Does macrophyte fractal complexity drive invertebrate diversity,

biomass and body size distributions?

L. McAbendroth, P. M. Ramsay, A. Foggo, S. D. Rundle and D. T. Bilton

McAbendroth, L., Ramsay, P. M., Foggo, A., Rundle, S. D. and Bilton, D. T. 2005.Does macrophyte fractal complexity drive invertebrate diversity, biomass and body sizedistributions? �/ Oikos 111: 279�/290.

Habitat structure is one of the fundamental factors determining the distribution oforganisms at all spatial scales, and vegetation is of primary importance in shaping thestructural environment for invertebrates in many systems. In the majority of biotopes,invertebrates live within vegetation stands of mixed species composition, makingestimates of structural complexity difficult to obtain. Here we use fractal indices todescribe the structural complexity of mixed stands of aquatic macrophytes, and theseare employed to examine the effects of habitat complexity on the composition of free-living invertebrate assemblages that utilise the habitat in three dimensions.Macrophytes and associated invertebrates were sampled from shallow ponds insouthwest England, and rapid digital image analysis was used to quantify the fractalcomplexity of all plant species recorded, allowing the complexity of vegetation standsto be reconstructed based on their species composition. Fractal indices were found tobe significantly related to both invertebrate biomass�/body size scaling and overallinvertebrate biomass; more complex stands of macrophytes contained a greater numberof small animals. Habitat complexity was unrelated to invertebrate taxon richness andmacrophyte surface area and species richness were not correlated with any of theinvertebrate community parameters. The biomass�/body size scaling relationship oflentic macroinvertebrates matched those predicted by models incorporating bothallometric scaling of resource use and the fractal dimension of a habitat, suggestingthat both habitat fractal complexity and allometry may control density�/body sizescaling in lentic macroinvertebrate communities.

L. McAbendroth, P. M. Ramsay, A. Foggo, S. D. Rundle and D. T. Bilton, School ofBiological Sciences, Univ. of Plymouth, Drake Circus, Plymouth, UK, PL4 8AA([email protected]).

Habitat structural complexity is of broad ecological

significance because it limits the distribution of species

across all scales (Holling 1992). At local scales, complex

habitats are normally richer in species (Downes et al.

1998), which can be explained by the increased avail-

ability of microhabitats (Mcnett and Rypstra 2000),

modification of biotic interactions (Finke and Denno

2003) and changes in resource partitioning and niche

breadth (May 1972, McCoy and Bell 1991). Habitat

complexity might also alter assemblage structure by

affecting the frequency of body sizes, because animals of

different sizes utilise habitat space differently (Raffaelli

et al. 2000, Schmid et al. 2002). However, the importance

of habitat structure has not always been recognised

because of taxonomic biases within studies and problems

quantifying the structural complexity of habitats

(McCoy and Bell 1991). Furthermore, it is difficult to

distinguish between the effects of habitat complexity and

habitat area - they often co-vary in the field (Johnson

et al. 2003). Resolving these difficulties would allow

Accepted 22 April 2005

Copyright # OIKOS 2005ISSN 0030-1299

OIKOS 111: 279�/290, 2005

OIKOS 111:2 (2005) 279

cross-system and cross-scale comparisons of the effects

of habitat structural complexity on assemblage composi-

tion and structure (McCoy and Bell 1991).

A range of measures of vegetation structure have been

used to investigate relationships between vegetation

architecture and invertebrate assemblages, including

shoot density (Kurashov et al. 1996, Hovel 2003),

biomass (Attrill et al. 2000, Wyda et al. 2002) and

surface area (Mathooko and Otieno 2002). However,

these measures examine the amount of available habitat

rather than complexity per se. Other studies have

compared invertebrate assemblages amongst plants

with different gross morphologies (Cyr and Downing

1988, Feldman 2001, Cheruvelil et al. 2002) or developed

complexity indices based on the number and arrange-

ment of stems and leaves (Lillie and Budd 1992).

Although plants occupy particular volumes in space, it

is not easy to estimate the actual volumes occupied or

the surface areas provided, because measurement is

often difficult and the results vary depending on the

scale at which measurements are made (Bradbury et al.

1984, Morse et al. 1985). For this reason, habitat fractal

dimensions have been used as indices of structural

complexity (Jeffries 1993, Gee and Warwick 1994a,

1994b, Attrill et al. 2000, Schmid et al. 2002). Though

plants are not ideal fractals, some of their properties are

sufficiently similar across a range of scales that the tools

of fractal geometry can be used (Hastings and Sugihara

1993). Ideal fractal objects are self-similar at all scales

(Mandlebrot 1983, Sugihara and May 1990, Simon and

Simon 1995). Fractal dimensions of imperfect fractal

objects can be estimated from the perceived rate of

increase in a structure’s perimeter (or area) as the scale

of measurement is decreased */ Sugihara and May

(1990) and Schmid (2000) have reviewed common

techniques used to measure the fractal structure of

habitats.

The interaction of body size with a fractal environ-

ment may have major consequences for community

structure (Halley et al. 2004). The scale at which

organisms perceive and use their environment differs

according to body size (Levin 1992, Gee and Warwick

1994a, 1994b) and habitat structure might therefore

shape the distribution patterns of species in different

ways at different spatial scales. For instance, small

animals may live on, or in, parts of a plant’s structure

that are not utilised by larger animals (Lawton 1986)

and, as a consequence, there is likely to be more

perceived space on vegetation for small animals than

large, and plants with more complex structure would be

expected to support more small animals than simple

plants. Habitats of greater complexity might thus be

expected to have both increased richness and smaller

modal body size, when compared to habitats which are

structurally simple (Morse et al. 1985, Raffaelli et al.

