The effects of complexity, especially species richness, on the stability of aggregate properties of whole communities, such as their biomass or productivity, seem rather more straightforward, at least from a theoretical point of view (Cottingham et al., 2001). Broadly, in richer communities, the dynamics of these aggregate properties are more stable. In the first place, as long as the fluctuations in different populations are not perfectly correlated, there is an inevitable 'statistical averaging' effect when populations are added together - when one goes up, another is going down - and this tends to increase in effectiveness as richness (the number of populations) increases.
This effect interacts in turn with aggregate properties the variance to mean relationship of are more stable in Equation 20.2. As richness increases, richer communities average abundance tends to decrease, and the value of 2 in Equation 20.2 determines how the variance in abundance changes with this. Specifically, the greater the value of 2, the greater the proportionate decrease in variance, and the greater the increase in stability with increasing richness (Figure 20.8). Only in the rare and probably unrealistic case of 2 being less than 1 (variance increases proportionately as mean abundance declines) is the statistical averaging effect absent.
Note that the related topic of the relationship between richness and productivity - in so far as this is different from the relationship between richness and the stability of productivity -is picked up in the next chapter (see Section 21.7), which is devoted to species richness.
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