Blakely & Didham Mechanistic drivers of ecosystem-size effects
Supporting Information for: Blakely & Didham, Disentangling the
mechanistic drivers of ecosystem-size effects on species diversity
Supporting methods
Text S1: Detailed methods used in Nothofagus fusca leaf pack construction. Nothofagus
fusca (Fagaceae) is an evergreen southern beech species, and is the dominant canopy tree
species in the Orikaka Ecological Area (Blakely & Didham 2008). There is no single peak
season in which naturally-senescent falling leaves can be collected in large quantities, so we
hand-picked green N. fusca leaves from trees in the study area in December 2004. Leaves
were then soaked in tap water for 24 hours, to remove many of the tannins from the green
leaves, and dried at 50°C for three days. Leaf packs were constructed from 2.5 g (±0.001 g
dry weight) of these N. fusca leaves contained in a 10 mm-mesh nylon bag.
Figure S1: Venn diagram of shared species in natural (left) and experimental (right)
water-filled tree holes. The majority (80 %) of the species colonizing the 108 experimental
microcosms were also found in a survey of 25 water-filled and very damp natural tree holes
on red beech (Nothofagus fusca) trees in the Orikaka Ecological Area, April 2009. This
pattern has also been found in previous studies overseas (Pimm & Kitching 1987; Fincke,
Yanoviak & Hanschu 1997; Srivastava & Lawton 1998; Yanoviak 2001), and confirms for
New Zealand systems that artificial container habitats do indeed attract the same suite of
aquatic insects as natural water-filled tree holes.
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Blakely & Didham Mechanistic drivers of ecosystem-size effects
Figure S2: Leaf-litter resources in natural tree holes. In natural water-filled tree holes (n =
25), resource availability was positively correlated with ecosystem size (a), whereas resource
concentration did not vary significantly with ecosystem size (b). Data are from a survey of 25
naturally-occurring water-filled and very damp tree holes that were randomly selected on red
beech (Nothofagus fusca) trees in Orikaka Ecological Area, Buller District, New Zealand, in
April 2009. The effects of tree-hole volume on total resource and resource concentration were
tested with linear mixed-effects (LME) models, using maximum likelihood and model
simplification (Crawley 2007), where tree identity was treated as a random factor to control
for pseudoreplication (i.e., multiple holes were sampled on each of 16 trees), and the
dependent and independent variables were ln-transformed for analyses. The fitted line in (a)
is: ln(y) = -2.68 + 0.74.ln(x), and the slope of the line differs significantly from zero (χ2 =
12.87, d.f. = 1, P < 0.001). No significant relationship was found for resource concentration
(χ2 = 2.35, d.f. = 1, P = 0.125). Note that the axes are plotted on logarithmic scales.
By adding the same amount of leaf litter (7.5 g dry weight) to our experimentallyconstructed water-filled tree-hole microcosms, we manipulated the naturally-occurring total
resource relationship from a positive relationship to an experimentally-created null
relationship (i.e., total resource availability did not differ across microcosms of differing sizes
in the experiment). Consequently, this meant that the naturally-occurring resource
concentration relationship was modified from a null relationship to an experimentally-created
negative relationship (i.e., resource concentration decreased with increasing microcosm size
in the experiment).
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Blakely & Didham Mechanistic drivers of ecosystem-size effects
Figure S3: Relationship between resources and tree-hole opening. Natural tree holes with
large openings accumulate more detritus. Senescent leaf inputs are generally positively
correlated with the size of tree-hole openings (Kitching 1987; Sota 1996). We found this to
be the case when we surveyed 25 randomly selected water-filled and very damp tree holes,
with different sized openings, on red beech (Nothofagus fusca) trees in Orikaka Ecological
Area, Buller District, New Zealand, in April 2009. The effect of tree-hole opening size (cm2)
on total resource (g) was tested with a linear mixed-effects (LME) model, using maximum
likelihood and model simplification (Crawley 2007), where tree identity was treated as a
random factor to control for pseudoreplication (i.e., multiple holes were sampled on each of
16 trees), and the dependent and independent variables were ln-transformed for analysis. The
equation of the fitted is: ln(y) = -0.98 + 0.81.ln(x), and the slope was significantly different
from zero (χ2 = 9.00, d.f. = 1, P = 0.003). Note that the axes are plotted on logarithmic scales.