2000, Schmid et al. 2002).

Habitat structure is, however, unlikely to be the only

factor shaping the form of animal body size distributions

within habitats. Small-bodied animals utilise less energy

per individual than large bodied ones, with metabolic

rate increasing by body size0.75 (Schmidt-Nielsen 1984,

Brown and West 2000). The relationship between

population density and body size generally scales with

an exponent of �/0.75 (Damuth 1981). Morse et al.

(1985) incorporated both this allometric scaling of

resource use and the fractal dimension of habitat into

a model that predicts the expected increase in density of

organisms as body size decreases. The validity of this

model has not been widely tested to date, particularly in

aquatic systems.

Investigations that have attempted to quantify the

structural complexity of plant species and relate it to

invertebrate assemblage composition and body-size dis-

tribution have so far been concerned with single plant

taxa, and limited mainly to terrestrial (Morse et al. 1985,

Lawton 1986, Shorrocks et al. 1991) and marine

environments (Gee and Warwick 1994a, 1994b, Daven-

port et al. 1999). It is clear that vegetation structure and

composition also influence the distribution and abun-

dance of macroinvertebrate species in freshwaters

(Dvorak and Best 1982, Scheffer et al. 1984), where

mixed-species macrophyte stands provide invertebrates

with food (Lodge et al. 1998, Jones et al. 1999), shelter

(Maurer and Brusven 1983, Heck and Crowder 1991),

oviposition sites (Welch 1935, Lawton 1986) and mod-

ified physicochemical conditions (Jeffries 1993).

A selection of studies has compared the invertebrate

assemblages associated with aquatic macrophytes of

different gross morphologies. Some found invertebrate

abundance to be highest on species with dissected leaves

(Krecker 1939, Dvorak and Best 1982, Cheruvelil et al.

2002), whereas others found no relationship between the

invertebrate assemblages living on plants with different

levels of leaf dissection (Rooke 1984, Cyr and Downing

1988). To date, only Jeffries (1993) has examined the

relationship between fractal habitat complexity and

invertebrate assemblage composition and density in

aquatic systems, and this study was restricted to the

epifauna associated with artificial pondweeds of differ-

ing fractal complexity.

Our study quantifies plant diversity, density and

fractal complexity in mixed stands of pond vegetation

in order to examine the influence of habitat structure on

the species richness, density and the biomass�/body size

distribution of freshwater macroinvertebrates living both

on and amongst the plants. We also compare biomass�/

body size relationships revealed in our data with those

predicted by an energy equivalence model (Damuth

1981) and the model of Morse et al. (1985) which

combines allometric scaling of resource use and the

fractal dimension of the habitat.

280 OIKOS 111:2 (2005)

Methods

Field sampling

In June 2001, fifteen samples of macroinvertebrates

and macrophytes were taken from each of two large,

semi-permanent ponds on the Lizard Peninsula in

Cornwall with similar macrophyte assemblage composi-

tion: Kynance Farm Pond (SW 682142) and Croft

Pascoe Pool (SW 731197). Bilton et al. (2001) and

Rundle et al. (2002) describe the sites in detail. These

ponds were chosen since they contained broadly similar

macroinvertebrate communities which did not differ

significantly in previous surveys (McAbendroth 2004).

Samples were taken at a fixed water depth of 15 cm

using a plastic core of 30 cm diameter (cross-sectional

area 0.07 m2, volume 10.6 l) with a 1 mm mesh bag

attached. Sampling effort was spread amongst a wide

range of vegetation densities and plant species composi-

tions. Each core was pushed rapidly down through the

water column into the substrate, to prevent the escape of

actively swimming macroinvertebrates. The plug of

substrate was then dug out and inverted to empty all

invertebrates into the mesh bag. The mud core was

carefully discarded to avoid sampling invertebrates not

associated with macrophytes. The sample was then

transferred to a white plastic tray and all macrophytes

were rinsed off, removed and sorted by species. Macro-

invertebrates were preserved in 70% alcohol for subse-

quent sorting, identification and enumeration. One

sample was later found to be damaged and excluded

from the analysis, resulting in a total of 29 samples.

Additional intact plants (four to ten specimens) of

each of the fifteen macrophyte species found in the

samples were also collected from the two ponds in order

to measure the fractal complexity of each species.

Quantification of macrophyte structural complexity

The additional intact macrophyte samples were floated

out in shallow trays to separate the branches and divided

leaves and then pressed carefully and dried for 48 h at

60oC.

We chose to calculate fractal dimensions at two

different scales - for the plant as a whole and for the

detailed structure (e.g. of leaves) - because these repre-

sent different, but biologically meaningful scales to

organisms that might live on or amongst the plants.

Given that the plants are not truly fractal, there is no

reason to expect a constant fractal dimension across all

scales. Nevertheless, at particular scales, the fractal

dimension does provide a measure of complexity.

In order to calculate the fractal dimensions (D) of the

plants, each replicate plant was photographed at two

different magnifications (‘‘low’’ and ‘‘high’’) with a

Nikon Coolpix 995 digital camera (Fig. 1). Each

resulting TIFF image was transferred to greyscale

and thresholded to produce a binary, black-and white

image, with pixel widths of 0.03 mm and 0.28 mm for

high magnification and low magnification, respectively.

