Modelling Plant Ecology - Environmental Modelling: Finding Simplicity in Complexity - page 200

of most ecological observations, making them ideal tools
with which to study the outcome of ecological processes
operating within ecosystems (see also Chapters 13 and 14).
In their traditional form, the computational cost and
complexity involved in modelling the fate of each individ-
ual tree has been a factor limiting the use of gap models in
larger scale (global) applications until recently. In addi-
tion, because of the explicit representation of individual
trees, mortality processes are typically represented using
a stochastic approach, where the outcome of the model
differs each time, given a different sets of trees that are
randomly selected to die in each timestep. Therefore,
the model outcome is typically reported as the mean
of an ensemble of model runs - hugely increasing the
computational requirements.
To overcome this problem, and simplify the structure
of gap models, Purves et al . (2007, 2008) developed the
'Perfect Plasticity Approximation' to simplify both the
spatial location and simulations of canopy light envi-
ronment in gap models. Gap models typically work by
selecting a random location for each individual tree stem.
From this location and the stem diameter, the spatial
extent of the canopy is defined. Typically, tree crowns
are simulated as being spherical in spatial extent, but the
use of deterministic crown size and shape results in the
spatial overlap of the hypothesized circular tree crowns.
This behaviour is typically not observed in real forests,
where tree crown size, shape and position are, to some
extent, plastic, and adapt to the size and shape of the
canopy gap in which a tree is growing. Adding plas-
tic crown behaviour creates a hugely complex and slow
model (Piboule et al ., 2005), but analysis of the outcome
converges on the simplifying feature that where the total
crown area equals or exceeds the ground area, then all of
the canopy space is filled, irrespective of the positioning
of individual stems (Purves et al ., 2007). This result is
analogous to the observation one obtains from looking
at a forest from above, where it is immediately apparent
that canopies appear to fit together 'perfectly' without
leaving any gaps (Figure 12.2). 'Perfect plasticity' is thus
an emergent feature predicted of idealized ecosystems
consisting of trees adapted to maximize their own evolu-
tionary fitness. If I assume that 'perfect plasticity' is a valid
assumption for forest trees, it is therefore not necessary to
model the 3D light environment for each individual tree.
Instead, I only need model the light resources available to
either the canopy or the understorey, resulting in a model
with similar levels of physiological detail, but greatly
reduced computational cost and no stochastic element.
The success of this new approach has been documented

12.2 Finding the simplicity

Looking at a diverse ecosystem, composed of numerous
plant types and species, operating on a surface that is
heterogeneous in soil type, aspect, elevation and climate
with unknown impacts of climate and disturbance his-
tory, it is possible, and reasonable, to be sceptical of the
chances of accurately modelling the behaviour of such a
system. However, this scepticism ignores many features
of ecological systems that confer the potential to predict
some aspects of their behaviour with a reasonable degree
of success. Many of these features are derived from opti-
mality criteria, the justification for which derives from the
complex adaptive nature of ecological systems (Holland,
1994), and the self-organizing emergent behaviour that
characterizes such systems. The use of optimality criteria
in ecological models is attractive because of the expecta-
tion that the processes of competition and evolution result
in systems whose emergent properties typically maxi-
mize the use of the available resources for plant growth
and reproduction (Falster, 2006) within the envelope of
possibilities. While it is not always the case (particularly
because evolution acts at the level of the individual and
species, not the community), approaches which either
implicitly or explicitly assume optimal behaviour have
had some success in helping us understand emergent pro-
cesses in both plant ecology and ecophysiology (Franklin,
2007). The next section reviews the three main classes of
predictive model, and the ways in which both new and
established models use the complex-adaptive properties
of ecosystems to assist with simplification of predictions
in each approach.

12.2.1 Differentmethods formodellingplant
function

Gap models

At a small scale, forest 'gap models', which track the
growth and location of individual trees, are often the
most appropriate tool for answering questions about
the ecology and physiology of an individual ecosystem
(Bugmann, 2001; Scheller and Mladenoff, 2007; Smith
et al ., 2001; Hickler et al ., 2008). These models succeed
because they have a relatively detailed approach to simu-
lating the canopy light environment and the processes of
recruitment, mortality, vegetation succession and hence
vegetation change (e.g. Deutschman et al ., 1999). Their
basic units are individual trees, so gap models can be
both parameterized and tested at the tree or stand scale