3.4 COMPLEXITY AND STABILITY IN MODEL COMMUNITIES

20.3.4 Complexity and stability in model communities:

Otherwise, they tended to be unstable.

whole communities

In other words, increases in the number of species, in connect-

ance and in interaction strength all tend to increase instability

(because they increase the left-hand side of the inequality above).

The effects of complexity, especially species richness, on the

stability of aggregate properties of whole communities, such as

Yet each of these represents an increase in complexity. Thus,

their biomass or productivity, seem rather more straightforward,

this model (along with others) suggests that complexity leads to

at least from a theoretical point of view (Cottingham et al., 2001).

instability, and it certainly indicates that there is no necessary,

unavoidable connection linking stability to complexity.

Broadly, in richer communities, the dynamics of these aggregate

properties are more stable. In the first place, as long as the fluctua-

Other studies, however, have sug-

tions in different populations are not perfectly correlated, there

many models defy the

gested that this connection between

complexity and instability may be an

is an inevitable ‘statistical averaging’ effect when populations are

conventional wisdom

added together – when one goes up, another is going down – and

artefact arising out of the particular

characteristics of the model communities or the way they have

this tends to increase in effectiveness as richness (the number of

been analyzed. In the first place, randomly assembled food webs

populations) increases.

This effect interacts in turn with

aggregate properties

often contain biologically unreasonable elements (e.g. loops of

the type: A eats B eats C eats A). Analyses of food webs that

the variance to mean relationship of

are more stable in

richer communities

are constrained to be reasonable (Lawlor, 1978; Pimm, 1979) show

Equation 20.2. As richness increases,

average abundance tends to decrease,

that whilst stability still declines with complexity, there is no

and the value of z in Equation 20.2 determines how the variance

sharp transition from stability to instability (compared with the

inequality in Equation 20.1). Second, if systems are ‘donor con-

in abundance changes with this. Specifically, the greater the

value of z, the greater the proportionate decrease in variance,

trolled’ (i.e. β

> 0, β

= 0), stability is unaffected by or actually

and the greater the increase in stability with increasing richness

increases with complexity (DeAngelis, 1975). And the relationship

(Figure 20.8). Only in the rare and probably unrealistic case of

between complexity and stability in models becomes more

complicated if attention is focused on the resilience of those

z being less than 1 (variance increases proportionately as mean

abundance declines) is the statistical averaging effect absent.

communities that are stable. While the proportion of stable

communities may decrease with increased complexity, resilience

Note that the related topic of the relationship between rich-

within this subset (a crucial aspect of stability) may increase

ness and productivity – in so far as this is different from the

(Pimm, 1979).

relationship between richness and the stability of productivity –

Finally, though, the relationship between species richness

is picked up in the next chapter (see Section 21.7), which is

devoted to species richness.

and the variability of populations appears to be affected in a

very general way by the relationship between the mean (m) and

variance (s

) of abundance of individual populations over time