Soil and Hillslope (Eco)Hydrology - Environmental Modelling: Finding Simplicity in Complexity - page 170

Peterson's (2002) use of the term, but may be regarded as
trivial in that it can be expected in most ecological systems,
except those governed by extreme contingency; i.e., those
in which external, often stochastic, events exert a domi-
nant control on the form and behaviour of the system.
Of more interest is whether cells 'remember' their pre-
vious states and whether this memory influences model
behaviour. If the cell has a transition rule based on a
nine-cell Moore neighbourhood or a five-cell von Neu-
mann neighbourhood, the transition rule will, by default,
include memory of the previous state of the cell under
consideration. However, for eight-cell Moore neighbour-
hoods and four-cell von Neumann neighbourhoods no
such memory is present and a 'conventional' CA with one
of these neighbourhoods may be said to be 'ahistoric' ( cf .
Alonso-Sanz, 2005).
If a cell's behaviour in a conventional 2-D CA depends
explicitly on the previous status of the cell over n time
levels, its rule set will be three-dimensional - that is, it
has a 2-D spatial neighbourhood and an n -deep temporal
neighbourhood. Such a CA may be said to be 'historic'
(Alonso-Sanz, 2005). We may think of this type of mem-
ory as being a local memory effect and also as a form
of strong memory , with memory strength increasing with,
and being defined by, n . Little research appears to have
been done on memory in CA except a series of papers
by Alonso-Sanz and his collaborators on 1-D CA (e.g.
Alonso-Sanz et al ., 2001; Alonso-Sanz, 2004; Alonso-Sanz
and Martın, 2002, 2004).
Strong memory may operate in many ways in ecological
systems. In the case of forests, the length of time a stand
of trees has been in place may be important because the
age of a tree can affect its susceptibility to physiological
shock (e.g. radiation and temperature shock) and diseases
and parasites (Hendry and McGlade, 1995). Longer term
strong memory effects may operate via the nutrient and
hydrological status of the soil in which trees grow. For
example, the depletion of nutrients or water from a soil,
caused by a previous plant assemblage in a forest ( cf .
Hendry and McGlade, 1995) will affect the growth of
the current assemblage. To date, the link between pat-
tern formation and ecological memory has received very
little attention. Hendry and McGlade (1995) found that
memory amplified mechanisms responsible for pattern
formation in a cellular model of a middle European beech
( Fagus sylvatica L.) forest-mosaic cycle. Similarly, using
a forest fire model, Peterson (2002) found that memory
increased the strength and persistence of patterns con-
sisting of patches, where patches were defined as areas of
similar properties (e.g. burnt ground, age of tree stand).

In a completely artificial ecology - Conway's Life CA
(Gardner, 1970) but with an added memory - Alonso-
Sanz et al . (2001) report that memory did not necessarily
strengthen pattern formation, although it led to patterns
becoming more stable or persistent.
How can memory effects be detected in ecohydrolog-
ical systems? As noted in Section 10.2, Puigdef abregas
(2005) reviews the various effects that plants have on
soils, including on radiation and rainfall receipt, organic
matter content, soil structure, biological activity, nutri-
ent content and cycling, and sediment accumulation (at
the soil surface). It is easy to envisage a situation where
the changes brought by the vegetation will depend on
how long the vegetation has been in place. Therefore,
soil properties in a landscape comprising vegetated and
bare patches might show memory effects if patch size or
position are changing over time. An area of bare ground
colonized by vegetation, as described by Dunkerley (1997)
(see Section 10.2) will initially have soil properties that
show features of both bare ground and vegetated ground.
If the colonized area remains vegetated for sufficiently
long, so that its memory of being bare ground is exceeded,
it will have features of vegetated ground only. It is easy
to see that such memory effects can help explain why
some subsurface patterns do not map simply onto surface
patterns. It is also easy to envisage how, in principle,
memory could be measured quite simply in the field.
For example, in drylands, areas that have been one state
or another (vegetated or bare) for many decades can be
expected to possess the canonical value of attributes such
as organic matter content or infiltrability. Areas that show
values of these attributes between the canonical values can
then be regarded as having 'remembered' their past state.
Problems arise, however, when using such an approach
to estimate the length of ecological memory and for pre-
dicting how memory affects ecohydrological behaviour;
much will depend on what is being remembered by the
ecosystem and the time over which it is remembered. The
sensitivity to memory could be determined using manip-
ulative field experiments but is probably best established
via numerical experimentation using models in which
memory strengths of a range of parameters are varied.
For such experiments, historical CA might prove suit-
able; adding a third dimension (the memory) to such
models partly overcomes the potentially simplistic treat-
ment of an ecosystem having simple categorical states (see
Section 10.2).
Perhaps the most extreme case of ecological memory
can be found in peatlands. Here, peat laid down at one
time may still be present in the peatland (i.e., it may