3.3 COMPLEXITY AND STABILITY IN MODEL COMMUNITIES

20.3.3 Complexity and stability in model communities:

local and global

local stability and global stability. Local

populations

stability

stability describes the tendency of a

community to return to its original state

(or something close to it) when subjected to a small perturbation.

The conventional wisdom, however, has by no means always

received support, and has been undermined in particular by the

Global stability describes this tendency when the community is

subjected to a large perturbation.

analysis of mathematical models. A watershed study was that by

May (1972). He constructed model food webs comprising a num-

A third aspect is related to the

ber of species, and examined the way in which the population

local/global distinction but concen-

dynamic fragility and

size of each species changed in the neighborhood of its equilib-

trates more on the environment of the

robustness

rium abundance (i.e. the local stability of individual populations).

community. The stability of any com-

Stable

combinations

Figure 20.7 Various aspects of stability,

used in this chapter to describe

communities, illustrated here in a

figurative way. In the resilience diagrams,

X marks the spot from which the

Environmental parameter 2

community has been displaced.

number of zeros. The webs could then be described by three

Each species was influenced by its interaction with all other species,

and the term β

was used to measure the effect of species j’s

parameters: S, the number of species; C, the ‘connectance’ of the

web (the fraction of all possible pairs of species that interacted

density on species i’s rate of increase. The food webs were ‘randomly

directly, i.e. with β

non-zero); and β , the average ‘interaction

assembled’, with all self-regulatory terms ( β

, β

, etc.) set at − 1,

strength’ (i.e. the average of the non-zero β values, disregarding

but all other β values distributed at random, including a certain

sign). May found that these food webs were only likely to be

the conflicting results amongst the models at least suggest that

stable (i.e. the populations would return to equilibrium after a

no single relationship will be appropriate in all communities. It

small disturbance) if:

would be wrong to replace one sweeping generalization with

another.

β (SC)

< 1. (20.1)