9780521861724htl 1..2

All streams are characterized by a class of multifractal distributions, as the

test criterion of linearity between the log-partition function and log area is

fulfilled, particularly for allq-moment<2 (Fig.8.9). The spectra of the general-

ized Re ́nyi dimensions forq-moments are a monotonically decreasing function

for allq-moments<2 in each stream community (Fig.8.10). Withq-moments

>2,Dqincreases slightly in all ecosystems (Fig.8.10) while the linearity criterion

log Partition function, log

μ^ q

(λ

)

0

20

40

60

80

–8

–4

SB

LL

1 10 100 1000

0

20

40

60

80

–8

–4

MY

Area, λ (m^2 )

0

20

40

60

80

100

–8

–4

1 10 100 1000

1 10 100 1000

Figure 8.9Log partition function, logq(l),

as a function of log area (l) forq-moments

in the range between10 and 10 at 0.5 lag

increments given for the streams Seebach

(SB), Llwch (LL) and Mynach (LL). For each

stream the upper panel gives the partition

function forq<0 and the lower panel for

q>0. Linear regressions are superimposed

for eachq-moment (allq<1 andq>2 with

r^2 >0.95;P<0.001).

Moment, q

–10 –5 0 5 10

Rényi’s generalised dimension,

Dq

0.0

0.2

0.4

0.6

0.8

1.0

SB

LL

MY

Figure 8.10Re ́nyi’s generalized dimensions

(Dq) versusq-moments for the SAR of all

benthic invertebrate species in three streams,

the Seebach (SB), Llwch (LL) and Mynach (MY).

Parameters are given in Table8.5.

BODY SIZE AND SCALE INVARIANCE 161