Stability and Instability in the Management of Mediterranean Desertification - Environmental Modelling: Finding Simplicity in Complexity - page 396

is exposed. The second is the effect of random chemical
changes in the gene pool that change its basic composition
and therefore the possible recombinations in reproduc-
tion. The third is the sum of all the chance variations that
occur in the reproductive processes. These three processes
can all lead to unexpected outcome as the 'internal' and
'external' forces operate through time. From the deserti-
fication point of view they can lead to the disappearance
of unfit populations in mixture of populations. As new
plants are introduced they may destabilize existing com-
munities and to this extent they could induce the type of
'contagious' desertification that is referred to above. Fur-
thermore, climatic fluctuations (Rowntree et al ., 2004)
and grazing densities (Thornes, 2005) are implicated in
desertification contagion.

are undertaken. Tiny changes can have major outcomes.
They can set the system along trajectories that have
far-reaching and (usually) unpredictable outcomes. In
this chapter, some of the major bifurcations have been
identified but, for desertification, many more wait to be
revealed. The second major implication for management
and history is that observed outcomes are not necessarily
a good guide to process mechanisms. The inference of
process from form is still in its infancy. The best hope
is that following the trajectories of specific changes from
known perturbations will lead us to a better appreciation
of the vegetation-degradation system.
It is too naıve always to seek climate-change expla-
nations for land degradation. This outlook is a residue
from the denudation-chronology preoccupation of early
to mid-twentieth century geomorphology, compounded
with the contemporary concerns with global climate
change. Semi-arid environments are often located at or
near to the isoclines and are therefore especially suscep-
tible to small perturbations of both physical and socio-
economic origins (see also the discussion in Wainwright
and Thornes, 2004 and Thornes, 2007). Recognition and
acceptance of the complexity (in the technical sense
intended in this chapter) is a first step towards bet-
ter management of desertification. Further research is
needed into complexity for more fruitful management.

24.7 Lessons and implications

In desertification, vegetation and land degradation are
inextricably mixed and strongly interactive. This interac-
tion can bemodelled using the predator-prey strategy that
produces clear separations (bifurcations) between stable
attractors and unstable repeller equilibria. By identifying
the bifurcations in phase space, with properly parame-
terized equations, we can anticipate how the behaviour
of the system will lead to one of the equilibria. As with
all complex systems, small variations in initial conditions
can lead to strongly different outcomes and, because nat-
ural systems are very noisy, there are many possibilities
for diversion along the routes to stability. The beauty of
the approach is that a basic knowledge of the underlying
dynamics provides a good insight into the likely possible
trajectories. Another important aspect is the separation
of the 'intrinsic' or 'internal' controls of evolution and
the external controls that push or force the trajectories. A
further dichotomy is between the deterministicmodelling
represented by the differential equations of change and
themanipulations that explore the nature of the equilibria
on the one hand, and the probabilistic modelling exposed
by the combinatorial possibilities within the genetic mod-
elling and the genetic drift as a stochastic process, on the
other hand. These are the intrinsic probabilistic elements.
The 'external' forcing, climate, human activities and nat-
ural spatial variability also lead to probabilistic behaviour
and modelling near the bifurcation sets (thresholds) and
at the attractors themselves.
The implications for desertification are beginning to
emerge. The first and most important is that the intrinsic
complexity has tobe appreciatedbeforemitigation actions

Postscript
John B Thornes passed away in 2008 and his chapter has
been reprinted from the first edition of this topic with
slight modification by the editors. John's contributions
to the fields of nonlinear dynamical systems modelling in
geomorphology, palaeohydrology and applied andpolicy-
relevant environmental research particularly in the area
of Mediterranean desertification were substantial. An
overview of them is given in Wainwright and Parsons
(2010) and in Dykes et al . (2012) and key elements of the
relevant research can be found in Brandt and Thornes
(1996), Mairota et al . (1997) and Geeson et al . (2002).

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