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Blakely & Didham Mechanistic drivers of ecosystem-size effects
Supporting statistical analyses
Text S2: Description of non-metric multidimensional scaling ordination (NMDS)
methods. A non-metric multidimensional scaling (NMDS) ordination, with 500 random
permutations, was conducted to reduce the species abundance matrix of the entire aquatic
insect community within the 108 microcosms down to the two major orthogonal axes of
variation in community composition (Figure S7), for use in later analyses. Species
abundances were square-root transformed to downweight the contribution of dominant
species and to better take into account the contribution of rare species to site similarity. The
NMDS ranks sites such that distance in ordination space represents community similarity (in
this case using the Bray-Curtis dissimilarity metric), where sites closest together are more
similar in species composition than those further apart (Quinn & Keough 2002). The
goodness-of-fit of the NMDS ordination is assessed by the magnitude of the associated
‘stress’ value. A stress value of 0.0 indicates a perfect fit, where the configuration of points
on the ordination diagram is a good representation of the actual community dissimilarities,
while stress values <0.2 correspond to a good ordination with no real prospect of misleading
interpretation (Quinn & Keough 2002).
We then tested for correlations between NMDS axes 1 and 2 and the abundance of the
six most abundant aquatic species (Monopelopia sp., Maorigoeldia argyropus, Eristalis
tenax, Limoniinae sp.1, Chironomidae sp.1 and Sylvicola fenestralis), to determine which
species were contributing most to differences in community composition with respect to
microcosm size and microcosm height.
Text S3. Description of Analysis of Similarities (ANOSIM) methods. We used Analysis of
Similarities (ANOSIM) to test if community composition was significantly different in
microcosms of differing sizes or heights. ANOSIM is a nonparametric permutation procedure
applied to the rank similarity matrix underlying the NMDS ordination. ANOSIM compares
the degree of separation among and within groups using the test statistic, R. When R equals 0
there is no distinguishable difference in community composition among groups, whereas an R
value of 1 indicates completely distinct communities among groups (Quinn & Keough 2002).
Text S4: Description of linear mixed-effects models (LME) methods. Linear mixedeffects (LME) models were used to test the fixed effects of microcosm size, height, and their
interaction on (a) habitat quality (pH, conductivity, water temperature, dissolved oxygen,
total resource and resource concentration) and (b) community structure (total abundance,
richness, Simpson’s diversity, and community composition) in the 108 microcosms, while
accounting for variation due to the spatial arrangement of the 20 N. fusca trees (random block
effect).
We used model simplification (as described by Crawley 2007), with maximum
likelihood (ML) estimation, to test the significance of the treatment effects, with χ2 statistics
and associated significance levels (P < 0.05) calculated following removal of each variable
one-by-one from the LME model. It is important to note that likelihood ratio (LR) tests are
thought to be unreliable for small to moderate sample sizes. However, we are confident that
using LR to test the significance of the fixed effects (using ML estimation) is adequate in our
situation, where our sample size is large (n = 108) and the random effect is large (i.e., block
or tree effect, n = 20) (cf. Bolker et al. 2009). Nevertheless, LR tests can be anti-conservative
(Pinheiro & Bates 2000), so caution needs to be used when interpreting these results.
