If an ecosystem is to maintain a constant biomass, energy degradation
through respiration is balanced by the rate of energy supply by the system
(Peters, 1983 ). This also implies in principle that variations in species composi-
tion are associated with concomitant variations in the degree of resource parti-
tioning, which are usually constrained by the environment.Linking scaling relationships to niche and dispersal-mediated
species-abundance patterns
Because total biomass is invariant acrossspecies communitiesand, thus, trophic
groups, it is expected that species-abundance distributions (SADs) based on bio-
mass should reflect a similarity of resource partitioning irrespective of trophic
guild. The SAD describes the relative abundance in terms of biomass or density of
species ranked within an assemblage and usually displays many rare and a few
highly-abundant species. More than 25 different probability distributions have
been suggested as fitting SADs best, ranging from statistical, niche- to dispersal-
assembly SAD models (e.g. Tokeshi, 1993 ; Hubbell, 2001 ). To explore which
mechanisms may be responsible for observed biomass invariance in stream
communities, the SADs of all species in the invertebrate community were fitted
to niche- and dispersal-assembly models. Few niche-assembly models are based on
ecological assumptions that allow the modelling of community-wide SAD patterns.
Two of these models, the Sugihara Fraction (SF) and the Power Fraction (PF) model
were fitted to the observed SADs, both on biomass and density, using the species-
oriented approach (sensuTokeshi, 1993 ). For comparative purposes a dispersal-
assembly model, the zero-sum multinomial distribution (ZSM; Hubbell, 2001 )
was also fitted to the observed SADs. However, this model involves a different
approach, because it is fitted to the totalnumber of individuals in an assemblage.
SF model: Sugihara ( 1980 ) assumed a sequential niche apportionment process
governing species assemblages with niche division ratiosk(0.5k<1) centred
around 0.75:0.25 producing a triangular probability distribution. Here, the SF
was fitted to the species community data, allowing for normally distributed
division ratios with a mean ofk.
PF model: among random niche-apportionment models, the PF follows the
concept that the resource volume is multidimensional and is sequentially and
randomly divided. In the PF model, the probability (p) of selecting a subsequent
resource partition is proportional to the resource use (x) of species following a
power function asp¼ xk(Tokeshi, 1996 ), where1kþ1and is a
proportionality constant common to all species in the community. PF extends
over a range of other species-abundance curves including Tokeshi’s Random
Fraction (k¼0) and the MacArthur Fraction model (k¼1). Because SADs are
expected to shift from stages of incompletely filled resource space to even
distributions, it is appropriate to use PF to assess the potential convergence of
k-values among communities.148 P.E. SCHMID AND J. M. SCHMID-ARAYA