ImageJ software (Rasband 1997�/2005) was then used to

analyse fractal structure of each image at the two

magnifications. ImageJ uses a box count algorithm

which is analogous to the general grid method of

Sugihara and May (1990) and can quantify the fractal

dimension of both perimeter and area. A series of grid

sizes ranging from 2 to 64 pixel widths (0.06�/1.92 mm

for high magnification and 0.56�/17.92 mm for low

magnification) were used to estimate both perimeter

and area of each photograph at each magnification.

Log10 plots of the perimeter and area estimates against

measurement scale (grid size) were then constructed

within ImageJ for each photograph, the gradients of

which provided alternative estimates of the fractal

dimension of the plant. Thus, for each of the fifteen

macrophyte species (based on replicate plants), four

estimates of D were derived, depending on the scale of

magnification of the photograph, and whether the area

or perimeter method was used.

For example, at low magnification, Potamogeton

polygonifolius, a species with large broad leaves, and

Apium inundatum , which has finely divided leaves,

would have similar fractal dimensions based on area

(DA), because branches finer than 0.56 mm wide

were not adequately resolved (Fig. 1a, 1b). At higher

Fig. 1. Thresholded macrophyte photographs. (a) Potamagetonpolygonifolius at low magnification, DA�/1.54, DP�/1.30, (b)Apium inundatum at low magnification, DA�/1.52, DP�/1.50,(c) Potamageton at high magnification, DA�/1.95, DP�/1.10and (d) Apium at high magnification, DA�/1.54, DP�/1.29.

OIKOS 111:2 (2005) 281

magnification, DA provides a clear contrast between

these two species. Fractal dimensions calculated on the

basis of perimeter (DP) indicate the degree of dissection

of the plant or plant parts. Differences in DP between

P. polygonifolius and A. inundatum are clear at both low

and high magnification.

Therefore, both DA (a ‘‘bulk’’ fractal, of area occu-

pancy, Halley et al. 2004) and DP (a ‘‘boundary

complexity’’ fractal) provide subtly different information

about the nature of complexity associated with each

plant. DA indicates how the perception of surface area

might change with scale, while DP relates to the nature of

the gaps between the plant parts - both potentially

meaningful for macroinvertebrates living on or amongst

the vegetation. In addition, contrasting the estimates of

D produced at the two scales of magnification (by taking

the arithmetic difference between them) adds further

information about the degree of self-similarity in each

macrophyte. For (hypothetical) ideal - fractal plants, this

arithmetic difference would be zero - showing the same

fractal dimension at both scales. Deviation from zero

demonstrates that a plant is not self-similar, and may

appear more or less complex at one scale compared to

another.

The mean fractal measures for each plant species were

then used to calculate complexity indices for entire

stands of macrophytes in the samples, weighting the

calculations according to the proportion of total macro-

phyte biomass contributed by each plant species within a

stand. To do this, the macrophytes from the core samples

were individually dried for 48 h at 60oC before weighing.

The total dry weight of each macrophyte species in each

sample was then calculated. Four fractal complexity

indices were calculated for each sample, based on DA

and DP at the two scales of magnification.

For comparison with our fractal approach, we also

recorded plant species richness and calculated total

macrophyte surface area for each sample, using a

traditional Euclidean approach. Each of the replicate

plants was weighed and surface area was measured from

the low power digital photographs at the finest resolu-

tion using ImageJ. The relationship between biomass

and surface area for each macrophyte species was then

examined using ordinary least squares (OLS) regression

and the linear equations used to estimate total macro-

phyte surface area in each sample stand.

Macroinvertebrate assemblages

Macroinvertebrates were sorted, enumerated and identi-

fied to species where possible. Chironomids, some

coleopteran larvae and early instar anisopteran larvae

were identified to genus, whilst other dipteran larvae and

pupae, juvenile corixids, ostracods, cladocerans and

Acari were identified to these major taxa.

Biomass�/body size distributions were also produced

for each sample. These are often presented in a normal-

ised form in aquatic systems (Ramsay et al. 1997). The

technique, developed by Sheldon et al. (1972), plots log2

biomass against log2 body size classes, transforming the

relationship into a negative log-linear form. Such

normalised biomass�/body size distributions simplify

between-sample comparisons of biomass�/body size

relationships (Sprules and Munawar 1986): different

slopes indicate different scaling relationships with body

size, and different intercepts but similar slopes suggest

different levels of overall biomass. The approach can be

useful for examining general patterns in ecological

assemblages. Biomass�/body size distributions are

usually derived by measuring the body length (or width)

of individual organisms and converting these measures

to biomass by means of power equations.

Body length (distance along the dorsal surface of the

organism from the anterior of the head capsule to the tip

of the abdomen, excluding antennae, anal prolegs and

cerci) was measured for each individual organism using a

binocular microscope with an eyepiece graticule. The

only exception to this was the chironomids: they were

highly abundant and length was difficult to measure

because they tended to curl up. Instead, a length�/width

relationship was constructed for chironomids using

digital photographs and Analysis image analysis soft-

ware. Chironomid width was then measured for a sub

sample (25%) of the individuals in each sample.

