Stability and Instability in the Management of Mediterranean Desertification - Environmental Modelling: Finding Simplicity in Complexity - page 395

methodology is a tool of dubious value, even when the
local processes and their responses are carefully defined
by field studies. Here is the rub. Which strategy, field
experiment and observation or heuristic modelling can
we most rely on? The limitations of models are identified
by Roughgarden (1979: 298) 'Most models in ecology are
intended for other ecologists, cooked up by scientists for other
scientists.' (See also the discussion in Chapter 20.)

q

A 2

R 1 T 1

B 2

A 1

R 3 T 3

R 2 T 2

B 1

V

(a)

24.6 Plants

R 2

So far in this chapter, we have concentrated on plant cover
as the key property in relation to desertification. Never-
theless, different plant functional types may be a more
appropriate level of analysis because something at least
is known about the relative efficacy of trees, shrubs and
grass with respect to erosion and this is mainly through
their morphology. Eventually the problem will devolve
to species. Here, prompted by the work of Pease et al .
(1989), some complex aspects of the reduction of vegeta-
tion through quite evolutionary population dynamics are
discussed, thoroughly explored in a complex dynamical
systems context by Roughgarden (1979). It is raised here
as a promising area for future research in the vegetation-
erosion paradigm. Essentially, plants survive in these
environments through their capacity to resist pestilence
and drought. This resistance of the parent plant is basi-
cally conferred by the genetic constitution of the plant,
the genotype. If the genotype is inadequate, then the
plant is unable to survive. The character of the genotype
determines the fitness of plants and so is an internal com-
plexity that controls the fitness of the species. The genes
have variants that make up the fibrous blueprint. These
variants combine and recombine in a complex fashion as
a result of reproduction.
Roughgarden (1979) demonstrated how the evolution
of the gene pool can determine the population of the
species. Essentially, the combinatorial possibilities can
produce complex behaviour that exhibits the usual char-
acteristics of complexity, convergence and divergence to
and from stable and unstable equilibria and the corre-
sponding fluctuations in the population numbers. He also
showed that three 'external' factors control the actual gene
pool. These are natural selection, mutation and genetic
drift. In the first, the fittest plants (and their contribution
to the gene pool) survive. This is a fast process, ranging
from a single to several thousand generations accord-
ing to the make up of the gene pool and the external
stresses that the phenotype (reproductive parent plant)

t

B 2

t

(b)

Figure 24.11 Hypothetical stability conditions for erosion
under changing rainfall ( R ) and temperature ( T ) along a
climatic gradient. See text for detailed explanation. Upper part
represents stability conditions on a plot of soil moisture (

θ

)and
vegetation biomass ( V ). Lower part shows time trajectories of
system against time (Reproduced with permission from
Mairota, P., J.B. Thornes and N. Geeson (eds) 1997 Atlas of
Mediterranean Environments in Europe: the Desertification
Context. John Wiley and Sons, Chichester).

may result from systematic or random perturbations
in the controlling variables, but also the very character of
future responses to perturbations, and accommodate the
'boom-or-bust' adjustments reported in May (1973) or
in Thornes (1985 and 1990).
To the extent that the behaviour of vegetation and
soil moisture is represented by the equations described,
then their responses to climate change or perturbations
in the controlling variables can be modelled tentatively
by the evolutionary modelling strategy described in this
section. Different values and combinations of the values
of coefficients k 1 - k 6 will determine the stability condi-
tions following climate change. The very existence of the
climate gradient implies that the stability conditions of
the response at different places and different times will
differ in kind rather than inmagnitude, that the responses
cannot be assumed to be simple and linear, but will be
complex and nonlinear, and that the gradient-change