Spatial Population Models for Animals - Environmental Modelling: Finding Simplicity in Complexity - page 216

and explored the influence of the spatial configuration
of reserves on the extinction risk of greater glider
populations. Similar to the study of Possingham et al .
(1994), McCarthy and Lindenmayer's model suggested
that large, contiguous areas of old-growth forest are
important for population persistence. The importance of
large old-growth forest patches identified by these models
is in direct conflict with the current use of these forests
for timber production, and in this context the modelling
served a particularly important role in recognizing the
need to modify the existing management strategy.

p * = 1 − (m/c)

p * = 1 − (m/c) − h

3. Individual-based models

0 50 100 150

Time (t)

Individual-based models (IBMs) have become widely
used by ecologists since the early 1990s (DeAngelis and
Mooij, 2005; Grimm and Railsback, 2005). Unlike the
frameworks presented above, IBMs represent individual
organisms (i.e. they are 'atomistic'), and so they
conceptualize the dynamics of the system of interest as a
result of individual interactions. Similar approaches have
been developed in other fields, including archaeology and
economics, where they are called 'agent-based models',
and physics where they are termed 'particle-based' (see
Bithell et al ., 2008; O'Sullivan, 2008). Individual-based
models span the full gamut of model complexities, from
strategic to tactical. They maybe grid-based (e.g. Bond
et al ., 2000; Perry and Bond, 2009) or represent space
continuously by assigning individuals x , y positions on
some plane (e.g. Morales and Carlo, 2008). The key
strength of IBMs is that they directly represent individuals
and hence the individual-level variability central to the
ecological and evolutionary dynamics of populations,
communities and ecosystems (Uchmanski and Grimm,
1996; DeAngelis and Mooij, 2005). Individual-based
models also provide a more appropriate representation
thanmore aggregated models when populations are small
and so subject to the vagaries of genetic, demographic and
environmental stochasticity, and are increasingly used
to aid in population viability assessment of threatened
species (Lacy, 2000).
The earliest ecological IBMs were developed for for-
est trees (see review in Perry and Millington, 2008).
However, many IBMs have been developed for animals
across a diversity of taxonomic groups (such as fish,
arthropods, invertebrates, mammals and birds). A recent
trend in the development of these models has been their
integration with GIS to look at resource and organ-
ism dynamics in real landscapes (e.g. Liu et al ., 1995;
Ahearn et al ., 2001). TIGMOD (Ahearn et al ., 2001) is a

Figure 13.2 Dynamics of the patch occupancy model (Eq. 3
and 4) with (the lower line) c = 0.16 and m = 0 . 08, ( p * = 0 . 5)

and (the upper line) c = 0 . 16, m = 0.08 and h = 0 . 2( p * = 0 . 3).

Note that the trajectory of the system follows that of the
familiar logistic curve.

(the equilibrium solution for Equation 13.3). These
models are spatially implicit; that is, space is 'implied'
by there being multiple patches, which may or may not be
occupied, but the model does not explicitly consider the
location of the patches in the landscape. Thus, we know
the proportion of patches that are occupied at any given
time but not exactly which patches are occupied or where
they are; whether knowing occupancy alone is sufficient to
understandmetapopulation dynamics remains uncertain.
The metapopulation concept has been used as a
framework to explore the population dynamics of
various arboreal marsupials in south-eastern Australia
(e.g. Leadbeater's possum Gymnobelideus leadbeateri ,
mountain brushtail possum Trichosurus caninus ,and
the greater glider Petauroides volans ). Possingham
et al . (1994) used spatial habitat information, the
relationships between habitat attributes and quality,
and the dynamics of those habitat attributes, to assess
long-term metapopulation viability of the greater glider
in old-growth Eucalyptus forest, south-eastern Australia.
They determined patch size to be the key factor in
metapopulation persistence with large patches having the
longest median population persistence. Similar studies
have shown the potential importance of interpatch
dispersal in metapopulation persistence, and the high
extinction risk of small and isolated subpopulations
(Lindenmayer and Lacy, 1995a, b). McCarthy and
Lindenmayer (1999) used metapopulation models, mod-
ified to include disturbance by fire, to assist in reserve
design for arboreal marsupials in old-growth forests,