The biomass of the organisms in the samples was

estimated from family-level length�/mass power function

relationships compiled from the literature. Equations

were taken from Benke et al. (1999) with the exception of

those for dipteran pupae, coleopteran larvae, and

microcrustaceans which were taken respectively from

Burgherr and Meyer (1997), Meyer (1989), and Manca

and Comoli (2000). Where a family level equation was

unavailable the order level equation was used, or, in the

case of the Coleoptera, the most appropriate alternative

family relationship, based on assessment of overall body

shape. Animals that were less than 1 mm long (the size

of the mesh used for sampling) were excluded.

Normalised biomass�/body size distributions were

then constructed for each sample, by plotting log2

biomass against log2 body size classes. Gradient and

intercept values were recorded from OLS regression, for

correlation with macrophyte fractal complexity indices,

surface area and species richness parameters.

Null model testing

An overall normalised biomass�/body size distribution

for the samples was constructed by taking the median

score of biomass for each size class from the replicate

samples.

282 OIKOS 111:2 (2005)

For comparison with this, two null models were

generated. Firstly, the ‘energy equivalence’ null model

(Damuth 1981) assumes that animals within each body

size category utilise the same amount of energy. For this

model, the expected biomass for each body size category

was calculated, assuming the number of organisms

in each size category scales as body mass�0.75, and

constraining the total number of macroinvertebrates to

the number observed in the samples. Therefore, the

resulting normalised biomass�/body size distribution (for

the mean number of organisms observed in the original

samples) had a gradient of �/0.75.

The null model described above does not take into

account the fractal dimension of habitat. Morse et al.

(1985) combined allometric scaling of resource use and

the fractal dimension of habitat into a single model that

predicts the relationship between the expected number of

organisms and body size. Owing to the difficulties in

determining the fractal dimensions of a surface, they

calculated heuristic upper and lower bounds to their

model, which form an envelope enclosing the relation-

ship. The expected total biomass for each body size class

(Mu and ML for the upper and lower bounds, respec-

tively) was calculated as follows:

Mu�B̄�(ffiffiffiffiB̄

3p

)�0:75�((ffiffiffiffiB̄

3p

)(1�D))2�N

ML�B̄�(ffiffiffiffiB̄

3p

)�0:75�((ffiffiffiffiB̄

3p

)(2�D))2�N

where B̄ is the median biomass for that size category

(derived from our samples), D is the overall mean fractal

dimension calculated for our sample stands, and N is the

total number of organisms found in that body size class.

Note that the ‘‘length’’ component of these calculations

was derived as the cubed-root of biomass, standardizing

for organisms of very different body shapes. The slope of

the lines representing the upper and lower bounds of this

model in the normalised biomass�/body size distribution

deviate from the �/0.75 slope of the ‘energy equivalence’

null model, according to the fractal complexity of the

macrophyte stands.

Data analysis

Initial correlations between macrophyte structural com-

plexity parameters showed that DA at high magnification

and DP at low magnification both covaried with macro-

phyte surface area. This was not surprising, given that

Euclidean area was measured at a resolution that picked

up fine-scale area�/occupancy (similar to DA at high

magnification) and many of the plants have a simple, yet

repeated, structure at the scale of the whole plant

(largely responsible for the DP scores at low magnifica-

tion). These two fractal complexity indices were there-

fore excluded from further analyses because they did not

add further information to the simpler measure of

surface area itself.

There was no significant difference between the two

ponds used to collect the samples for any of the

remaining macrophyte habitat parameters (t test, p�/

0.05). Therefore, the samples from both ponds were

pooled for subsequent analyses. Six of the 29 samples did

not produce a significant relationship between normal-

ised biomass and body size (p�/0.05), but nevertheless,

all 29 samples were included in the analyses.

All parameters were checked for normality (Anderson-

Darling test, p�/0.05) and inequality of variance before

product-moment correlations were performed between

three macroinvertebrate assemblage parameters (species

richness, biomass�/body size gradient and biomass

body size intercept) and the four macrophyte variables

(species richness, total surface area, DA for low magni-

fication and DP for high magnification). Where correla-

tions between macroinvertebrate assemblage parameters

and macrophyte structure were significant, reduced

major axis (model II) regression was used to examine

further the relationships, as both response and explana-

tory variables were subject to measurement error (Sokal

and Rohlf 1995). RMA software for reduced major

axis regression v1.14b (Bohonak 2002) was used with

10,000 bootstraps for each calculation. Analysis of

covariance was carried out with Statistica 6.

Results

Macrophyte physical complexity

There was considerable variation in the fractal measures

between macrophyte species (Table 1). At low magnifica-

tion, DA varied from 1.27 to 1.58 (mean for all species

1.43) and DP from 1.14 to 1.51 (mean 1.27). At high

magnification, DA varied from 1.50 to 1.90 (mean for all

species 1.69) and DP from 1.08 to 1.52 (mean 1.22).

Thus, for images of the whole plant and for plant parts,

area�/occupancy (DA) tended to be more complex than

the perimeter (DP).

Comparing DA and DP values at high and low

magnifications, five categories of plant were identified

(Fig. 2). Only Myriophyllum alterniflorum had similar

fractal dimensions when viewing the entire plant and

isolated plant parts, suggesting that its structure is

largely fractal across all the scales included in this

analysis. The other plants generated different fractal

dimensions at the two magnifications, indicating that

they are not true fractal objects. The manner in which

the fractal dimensions vary at the two magnifications,

and between DA and DP, discriminates between subtly

different structural architectures. The x-axis in Fig. 2

represents the contrast in area�/occupancy between

isolated plant parts and the entire plant, and this may

be relevant to organisms that inhabit the spaces between

OIKOS 111:2 (2005) 283

plants and their parts. The y-axis contrasts the complex-

ity of edge of the parts and the entire plant, and may be

more relevant to organisms that live on the plant parts.

