214
I) Grid Based Modelling
disturbance events. Lanice is sensitive to ice winters but has a good ability to settle
on empty cells. Finally, Arenicola is not very sensitive to disturbances and has
little difficulty colonizing empty space. The frequency of disturbance events is
assumed to be rather high. On average, one or two storms occur every two of three
years, and an ice winter occurs every ten years.
With these assumptions. Mytilus only has two mechanisms to persist in the system: firstly, via succession by replacing Lanice or Arenicola, and secondly via
dispersal into neighbouring cells. Nevertheless, the time series of Fig. 8.2.1 a shows
that the abundance of Mytilus is held at a constantly low level by the frequent disturbance events. Only in some rarely occurring periods with few or no disturbances
is Mytilus able to build up higher abundance.
This effect of disturbances on Mytilus is confirmed and demonstrated by
Fig. 8.2.1 b, where both the probability that two storms occur within a year (p2St)
and the probability of ice winters have been divided by two. Mytilus now shows
markedly higher abundances but is still prevented by the disturbances from taking
over more cells. Note that without disturbances Mytilus would take over the whole
grid sooner or later because of the dispersal mechanism described above.
But what is the significance of succession for Mytilus in this model system?
Fig. S.2.lc shows the results for parameters which are the same as for Fig. 8.2.1 b,
except for parameters describing succession, pAM and pLM, which are set to zero.
Under these conditions Mytilus almost becomes extinct rather quickly because the
very low recruitment (POM) can not compensate for losses due to disturbances.
Interestingly, further simulations showed that even small values of pAM and pLM
are sufficient to keep Mytilus in the system, albeit at a low level of abundance.
This result demonstrates the potential significance of mutualistic interactions during the settlement of macrozoobenthic species (e.g., the settlement of larval MytiIus on tubes of Lanice), even if these interactions are rather weak, i.e. do not occur
all the time and everywhere.
Another mechanism to keep Mytilus in the system is its dispersal into neighbouring cells. In Fig. 8.2.1 d, the same parameters are used as in Fig. 8.2.1 c, except
for the probability p8 that a non-Mytilus cell surrounded by eight Mytilus cells will
change to state "M" in the next time step: this probability is now 0.5 instead of 0.2
in Fig. 8.2.1 c. Despite the lack of succession of Mytilus in this scenario, Mytilus is
well established in the system now because it spreads rather quickly during periods
free of disturbance. Note that with this mechanism of persistence, the spatial distribution of Mytilus is characterized by clusters of cells in state "M".
8.3
Problems when Applying the Grid-Based Approach in the
Wadden Sea
The first model is useful because it helps demonstrate the potential significance of
disturbance events and succession in a hypothetical Wadden Sea. As a "conceptual" model (Wissel 1989, 1992) it helps analyse general relationships. The first
model thus belongs to the same class of models as the well-know logistic equation
or the Lotka- Volterra models of competition or predator-prey systems. However,
I) Grid Based Modelling
disturbance events. Lanice is sensitive to ice winters but has a good ability to settle
on empty cells. Finally, Arenicola is not very sensitive to disturbances and has
little difficulty colonizing empty space. The frequency of disturbance events is
assumed to be rather high. On average, one or two storms occur every two of three
years, and an ice winter occurs every ten years.
With these assumptions. Mytilus only has two mechanisms to persist in the system: firstly, via succession by replacing Lanice or Arenicola, and secondly via
dispersal into neighbouring cells. Nevertheless, the time series of Fig. 8.2.1 a shows
that the abundance of Mytilus is held at a constantly low level by the frequent disturbance events. Only in some rarely occurring periods with few or no disturbances
is Mytilus able to build up higher abundance.
This effect of disturbances on Mytilus is confirmed and demonstrated by
Fig. 8.2.1 b, where both the probability that two storms occur within a year (p2St)
and the probability of ice winters have been divided by two. Mytilus now shows
markedly higher abundances but is still prevented by the disturbances from taking
over more cells. Note that without disturbances Mytilus would take over the whole
grid sooner or later because of the dispersal mechanism described above.
But what is the significance of succession for Mytilus in this model system?
Fig. S.2.lc shows the results for parameters which are the same as for Fig. 8.2.1 b,
except for parameters describing succession, pAM and pLM, which are set to zero.
Under these conditions Mytilus almost becomes extinct rather quickly because the
very low recruitment (POM) can not compensate for losses due to disturbances.
Interestingly, further simulations showed that even small values of pAM and pLM
are sufficient to keep Mytilus in the system, albeit at a low level of abundance.
This result demonstrates the potential significance of mutualistic interactions during the settlement of macrozoobenthic species (e.g., the settlement of larval MytiIus on tubes of Lanice), even if these interactions are rather weak, i.e. do not occur
all the time and everywhere.
Another mechanism to keep Mytilus in the system is its dispersal into neighbouring cells. In Fig. 8.2.1 d, the same parameters are used as in Fig. 8.2.1 c, except
for the probability p8 that a non-Mytilus cell surrounded by eight Mytilus cells will
change to state "M" in the next time step: this probability is now 0.5 instead of 0.2
in Fig. 8.2.1 c. Despite the lack of succession of Mytilus in this scenario, Mytilus is
well established in the system now because it spreads rather quickly during periods
free of disturbance. Note that with this mechanism of persistence, the spatial distribution of Mytilus is characterized by clusters of cells in state "M".
8.3
Problems when Applying the Grid-Based Approach in the
Wadden Sea
The first model is useful because it helps demonstrate the potential significance of
disturbance events and succession in a hypothetical Wadden Sea. As a "conceptual" model (Wissel 1989, 1992) it helps analyse general relationships. The first
model thus belongs to the same class of models as the well-know logistic equation
or the Lotka- Volterra models of competition or predator-prey systems. However,