smaller species, the density of the larger species declines faster with area than the
abundance of smaller species. The reason for this observation is that rare species
have a smaller geographic range than abundant, mostly small-sized, organisms
(Schmidet al., 2002). Small aquatic invertebrates such as testate amoebae or
benthic rotifers have a much wider geographic distribution than larger species,
and free-living microbial eukaryotes are probably sufficiently abundant to have a
global distribution (sensuFinlay, 2002 ; see also Finlay & Esteban, this volume).
Conclusions
During the last few decades, evidence for scale invariance has appeared in
several fields other than physics, and ecology is no exception. All these rather
recent findings on power-law relationships and scaling in ecology, ranging from
species-biomass invariance to body-size mediated patterns of community struc-
ture, are suggestive of an underlying scale-free pattern of complex systems.
Biomass invariance across sites and stream systems may reflect the relative
balance between resource supply and use, mediated and maintained through
size-dependent resource partitioning processes of communities (Schmidet al.,
unpublished). The fit of species-abundance patterns to random resource-
assembly, but not to neutral models, emphasizes the link between resource
dependence, body size and species composition, irrespective of trophic group.
This also stresses that differences between species in response to variations in
resource supply and environmental heterogeneity question the core assump-
tion of demographically identical species under Hubbell’s ( 2001 ) neutral con-
cept. It is also evident that the dispersal probability of individuals plays a limited
role in shaping patterns of observed benthic community structure at local
scales. Moreover, food in the form of biofilm-enriched particles is not a limiting
factor in most temperate stream ecosystems (Schmidet al., 2000), while habitat
complexity has a profound influence on species composition and size structure
(e.g. Jeffries, 1993 ; Schmidet al., 2002; Taniguchi & Tokeshi, 2004 ). In benthic
stream systems, resource complexity is the product of physical and biological
processes acting on the shape and size distribution of organic particles (Schmid
et al., unpublished). The results presented here substantiate the view that the
dynamics of the interstitial habitat and the various scaling domains of particles,
which serve both as food and habitat, influence the size distribution of inverte-
brates and therefore, diversity and species composition in stream communities.
Fractals are certainly the simplest method we have for quantifying a measure
across a range of scales. As such, they provide the best null model against which to
judge the real behaviour of natural patterns across different spatial scales, just as
stochasticity is the null model against which to test spatial patterns at a single
scale. Moreover, measures on aggregates such as (a) species-abundance distri-
butions which influence SARs, (b) population densities underlying BSDs, or
(c) particle densities underlying PSDs, give rise to a very different type of scaling
BODY SIZE AND SCALE INVARIANCE 163