This demonstrates that DP and DA represent different

aspects of the architectural complexity of the macro-

phytes.

From this analysis, then, there are five broad cate-

gories of macrophytes, based on fractal dimension

scores. Myriophyllum alterniflorum is structurally self-

similar across the scales employed in this study. Apium

inundatum is more or less self-similar in the way that it

occupies space, but the plant’s outline is more complex at

the whole plant magnification than at the scale of just

part of the plant (Fig. 2). Chara fragifera is also more or

less self-similar in the way that it occupies space, but the

outline of plant parts is more complex than that of the

entire plant. Both area�/occupancy and the perimeters

of the sampled bryophytes were more complex when

looking at plant parts compared with the whole plants.

Finally, the group of species grouped together in Fig. 2

(Eleogiton fluitans, Juncus bulbosus, Galium palustris,

Ranunculus flammula , Carex spp, Potamogeton polygo-

nifolius, Glyceria fluitans, Eleocharis palustris, Juncus

articulatus, Littorella uniflora and Hydrocotyle vulgaris )

generally had more complex outlines at the whole plant

magnification, but area�/occupancy was more complex

at the plant-part magnification. Within this large group,

however, there is some variance in form, particularly

in regard to DP, shown by the contrast between the

simple, but repeated, architectures of plants like Glyceria

and Carex , and the simply-branched but finely-leaved

Galium .

Relationship between macrophyte structure

parameters and macroinvertebrates

Macrophyte species richness and the total Euclidean

surface area of macrophytes were unrelated to biomass�/

body size scaling, total biomass, or macroinvertebrate

taxon richness (Table 2).

A negative relationship was found between macro-

phyte stand complexity (estimated by DP at the higher

magnification and DA at the lower magnification) and

the slope of the biomass�/body size scaling relationship

(Fig. 3). In other words, a greater number of small-

bodied macroinvertebrates were present in more complex

macrophyte stands, with more proportional biomass

Table 1. Mean fractal dimension (9/SE) based on area (DA) and perimeter (DP) methods for each macrophyte species at high andlow magnification. n�/5, except: *, n�/4; $, n�/8; %, n�/10.

Macrophyte species DA DP

Low mag High mag Low mag High mag

Myriophyllum alterniflorum 1.589/0.027* 1.569/0.034 1.519/0.053* 1.529/0.027Glyceria fluitans 1.419/0.017 1.839/0.006 1.239/0.012 1.089/0.054Carex spp. 1.399/0.029 1.729/0.043 1.279/0.005 1.139/0.017Eleocharis spp. 1.369/0.013 1.799/0.019 1.229/0.026 1.099/0.005Juncus articulatus 1.309/0.018 1.719/0.029 1.249/0.010 1.169/0.014Juncus bulbosus 1.289/0.051 1.509/0.015 1.269/0.042 1.259/0.024Chara spp. 1.489/0.026 1.529/0.036 1.149/0.033 1.429/0.017Littorella uniflora 1.449/0.035 1.819/0.024 1.209/0.022 1.149/0.006Potamogeton polygonifolius 1.549/0.024 1.899/0.023$ 1.279/0.009 1.129/0.014$

Apium inundatum 1.509/0.038 1.549/0.013% 1.469/0.050 1.349/0.037%

Eleogiton fluitans 1.389/0.036 1.519/0.021 1.389/0.039 1.339/0.033Hydrocotyle vulgaris 1.329/0.036 1.909/0.024 1.189/0.010 1.109/0.006Bryophyte spp. 1.499/0.026 1.679/0.011 1.259/0.018 1.349/0.009Galium palustris 1.279/0.026 1.689/0.022 1.189/0.017 1.199/0.005Ranunculus flammula 1.469/0.012 1.759/0.033 1.279/0.001 1.159/0.018

-0.25

-0.30

-0.20

-0.15

-0.10

-0.05

0

0.05

0.10

0.15

-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.1

DA low – DA high

Myrio

Apium

0.20

Chara

Bryo

Ranu

CarexPotaGlyc

Eleoch

Hydro Juncarti Litt Junc

bulb

Eleog

Galium

DP low – DP high

Fig. 2. Deviations from ideal fractal scaling for 15 macrophytespecies. Each axis shows the arithmetic difference betweenfractal dimensions (D) derived from low and high magnificationimages (x-axis based on perimeter, ‘‘DP low �/ DP high’’; y-axisbased on area, ‘‘DA low �/ DA high’’). A value of zero wouldindicate that the same value of D was derived from bothmagnifications. Macrophyte species: Apium, Apium inundatum ;Bryo, Bryophyte spp.; Carex, Carex spp.; Chara, Chara spp;Eleoch, Eleocharis spp; Eleog, Eleogiton fluitans ; Galium,Galium palustris ; Glyc, Glyceria fluitans ; Hydro, Hydrocotylevulgaris ; Junc arti, Juncus articulatus ; Junc bulb, Juncusbulbosus ; Litt, Littorella uniflora ; Myrio, Myriophyllum alterni-florum ; Pota, Potamogeton polygonifolius ; Ranu, Ranunculusflammula .

