Multifractal distributions are best suited for representing the multiplicative
action of the various biotic and physical processes acting on, for instance, the
parent particle material that results in a given distribution of particle sizes.
Consequently, similarities in the irregularities of a measure over several scales
give rise to a multifractal distribution of that measure (Feder, 1988 ; Schmid,
2000 ). The conditions leading to observed size distributions and SARs in nature
could lead us to anticipate that these measures should generally display multi-
fractal behaviour (Posadaset al., 2001; Schmidet al., 2002).
This chapter is concerned with scale-related patterns within river ecosystems
and it demonstrates that body-size scale invariance observed in benthic inver-
tebrate communities and their habitat should conform to multifractal relation-
ships. In addition, the body size of benthic invertebrates may relate to habitat
size-structure and, therefore, species-abundances patterns, in turn, may be
governed by habitat heterogeneity. Using empirical, quantitative data on
benthic invertebrate species from three geographically separate stream sys-
tems, we illustrate the inappropriateness of the homogeneous power-law inter-
pretations and we demonstrate that multifractal behaviour often governs
species-rich communities.
Data collection
The data sets were drawn from three geographically separate stream ecosys-
tems, the second-order streams Oberer Seebach (SB) in Austria and the Afon
Mynach (MY) in North Wales and a first-order stream of the Nant Cwm Llwch (LL)
catchment in South Wales, UK. Quantitative benthic samples (n¼867) were
collected to obtain data on invertebrates and interstitial habitat between 1991
and 2004. In each stream, stratified random sampling was conducted at variable
time intervals, mainly bimonthly in SB and MY and seasonally in LL. Samples
were collected within 100 m reaches with modified Hess samplers (mesh-size for
LL: 20mm and for SB and MY: 50mm) to a sediment depth of 10 cm. The data sets
for these stream communities included a total of 1040 species ranging from
testate amoebae and benthic rotifers to insect larvae, including more than 10^6
measured individuals. Gut contents analyses of these species revealed that they
represented mostly detritivores and to a lesser extent omnivores. In headwater
streams, detritus, or particulate organic matter, contributes substantially to the
total food consumed by individuals of all trophic groups (Schmid & Schmid-
Araya, 1997 , 2002).
The data were standardized to a common sample size of 1 m^2 , while data on
larger areas were obtained by amalgamating randomly aggregated samples
taken at different sites during the sampling period. To analyze relationships
between the habitats and their organisms, the organic and inorganic particles
from the interstitial streambed were collected simultaneously at each sample
site in each stream. Because invertebrates use particles both as habitat and food
BODY SIZE AND SCALE INVARIANCE 143