Spatial Population Models for Animals - Environmental Modelling: Finding Simplicity in Complexity - page 219

when combined with empirical research. One possible
avenue tomarrymodels and empirical/experimental ecol-
ogy at large spatial scales, and to apply the outcomes of
this approach, is through the idea of 'adaptive manage-
ment' (Walters, 1993). Under an adaptive management
framework, model predictions and empirical observa-
tions influence, in an iterative sequence, management
decisions and in turn enhancemodel development. In this
framework, successive management decisions represent
the experimental treatments of a traditional experimental
framework, although, thus far, failure to monitor the out-
comes of particular management decisions properly has
limited the effectiveness of the strategy as a whole (e.g. see
Downs and Kondolf, 2002, in the context of river restora-
tion). Clearly though, models developed and applied for
management must make predictions that managers need
and can use, and as much as possible these predictions
should be thoroughly evaluated (Mac Nally, 2002).
In our view, overcoming the divide between empiri-
cal and theoretical developments stands at the forefront
of current research needs. A number of possibilities
exist. One is for theory to take a more pattern-oriented
approach (i.e. to consider and be motivated by specific
'real' world patterns), while at the same time adopting
an experimental approach to model analysis (Wiener,
1995; Grimm et al ., 2005). Perhaps the greatest successes
will come where ecological modelling is applied to spe-
cific research needs in which empirical methods (or lack
thereof) limit our ability to study particular phenomena.
Such a problem is explored in detail below. It is also
worth remembering that prediction is not the only rea-
son to conduct experiments or to build models; seeing
models as 'tools for experimenting on theory' (Dowl-
ing, 1999) places them alongside, rather than isolating
them from, the other methodological approaches that
ecologists routinely use.

fill a wide range of ecological roles (predators, grazers,
detritivores, etc.), and many exhibit complex life-cycles
spending only part of their life in the stream (Allan,
1995). In upland streams where average flow velocities are
relatively high, most invertebrates (while in the stream)
live on or among rocks on the streambed; hence acquiring
the label of 'benthic' fauna. Yet, despite their strong
streambed relation, the tendency periodically to leave the
streambed and 'drift' downstream in the water current
(eventually to return to the streambed) is a behavioural
characteristic common to many species, and a distinctive
feature of most benthic streamcommunities (Brittain and
Eikekland, 1988; Allan, 1995).While the behavioural basis
of this drift phenomenon has long been debated (Waters,
1972), its importance in the dispersal of benthic fauna
and the colonization of downstream areas is now quite
well understood (Downes and Keough, 1998). To aquatic
ecologists interested in drift, factors influencing drift
distances have come to the fore as an important theme - of
particular interest is how drift might affect upstream-
downstream population linkages and the recovery rates
of benthic assemblages following disturbance (Lancaster
et al ., 1996; Moser and Minshall, 1996).
There has thus been great interest in determining the
drift distances of benthic fauna in real streams (e.g. Elliott,
1971; Lancaster et al ., 1996; Elliott, 2002). Three initial
observations have an important bearing on the develop-
ment of such models. First, most of these animals are
weak swimmers relative to the current speeds they expe-
rience when they drift downstream (Fonseca, 1999). This
means that drift distances can (at least as a starting point)
be modelled by thinking of drifting animals as passive
particles (Fonseca, 1999). Second, the flow environment
in streams is often extremely complex when examined
at small spatial scales but this complexity in flow can
be factored (or averaged) out when examined at larger
spatial scales (Carling, 1992). And last, attempting to
track the drift and settlement of individual animals is a
complex task that has met with limited success (Downes
and Keough, 1998). As a mean-field problem (i.e. at the
larger scale), the field of drift-distance models developed
quickly, describing drift distance as a simple exponential
decay function in which drift distance is governed by
height above the bed at which animals enter the drift
(itself an interesting issue!) and average stream veloc-
ity (e.g. Ciborowski, 1983; Reynolds et al ., 1990). These
models were, in places, quite successful at describing
actual observed drift distances, but discrepancies in drift
distances between sites with similar mean field velocities
were also common (Lancaster et al ., 1996).

13.4 Case study: dispersal dynamics in
stream ecosystems

Our aim here is to illustrate the way in which a relatively
simple spatial model can produce quite complex and
unexpected outcomes when applied to a relatively basic,
yet experimentally 'challenging', ecological phenomenon.

13.4.1 Theproblem

The beds of streams and rivers typically harbour a rich
and abundant assemblage of invertebrates, dominated
by insects, crustaceans and gastropods. These organisms