ZSM-neutral model: in contrast to niche-assembly theory, the unified theory of
biodiversity (UTB) predicts that species diversity and relative abundances can be
explained by neutral drift of abundances of different species (Hubbell, 2001 ).
Neutral or dispersal-assembly concepts neglect functional and ecological differ-
ences between individuals and species, implicitly assuming that they have
identical probabilities of birth, death, dispersal and speciation (Hubbell, 2001 ).
The compounded effects of dispersal limitation, speciation and the role of
chance through time would influence the way species form patterns of SAD
similar to those found in nature. The model assumes that SADs are dynamic and
reflect the spatial diversity-equilibrium among ongoing processes of speciation,
dispersal and extinction. The UTB predicts that SADs should generally follow the
zero-sum multinomial distribution (ZSM). This model has three main par-
ameters, the number of individuals in a community,JM, the fundamental bio-
diversity number,, and the dispersal probability,m. Hubbell’sis a linear
function of the area occupied by the assemblage and it controls the shape of
SADs. The ZSM was implemented using a log-likelihood approach to loop over
all possible values ofandmmaximizing the fit of ZSM to the data (Hubbell,
2001 ; McGill, 2003 ; Etienne, 2005 ). To obtain a reasonable estimate of the ZSM,
500 samples were generated for each set of parameters.
For each stream community 10^5 model communities were generated and the
mean model SAD compared to the observed SADs. To test departures of the
observed SADs from the model predictions, conventional goodness-of-fit statis-
tics, such as the Kolmogorov-Smirnov (KS) test and the coefficient of variation
were applied. In addition, another test was used, based on the probability of
deviations from the model using the sum of deviations of those species lying
outside the 95% confidence limit of the modelled community (PCL).
The observed SADs of biomass and density data followed closely both sequen-
tial resource apportionment models (SF and PF) as shown by KS statistics and the
coefficient of variation (Fig.8.3; Table8.2). However, the KS test and the coef-
ficient of variation are not reliable enough to differentiate minor departures
from the model predictions (Table8.2). In contrast, using the deviation prob-
ability (PCL), it can be shown that, among these two models, the observed SADs
fitted significantly to the predictions of the PF model with k0.0–0.16
(PCL<0.05: Table8.2; Fig.8.3), while the density distribution of the Afon
Mynach (MY) departed from any model prediction. More species departed
from the SF model, although it correlated well with the overall shape of the
distribution (r^2 values in Table8.2). These results would suggest that stream
communities are formed by resource apportionment processes where the prob-
ability of successive resource divisions tends to be slightly higher (k>0) for
species with higher abundances. In general, smaller species are more common
(see inset Fig.8.1) because they are more likely to subdivide food and habitat
space available for other species.
BODY SIZE AND SCALE INVARIANCE 149