284 OIKOS 111:2 (2005)

associated with these smaller organisms. Area�/occu-

pancy (DA at low magnification; reduced major axis

regression, R2�/0.206) explained more variation in the

biomass-body size gradient than boundary complexity

(DP at high magnification; R2�/0.111).

More complex macrophyte stands also supported

greater overall macroinvertebrate biomass (Table 2,

Fig. 3: R2�/0.179 and 0.151 for DA at low magnification

and DP at high magnification, respectively). Removing

data points with high leverage values and standardised

residuals did not alter the significance of any of the

correlations or make a significant difference to the R2

values.

There was no relationship between macrophyte struc-

tural complexity indices and macroinvertebrate species

richness (Table 2).

Null model testing

From our pond data, the overall biomass-body size

spectrum had a gradient of �/0.85 (R2�/0.963, pB/

0.001), and an intercept of 8.58 (Fig. 4a). Although the

gradient of this line is steeper than that expected from

the ‘energy equivalence’ null model, it is not significantly

different from the predicted slope of �/0.75 (ANCOVA,

F-ratio�/0.175, p�/0.680).

Mean DP at the higher magnification across all

samples was 1.240, and mean DA at the lower magnifica-

tion was 1.423. Based on these estimates of fractal

dimension, null models taking into account the fractal

dimension of the macrophyte stands estimated the

normalised biomass�/body size gradient at between

�/0.64 and �/1.39 (Fig. 4b, 4c). The fitted regression

lines for the sample data fall within the envelopes

Table 2. Correlations between macroinvertebrate body size scaling, overall biomass and macroinvertebrate taxon richness withmacrophyte fractal complexity, surface area and species richness for each sample. Body size scaling was estimated by the gradient ofthe normalized biomass�/body size relationship for the sample, and overall biomass from the intercept.

Macroinvertebrateassemblages

Macrophyte structure

Complexity Diversity Density

DA at low magnification DP at high magnification Number of species Total surface area

Body size scaling R�/�/0.466 R�/�/0.367 R�/0.267 R�/�/0.026pB/0.05 pB/0.05 ns ns

Overall biomass R�/0.449 R�/0.412 R�/0.076 R�/0.292pB/0.05 pB/0.05 ns ns

Taxon richness R�/0.259 R�/0.202 R�/0.330 R�/0.354ns ns ns ns

Fig. 3. Reduced major axisregression relationshipsbetween habitat complexity,in terms of fractal dimensionsDA at low magnification andDP at high magnification, andthe slopes and intercepts ofthe normalized totalbiomass�/body sizedistributions for each of the29 samples. DPDA

DA v slope

DA at low magnification1.30 1.35 1.40 1.45 1.50 1.55 1.60

Slo

pe

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2 PD v slope

DP at low magnification1.0 1.1 1.2 1.3 1.4 1.5 1.6

Slo

pe

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

DP v intercept

at low magnification1.0 1.1 1.2 1.3 1.4 1.5 1.6

Inte

rcep

t

1

2

3

4

5

6DA v intercept

at low magnification1.30 1.35 1.40 1.45 1.50 1.55 1.60

Inte

rcep

t

1

2

3

4

5

6

OIKOS 111:2 (2005) 285

defined by the bounds of these models. Although the

slope from the sample data does not differ significantly

from the lower bound estimates of the models, it is

significantly different from the upper bound estimates

(ANCOVA, F-ratio�/5.305, pB/0.001, followed by a

Newman�/Keuls test).

Discussion

Although the macrophytes in our ponds were not true

fractal objects, estimating architectural ‘‘complexity’’

using the tools of fractal geometry proved to be a useful

approach. The use of digital image analysis greatly

simplified the analysis of fractal complexity and this

technique could prove useful for quantifying and separ-

ating the effects of habitat structural complexity from

habitat density and species richness in any system where

mixed vegetation stands are the norm. The quantitative

indices of complexity derived from our estimates of

fractal dimension (D) were consistent with intuitive

expectations of overall complexity, and managed to

discriminate clearly between the different forms this

complexity may take.

Fractal models of habitat complexity assume objects

are identical across the full scale range. Alternative,

hierarchical approaches assume ecological processes

operate independently at different scales (Halley et al.

2004). Our approach was a hybrid of the two methods,

employing a wide range of grid sizes (0.06�/18 mm), and

therefore making fewer assumptions about the scale of

perception of invertebrates or the ‘grain’ at which they

utilise space. Such an approach also acknowledges the

fact that a single value of D may not necessarily be

meaningful across the entire range of scales, by estimat-

ing D from images of whole plants and plant parts

separately.

However, with non-fractal objects, fractality can

sometimes appear as an artefact of sampling. An

indicator of this is when very different fractal dimensions

occur at larger and smaller scales (Hamburger et al.

1996). Macrophytes are not genuinely fractal objects

and, in this sense, D is merely an estimate of ‘‘complex-

ity’’ for a given scale range �/ in our case, two values of D

taken from the two magnifications that represent differ-

ent, biologically-meaningful scales. Most of the macro-

phytes in this study had contrasting fractal dimensions at

these two magnifications, though each was calculated

across a range of scales. This is consistent with other

studies: Morse et al. (1985), Lawton (1986) and Gee and

Warwick (1994b) all found a change in plant fractal

dimension between two levels of magnification, indicat-

ing that most plants are not self similar across the scales

of observation but exhibit non-uniform fractal structure.

Bradbury et al. (1984) also found this to be true at larger

scales for a coral reef, where D changed across scales of

centimetres, metres and hundreds of metres.

