5A Modclllllg the Spatial and Temporal Distribution or Laniel' ('onehi/ega
147
5.4
Modelling the Spatial and Temporal Distribution of Lanice
conchilega
Volker Grimm
Abstract: A preliminary grid-based simulation model is presented designed to
explore the mechanisms responsible for the large differences in density of Lanice
conchilega in the backbarrier tidal flats of Spiekeroog. Patches with low or high
density occur in areas with low or high overall velocity respectively of the nearbottom flow. In the model, the relationship between near-bottom flow, local density of tubes, and local recruitment is described phenomenologically. The results of
the model lead to the testable hypothesis: observed differences in density are not
due to different larval supply.
Two reasons make the spatial and temporal distribution of Lanice conchilega particularly suitable for spatially explicit modelling (cf. Chap. 8): firstly, in contrast
with almost all other macrozoobenthic species of the Wadden Sea, Lanice adults
are sessile, and secondly, as has been revealed by studies under ELA WAT, there is
a direct relationship between local abundance and recruitment (Chap. 5.3).
Areas with low and high densities of L. conchilega (Chap. 3.5) are described by
Hertweck (1995) from the backbarrier tidal flats of Spiekeroog Island. After ice
winters during which almost all worms are killed, these differences in density are
restored within two to four years (Chaps. 3.6 and 7). Here we present a preliminary
grid-based model (see Chap. 8 for an introduction to grid-based modelling) which
was designed at the end of the ELA W AT project to explore the mechanisms responsible for the large differences in density of L. conchilega observed in the field
(for a more detailed description of the model, see Heuers et al. 1998).
The model describes a transect of one to three metres in length with a depth of
10 cm. This transect is divided into virtual grid "cells" (cf. Chap. 8) each I cm
wide. The model is essentially one-dimensional, because the depth of the transect
is not considered explicitly but only to obtain an idea of the carrying capacity of a
cell. Each cell may contain between zero and ten tubes of adult L. conchilega.
Time is not described continuously in the model, but proceeds in discrete one-year
steps. During a time step, the number of tubes within each cell is updated twice.
The first update is due to recruitment, the second one summarizes the effects of
mortality throughout the whole year.
Concerning recruitment, for each grid cell a number of maxL (for example, 20)
larvae have the chance to settle in accordance with the individual recruitment (or
settlement) probability Ps. In the programme which implements the model, a random number is drawn from a uniform distribution for each individual larva (i.e.,
from the interval 10, I lJ. Only if this number is smaller than Ps the larva settles in
the grid cell. Ps is calculated as the sum of the spontaneous, very small probability
Psp, and probability Pd which depends on the local density of the adult's tubes.
Psp describes recruitment which occurs irrespective of the adult's tubes.
To calculate Pd, first the local tube density, N, is determined as the mean of the
number of tubes in the cell and its four neighbouring cells. In this way the model
takes into account the fact that settlement occurs in two stages. First, aulophora
147
5.4
Modelling the Spatial and Temporal Distribution of Lanice
conchilega
Volker Grimm
Abstract: A preliminary grid-based simulation model is presented designed to
explore the mechanisms responsible for the large differences in density of Lanice
conchilega in the backbarrier tidal flats of Spiekeroog. Patches with low or high
density occur in areas with low or high overall velocity respectively of the nearbottom flow. In the model, the relationship between near-bottom flow, local density of tubes, and local recruitment is described phenomenologically. The results of
the model lead to the testable hypothesis: observed differences in density are not
due to different larval supply.
Two reasons make the spatial and temporal distribution of Lanice conchilega particularly suitable for spatially explicit modelling (cf. Chap. 8): firstly, in contrast
with almost all other macrozoobenthic species of the Wadden Sea, Lanice adults
are sessile, and secondly, as has been revealed by studies under ELA WAT, there is
a direct relationship between local abundance and recruitment (Chap. 5.3).
Areas with low and high densities of L. conchilega (Chap. 3.5) are described by
Hertweck (1995) from the backbarrier tidal flats of Spiekeroog Island. After ice
winters during which almost all worms are killed, these differences in density are
restored within two to four years (Chaps. 3.6 and 7). Here we present a preliminary
grid-based model (see Chap. 8 for an introduction to grid-based modelling) which
was designed at the end of the ELA W AT project to explore the mechanisms responsible for the large differences in density of L. conchilega observed in the field
(for a more detailed description of the model, see Heuers et al. 1998).
The model describes a transect of one to three metres in length with a depth of
10 cm. This transect is divided into virtual grid "cells" (cf. Chap. 8) each I cm
wide. The model is essentially one-dimensional, because the depth of the transect
is not considered explicitly but only to obtain an idea of the carrying capacity of a
cell. Each cell may contain between zero and ten tubes of adult L. conchilega.
Time is not described continuously in the model, but proceeds in discrete one-year
steps. During a time step, the number of tubes within each cell is updated twice.
The first update is due to recruitment, the second one summarizes the effects of
mortality throughout the whole year.
Concerning recruitment, for each grid cell a number of maxL (for example, 20)
larvae have the chance to settle in accordance with the individual recruitment (or
settlement) probability Ps. In the programme which implements the model, a random number is drawn from a uniform distribution for each individual larva (i.e.,
from the interval 10, I lJ. Only if this number is smaller than Ps the larva settles in
the grid cell. Ps is calculated as the sum of the spontaneous, very small probability
Psp, and probability Pd which depends on the local density of the adult's tubes.
Psp describes recruitment which occurs irrespective of the adult's tubes.
To calculate Pd, first the local tube density, N, is determined as the mean of the
number of tubes in the cell and its four neighbouring cells. In this way the model
takes into account the fact that settlement occurs in two stages. First, aulophora