The semi-dichotomous variables, microcosm size (0.56, 1.54 or 3.07 L volume) and
height (2, 3, 4, 16, 17 or 18 m above ground), were treated as continuous variables, as one
microcosm of each of the three sizes was randomly assigned to one of three possible heights
4
Blakely & Didham Mechanistic drivers of ecosystem-size effects
within the two height categories. We treated the microcosm size and microcosm height
variables as continuous for two reasons, as reviewed by Cottingham, Lennon & Brown
(2005). Firstly, regression-type analyses are more powerful than analysis of variance
(ANOVA) (cf. Cottingham et al. 2005). That is, the probability of detecting an effect when
that effect is present is greater when using regression. Secondly, regression (or in our case,
mixed-effects models with continuous data) provide quantitative outputs that can be
incorporated into ecological models more effectively than ANOVA. Thus, analysis of
continuous variables allows predictions or extrapolation from the data more readily than
ANOVA (Cottingham et al. 2005).
Further to this, we conducted a sensitivity analysis on the LME models with
microcosm size and height treated as categorical, rather than continuous variables and found
qualitatively similar results. There were, however, very slight differences in the effect of
microcosm height on community composition (i.e., NMDS axis 1 and NMDS axis 2) where a
significant effect of height was found on community composition when height was treated as
continuous, versus when treated as categorical (cf. Table 1 and Table S1). There was a minor
effect of microcosm size on total resource and moderate size: height interaction effects on
total resource and resource concentration when we treated height and size as categorical
variables, compared with the non-significant effects when treated as continuous (cf. Table 1
& Table S1). These results highlight that regression-type analyses are more powerful (i.e.,
higher probability of rejecting the null hypothesis, when the null hypothesis is false).
Text S5: Description of Structural Equation Modeling (SEM) methods. We used
structural equation modeling (SEM) to discriminate the relative direct, indirect and total
effects of microcosm size, microcosm height, and a height*size interaction on in situ habitat
quality and aquatic insect species richness or composition in water-filled tree-hole
microcosms, using Amos version 16.0.1 (Arbuckle 2007; see Figure S4). The SEM approach
has advantages over multiple regression, correlation and path analysis techniques as it allows
variables in each model to be specified as both a predictor and a response variable, enabling
the causal structure of a composite path model to be tested (Grace 2006). More importantly,
unlike ordinary least-squares methods, the entire suite of paths (hypothesized relationships
among independent and dependent variables) in the SEM is tested at once via maximum
likelihood (ML) estimation, weighted least squares, or other methods (Grace 2006).
Maximum likelihood estimation minimizes the difference between the observed covariance
matrix of variables included in the model and the predicted covariance matrix calculated from
the model structure. As a result, SEM presents standardized path coefficients (pc), which are
equivalent to standardized regression coefficients, and used to quantify the direct effects of an
independent variable on a dependent variable, while controlling for the effects of other
independent variables (Mitchell 2001). Standardized path coefficients are expressed as the
number of standard deviations of change in the dependent variable for every one standard
deviation of change in the independent variable.
We used two separate SEMs, tested with ML estimation, in which we investigated
whether the effects of microcosm size on (a) species richness and (b) community
composition, were entirely mediated by the indirect proximate effects of water chemistry,
temperature or resource concentration on aquatic insects, or whether there were unexplained
direct effects of ecosystem size, per se, that could not be accounted for by resource
concentration or the other proximate mechanisms tested. We included error variables to
represent unknown or unspecified effects on each of the endogenous variables (see Figure
S5).
We began by running separate SEMs on the full model for (a) aquatic insect species
richness and (b) community composition (Figure S5). To find the most parsimonious SEM
5
Blakely & Didham Mechanistic drivers of ecosystem-size effects
with the minimum adequate suite of paths necessary to explain variation in species richness
among microcosms, we compared multiple hierarchical models using a stepwise specification
search in Amos 16.0.1 (Arbuckle 2007), where all paths directly and indirectly affecting
species richness were treated as optional (i.e., pc = 0). The stepwise specification search fits
models both with and without such optional arrows, performing a heuristic search by
alternating between forward and backward selection.