This demonstrates clearly that the fractal approach is

often a pragmatic rather than strict theoretical one.

When attempting to determine whether macrophytes are

more or less fractal in a strict sense, one should ideally

estimate D across at least two order of magnitude of

measurement (Halley et al. 2004). This presents signifi-

cant difficulties for the estimation of D using volumes,

because the level of resolution required would be finer

than currently practical in many cases, and may not be

particularly meaningful biologically. Given that aquatic

macrophytes are not true fractal objects, macroinverte-

brates of different body sizes might be expected to

perceive the same macrophyte stand as having different

gol2

)gm( ssa

moib latot

-4

-2

0

2

4

6

8

10

12

14

gol2

)gm( ssa

moib latot

0

2

4

6

8

10

12(a)

log2 individual biomass class (mg)

-4 -2 0 2 4 6 8 10

gol2

)gm( ssa

moib latot

-4

-2

0

2

4

6

8

10

12

14(c)

(b)

y = -0.850x + 8.580

y = -0.750x + 8.439

upper boundy = -1.386x + 8.489

lower boundy = -0.744x + 8.574

lower boundy = -0.638x + 8.596

upper boundy = -1.276x + 8.501

Fig. 4. Comparison of the normalised total biomass�/body sizedistribution for pond invertebrate samples with predicteddistributions. (a) Comparison of pond data (filled circles andsolid RMA regression line) with the prediction of the energeticequivalence model (dotted line). (b) Comparison of pond data(filled circles) with predicted envelope of Morse et al.’s (1985)allometric scaling and habitat complexity model using DA athigh magnification as the measure of fractal dimension (smallcrosses and solid RMA regression lines). (c) As (b), but usingDP at low magnification as the measure of fractal dimension.

286 OIKOS 111:2 (2005)

levels of structural complexity. In such cases, a single

fractal measure would fail to resolve ecologically rele-

vant features of plant architecture, making an approach

such as ours, which examines different scales separately,

more useful. Halley et al. (2004) note that even though

ecological phenomena are not truly fractal, models that

assume fractality can get closer to the messy, multi-scale

nature of these natural phenomena than other simple

models.

Defining D in terms of boundary fractals (DP, an

estimate of edge complexity) and bulk fractals (DA, an

estimate of area occupancy) accounted for different,

complementary aspects of the complexity of the macro-

phytes, and employing both measures added useful

detail to the description of macrophyte architecture. If

DP alone had been calculated for the whole plant

(minimum resolved distance 0.56 mm), as in previous

studies of plant structure (Gee and Warwick 1994b,

Davenport et al. 1999), significant relationships between

macrophyte complexity and macroinvertebrate biomass

patterns would not have been detected. Furthermore,

stand DP calculated from the low magnification images

co-varied with both macrophyte surface area and species

richness in our study, so if we had relied on this

commonly used measurement of fractal structure the

individual effects of all three measures of habitat

structure on macroinvertebrate assemblages would have

remained confounded. There have been similar problems

in earlier studies: Hills et al. (1999), for instance, found

barnacle settlement density to be related to both

Euclidean and fractal substrate complexity measures

which co-varied.

The fractal complexity of macrophytes varied con-

siderably from species to species, though all species

tended to have greater complexity when estimated by

DA rather than DP �/ the plants were more complex in

the way their areas were divided up in space, when

compared with the nature of their edges. The variation

between species demonstrates that the composition of a

macrophyte stand can make an important difference to

the architectural complexity of that stand. Those

stands with higher proportions of complex plants

were necessarily rated as more complex in our method.

In this study, we were not able to measure the

additional contribution to stand complexity made by

the spatial interactions between plants with different

fractal scores.

Macrophyte surface area and species richness, mea-

sures of habitat structure that have received the most

attention in freshwater studies, were not significantly

related to macroinvertebrate richness, biomass scaling or

overall biomass. Other studies of the effects of these two

parameters have given mixed results (Dvorak and Best

1982, Rooke 1984, 1986, Scheffer et al. 1984, Brown

et al. 1988, Cyr and Downing 1988, Cattaneo et al. 1998,

Cheruvelil et al. 2002). Attrill et al. (2000) found

that seagrass surface area positively affected species

richness and density of macroinvertebrates, whereas an

index of complexity incorporating fractal dimension

had no significant effect. However, this study contrasts

with our own in that most macroinvertebrates were

epifaunal, whereas our pond macroinvertebrate assem-

blages were dominated by actively swimming Coleoptera

and Hemiptera, and contained relatively few epifaunal

species.

The structural complexity of mixed macrophyte

stands-estimated by D-in the ponds was related to

overall biomass and biomass�/body size scaling of

macroinvertebrates. This confirms the potential useful-

ness of D as a complexity measure, when compared with

more usual measures like Euclidean surface area. It is

worth noting that our estimates of D were relatively

simple, and do not take account of the three-dimensional

nature of the macrophyte stands. Nonetheless, the

relationship between D and macroinvertebrate biomass

patterns was still evident.

Gaston and Blackburn (2000) stated that if the

environment is fractal and there is a functional response

to the space available, the smallest body size class should

be the mode. This was true for the majority of samples in

our study (23 out of 29) as they had significant negative

normalised biomass�/body size gradients. Complexity

(estimated by DA and DP) showed a significant negative

relationship with the gradients of the biomass�/body size

distributions, suggesting that two-dimensional macro-

phyte complexity has a significant effect on the body size

distribution of aquatic invertebrates living in three-

dimensional space.

