal and disturbance events. In
Fig. 8.2.1, abundances are presented at the point of time in a year immediately
before disturbance events might occur. Likewise, the spatial snapshots show the
situation for a certain point of time. Figs. 8.2.1 a and d show situations immediately
after a disturbance has occurred (note the "white", i.e. empty cells), whereas the
~ (jill! Based Modelling
will be overgrown by Mytilus and thus also change to state "M" in the next time
step, irrespective of the current state of the cell.
The parameter quantifying the dispersal probability of Mytilus, p8, is the probability that a cell which is not in state "M" but whose eight neighbouring cells are
in state "M" will itself change to "M" in the next time step. Accordingly, the probability that a cell with n neighbours, n= 1 .. 7, in the state "M", will itself change to
"M", is pl1= 1-( l_p8)"m
Disturbance events
Storms and ice winters are taken into account in the model. As far as storms are
concerned, we distinguish between years without storm, with one storm, and those
with two storms. Irrespective of the occurrence of storms, ice winters may also
occur. The corresponding probabilities of these extreme disturbance events are
listed in Table 8.2.1.
The simulation programme determines the occurrence of storms by drawing a
uniformly distributed random number each year. If this number is smaller than
pISt, one storm will occur. If it is greater than pISt but smaller than pISt+p2St,
two storms occur. Otherwise, there is no storm. The occurrence of ice winters is
determined in the same way using another random number.
Storms and ice winters affect individual grid cells, i.e. whether the cell will
change to state "0" is determined randomly for each grid cell in accordance with
the transition probabilities specified in Table 8.2.1. In the case of two storms, the
cell is disturbed twice with the corresponding transition probability. This way of
modelling the effects of a disturbance event means that we do not take into account
the fact that disturbance events might alter entire areas, i.e. clusters of grid cells, at
the same time.
Simulation
At the beginning of a simulation, the grid is randomly initialized, i.e. each grid is
assigned to one of the four possible states with a probability of I in 4. The simulation is run for fifty years.
8.2.1
Results of the First Model
Fig. 8.2.1 presents the typical results of the first model for four different parameter
combinations. It shows time series of the abundances of the three species (quantified by the number of occupied grid cells), time series of the disturbance events,
and snapshots of the spatial distribution of the species on the grid. Note that within
each year, the abundance of grid cells may take four different values, depending on
the processes settlement, succession, dispersal and disturbance events. In
Fig. 8.2.1, abundances are presented at the point of time in a year immediately
before disturbance events might occur. Likewise, the spatial snapshots show the
situation for a certain point of time. Figs. 8.2.1 a and d show situations immediately
after a disturbance has occurred (note the "white", i.e. empty cells), whereas the