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But is it appropriate to treat this as a mean-field prob-
lem, or could small-scale spatial variation in velocities
be affecting drift distances in ways that did not average
out between sites? Generalizing from both theoretical and
empirical studies in other systems, we hypothesized that
spatial variation in localized flow environments could
influence dispersal even where mean conditions are sim-
ilar. Central to this argument is the assumption that
drifting animals settle in complex flow environments
when they enter local areas of near-zero flow (so-called
dead-water zones - DWZ) behind small obstacles and
in backwaters along the stream margins (Lancaster and
Hildrew, 1993). Thus while average velocities will be
influenced only by the abundance of such DWZ within
a stream reach, differences in the spatial distribution
of DWZ may have independent effects on average drift
distances (Bond et al ., 2000).
problem of modelling complex flow dynamics (see Car-
ling, 1992).
13.4.3 Thequestion
Here we discuss two central questions addressed with
our model. First, how does the proportion and spatial
patchiness of obstacles in a stream reach affect the mean
distance travelled by drifting animals? We fixed the pro-
portion of obstacles at either 5% or 15%, and at each
of these proportions we varied the size (mean
±
SD)
of individual DWZs from 2
1 square cells
(Figure 13.4). We hypothesized that both of these factors
±
1to6
±
Direction
of flow
13.4.2 Themodel
Because of our interest in understanding how the spatial
pattern of DWZ (settlement sites) might affect drift dis-
tances of individual organisms, we adopted a grid-based
model structure that predicts the fate of each individual.
We used a spatial lattice to represent the stream reaches,
which provided a simple control on the proportion and
spatial pattern of obstacles (which created downstream
DWZ) within the streamscape. Individual organisms were
introduced into this streamscape and allowed to move
(drift) according to a set of predefined behavioural rules.
These rules varied depending on the position of individ-
uals relative to DWZ and obstacles, and were designed
to encapsulate in a simple fashion the ways in which
turbulent flow occurs around obstacles in real streams.
Complete details of the model can be found in Bond
et al . (2000). Essentially, streams were represented as a
two-dimensional lattice (depth was ignored) 30 cells wide
and 1000 cells long. Cells within the lattice took one of
three states: flowing water, obstacles or DWZs. Dead-
water zones were always located directly below obstacles,
and were also always of equal size. Obstacles represented
rocks and other obstructions observed in streams; their
size (and that of associated DWZ) was taken from field
surveys of several streams. Organisms moved through the
landscape according to a biased (downstream) random
walk, with a set of simple probabilistic behavioural rules
determining their movement patterns around obstacles,
and their likelihood of entering DWZ, where settlement
occurred (ending drift). These simplified rules provided
a practical way of overcoming the otherwise intractable
(a)
(b)
(c)
(d)
Empty stream
Obstacles
DWZ
Figure 13.3 Sample streamscapes at two different proportions
of obstacles and with two different obstacle size distributions.
(a) 5% obstacles; size (mean
±
SD) 2
±
1 cells; (b) 15%
obstacles, size 2
±
1 cells; (c) 5% obstacles, size 6
±
1 cells; (d)
15% obstacles, size 6
±
1 cells. Source: Bond et al . (2000).
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