RA TOPOGRID
219
macroalgal mats which are partly buried in the sediment, eroded tube mats of other
tube-building polychaetes, or other, more or less ephemeral epibenthic structures.
The population growth of a local population of Lanice after an ice winter ought,
at the beginning, to be exponential with a growth rate r. On the other hand, there is
obviously a local "carrying capacity", K" as an upper limit of local abundance (cf.
Hertweck 1995). The most simple way to combine exponential growth and density
dependence in a model is the "logistical equation" (e.g., Wissel 1989) which, in its
time-discrete form, is:
L" = LB + rLB (I - LB / KL)·
The indices "B" and "A" indicate the abundance before ("B") and after ("A")
settlement. According to the map of Hertweck (1995) we assume that Lspontan
and K, depend on topographic height (Fig. 8.4.2). The growth rate r is then chosen
to mimic the observation that it takes three to four years before abundance approaches local carrying capacity. If, however, a cell is very densely populated by
My til us (80 % of the maximum local density of Mytilus), we assume that Lanice
will not settle in this cell.
10
Lspontan
5
0
200
100
0
200
KL
100
0
200
KM
100
0
50 100 150 200 250
Height [relative units]
Fig. 8.4.2 Dependence of the parameters describing the settlement and local carrying capacity
of Laniel' (Lsponlan, r ['YoLK,) and Mylilus (K M ) on topographic height. Only the values indicatcd by points in the diagram are specificd in the simulation programme; all other values are
determined by linear interpolation
219
macroalgal mats which are partly buried in the sediment, eroded tube mats of other
tube-building polychaetes, or other, more or less ephemeral epibenthic structures.
The population growth of a local population of Lanice after an ice winter ought,
at the beginning, to be exponential with a growth rate r. On the other hand, there is
obviously a local "carrying capacity", K" as an upper limit of local abundance (cf.
Hertweck 1995). The most simple way to combine exponential growth and density
dependence in a model is the "logistical equation" (e.g., Wissel 1989) which, in its
time-discrete form, is:
L" = LB + rLB (I - LB / KL)·
The indices "B" and "A" indicate the abundance before ("B") and after ("A")
settlement. According to the map of Hertweck (1995) we assume that Lspontan
and K, depend on topographic height (Fig. 8.4.2). The growth rate r is then chosen
to mimic the observation that it takes three to four years before abundance approaches local carrying capacity. If, however, a cell is very densely populated by
My til us (80 % of the maximum local density of Mytilus), we assume that Lanice
will not settle in this cell.
10
Lspontan
5
0
200
100
0
200
KL
100
0
200
KM
100
0
50 100 150 200 250
Height [relative units]
Fig. 8.4.2 Dependence of the parameters describing the settlement and local carrying capacity
of Laniel' (Lsponlan, r ['YoLK,) and Mylilus (K M ) on topographic height. Only the values indicatcd by points in the diagram are specificd in the simulation programme; all other values are
determined by linear interpolation