In a simple sense, DA can be seen as a measure of the

way the macrophyte stands are divided up, describing

the gap structure within stands: samples with higher

values being more highly divided and having a smaller

mean gap size in the vegetation (Bartholomew et al.

2000). Since most of the pond macroinvertebrates in our

samples utilise the inter-vegetation gaps, it is not

surprising that this version of D had a tighter relation-

ship with macroinvertebrate biomass patterns. Smaller-

bodied organisms would be favoured where gaps within

the vegetation are smaller and more complex, whereas

larger-bodied invertebrates (e.g. large Dytiscidae) would

find it more difficult to move around �/ though

differences in the rigidity of macrophyte species have

not been taken into account, so larger individuals may

still be able to move through complex habitat by pushing

aside finer stems and leaves. Although DA explained

more of the variability in biomass�/body size distribution

gradients than DP, higher values of DP were also

associated with greater proportions of small-bodied

organisms. In essence, DP indicates the degree of

convolution of macrophyte edge; high values indicate

further division of space at smaller scales.

OIKOS 111:2 (2005) 287

Studies in other systems have found similar relation-

ships between habitat fractal complexity and the body

size distributions of invertebrates. Williamson and Law-

ton (1991) compared the distribution of arthropod body

sizes with the complexity of birch trees. Their data

indicate a linear trend between body size gradient

and complexity, but no test statistics were reported.

Schmid et al. (2002) found that fractal scaling of stream

sediment particles was related to macroinvertebrate

biomass scaling: more complex habitat had a greater

number of small species. Schmid (2000) and Schmid

et al. (2002) showed that habitat fractal dimension has a

positive effect on the density and number of macro-

invertebrate species, and Jeffries (1993) found similar

effects with an increase in the fractal dimension of

artificial pondweeds.

More complex stands had greater overall invertebrate

biomass, this again being particularly true when com-

plexity was estimated using a bulk fractal (DA). In

addition to shifting the distribution of biomass

amongst size classes, habitat complexity therefore

appears to have a role in determining the absolute

animal biomass in these systems, with more complex

vegetation stands supporting more biomass. However,

there is no evidence, at the scale of this study, to

support the hypothesis that habitat structure regulates

macroinvertebrate species diversity within water bodies

or that habitat complexity determines the number of

fundamental niches that could be maintained in the

environment (May 1972), since fractal complexity was

unrelated to species richness.

The overall biomass�/body size relationship observed

in our data does not differ significantly from that

predicted under the energy equivalence model (Damuth

1981). Both our observed distribution, and that expected

under the energy equivalence model fit well within the

range of values predicted by models incorporating both

allometric scaling of resource use and fractal complexity

of the habitat (Morse et al. 1985). Morse et al. (1985)

showed that five data sets for invertebrates on terrestrial

vegetation approximately fitted such a model and

Shorrocks et al. (1991) found similar accordance at

small scale when examining the fractal dimension of

lichen thalli and the body size distribution of arthropods.

Both authors attributed slopes steeper than �/0.75 to the

fractal complexity of habitat structure. In contrast, the

only aquatic study that examines this relationship

(Gee and Warwick 1994a) found the gradient of

density�/body size distribution for invertebrates on

marine macroalgae to be too shallow to be in accordance

with Morse et al.’s (1985) model. Our study suggests that

such results should be treated with caution. The

combined model of Morse et al. can give wide ranges

of prediction for the biomass�/body size relationship,

which may (as here) encompass curves predicted by

energy equivalence alone. In such cases it is difficult,

if not impossible, to determine the contribution fractal

complexity makes to the form of the relationship

observed. As in some of the studies listed above, the

gradient we observe is indeed steeper than that predicted

by the energy equivalence model, which could be taken

to suggest the importance of habitat complexity in

accordance with Morse et al.’s model, were it not for

the lack of significant differences between our relation-

ship and that predicted by the energy equivalence

hypothesis. In addition, Griffiths (1992) points out that

the slope of biomass�/body size relationships may be

sensitive to the regression method used, with the

preferred approach of reduced major axis regression

(RMA) typically resulting in steeper slopes than gener-

ated by methods such as ordinary least squares (OLS).

As noted by Griffiths (1992), RMA can often produce

slopes greater than �/0.75 under the energy equivalence

model, meaning that care should be taken when

comparing across studies employing different regression

techniques. In the case of our data, OLS produced a line

with a slope of �/0.84, marginally shallower than that

under RMA, but not affecting the discussion above.

In summary we have presented a rapid and straight-

forward approach to determining biologically mean-

ingful measures of structural complexity from mixed

stands of vegetation, and demonstrated that this pro-

vides insight into the nature of invertebrate assemblages

which would not be forthcoming from the study of more

traditional vegetation metrics such as plant surface

area or species richness. We would suggest that the

approach taken here is applicable to a wide range of

situations where animals utilize a habitat mosaic in three

dimensions.

Acknowledgements �/ We are grateful to Jeremy Clitherowand Ray Lawman (English Nature), and Alistair Cameron(National Trust) for permission to work on the LizardPeninsula. Anne Torr and Jo Vosper provided assistance inthe field and laboratory, Alan Bedford identified chironomidlarvae, and Paul Russell gave valuable advice on image analysis.This study was supported by a PhD studentship funded byEnglish Nature and the University of Plymouth.

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