Geoscience Reference
In-Depth Information
ranging from species composition to biogeographical regions to social systems
(Malanson, 1999; Plotnick and Sepkoski, 2001; Stewart, 2001).
Equilibrium and Change
Science in general has had great success in analysing systems such as economies or
ecologies by assuming they are in equilibrium. Complexity moves away from the
common defi nition of equilibrium, in which opposing forces are in balance, and
towards more dynamic forms of system stability and resilience. On a surfi cial level,
sensitivity and non-linearity in a system appear antithetical to equilibrium because
small perturbations in one part of a system can lead to large shifts in system behav-
iour elsewhere. However, sensitivity and non-linearity are typically found only at
particular thresholds, with the result that sudden shifts in system behaviour or
structure are fairly limited and occur as shifts among multiple varying attractors. A
host of physical phenomena, ranging from vegetation-soil dynamics to stream
systems, demonstrate the ability of sensitive systems to reach two or three stable
states (Sivakumar, 2000; Phillips, 2006). The question becomes whether to focus
on the large shifts among attractors due to sensitivity or on the fact that the system
is insensitive in the sense that it ends up being defi ned by attractors regardless of
initial values. These subtle, yet important, differences in the meaning of sensitivity
are evident in two related defi nitions: sensitivity to initial conditions (emphasising
the effect of small changes) and independence of initial conditions (emphasising
attractors) (Phillips, 2003).
The interplay among sensitivity, non-linearity, and equilibrium forces researchers
and policymakers to question the extent to which models can help project the
future of human or natural systems, especially if a small change in one location
results in large changes elsewhere (Ortegon-Monroy, 2003). At the same time, we
can understand the general characteristics of a system even when its precise state
may be beyond prediction. These general characteristics are gleaned through simple
rules under aggregate complexity, equations with deterministic complexity, and
measures under algorithmic complexity (Byrne, 2005). A complex system can also
be path-dependent; that is, its present state can be contingent on past states. In
the extreme, a complex system such as an ecosystem can lock into a fi xed state
due to positive or negative feedback (Hendry and McGlade, 1995). Wildfi res can
be path-dependent, for example, because the ability of a fi re to spread is largely
a function of its size; large fi res have greater capacity than small ones to expand
until they run out of fuel or encounter adverse weather conditions (Moritz et al.,
2005).
Two characteristics of complex systems help offset the destabilising effects of
sensitivity and non-linearity. The fi rst is resilience, which is the ability of the system
to change without drastically affecting the relationships among its components. The
second is transformability, or the capacity of a system to move to new confi gura-
tions (Walker et al., 2004). The combination of resilience and transformability can
give a complex system a form of stability and equilibrium in the larger sense that
its internal components remain intact even if some of their relationships shift. Deter-
ministic complexity focuses on the manner in which attractors and sensitivity
capture this dynamic, while aggregate complexity places greater emphasis on how
systems hover between randomness and stasis through self-organisation and self-
organised criticality.