In order to select the best-fitting hierarchical model (the full model or one of the
reduced models) from the stepwise specification search results, we determined the root mean
square error of approximation (RMSEA) with its upper boundary of a two-sided 90%
confidence interval, the minimum discrepancy function (ĈMIN), as well as ĈMIN / df (i.e., ĈMIN
adjusted for sample size) and the likelihood ratio (χ2M), tested with the model degrees of
freedom (dfM). The RMSEA is a parsimony-adjusted index so that when two models with
similar overall explanatory power for the same data are compared with this index, the simpler
model will be favored (Kline 2005). The readily accepted rule of thumb is that an RMSEA
value ≤ 0.05 indicates exceptional model fit, a value between 0.05–0.10 suggests good model
fit, but values ≥ 0.10 indicate a poor fit of the overall SEM (Kline 2005). Similarly, lower
ĈMIN / df values indicate good model fit, where ĈMIN / df ≤ 2 is an acceptable minimum value
(Bollen 1989). The likelihood ratio (χ2M) tests the null hypothesis that the model fits the data,
where PM ≥ 0.05 indicates that the null hypothesis cannot be rejected and the predicted
correlations and covariances of the model equal their observed counterparts (Kline 2005).
Using all four goodness-of-fit indices (RMSEA, ĈMIN / df, χ2M, PM) we were able to determine
the best fitting, most parsimonious models explaining both species richness and community
composition. Finally, we used bias-corrected bootstrapping with 1,000 random samples
generated from the observed covariance matrix to estimate the standard error and significance
values for the standardized direct, indirect and total effects (Kline 2005) for each of the final,
most parsimonious models.
6
Table S1: Results of categorical linear mixed-effects models. A sensitivity analysis conducted on the linear mixed-effects (LME) models in
Table 2, with microcosm size and height treated as categorical, rather than continuous, variables. The LME models, tested with maximum
likelihood estimation, investigate the main and interactive effects of microcosm size and height (fixed, categorical variables) on (a) six habitat
quality parameters (pH, conductivity, dissolved oxygen, water temperature, total resource and resource concentration), and (b) four measures of
aquatic insect community structure (insect density, species richness, species diversity and community composition [represented by axes 1 and 2
scores from a non-metric multidimensional scaling, NMDS, ordination]), while accounting for variation due to the spatial arrangement of the 20
N. fusca trees (random block effect). We used model simplification to estimate the chi-square (χ2) statistic and its significance level (P value) for
each of the fixed effects and their interaction (Crawley 2007). df = degrees of freedom, var. = variance explained by the random block effect
(Tree). P values < 0.05 are indicated in bold.
Response
(a) Habitat quality
pH
Predictors
var.
Tree
Size
Height
Height:Size
0.39
Conductivity
(µS25 cm-1)
Tree
Size
Height
Height:Size
0.22
Water temperature
(°C)
Tree
Size
Height
Height:Size
0.02
Dissolved oxygen
(mg L-1)
Tree
Size
Height
Height:Size
0.04
Total resource
(g)
Tree
Size
Height
Height:Size
0.02
Resource concentration
(g L-1)
Tree
Size
Height
Height:Size
0.02
χ2
df
P value
0.06
0.23
4.48
2
1
2
0.971
0.632
0.107
5.94
4.44
0.74
2
1
2
0.051
0.035
0.691
9.87
29.15
0.54
2
1
2
0.007
<0.001
0.762
10.88
19.86
8.20
2
1
2
0.004
<0.001
0.004
Response
Predictors
(b) Community structure
Abundance
Tree
Size
Height
Height:Size
Species richness
2
1
2
0.032
0.807
0.024
123.36
0.06
7.50
2
1
2
<0.001
0.807
0.024
χ2
df
P value
19.52
6.47
1.71
2
1
2
<0.001
0.011
0.425
11.26
3.82
0.10
2
1
2
0.004
0.050
0.953
8.77
8.73
0.48
2
1
2
0.013
0.003
0.785
<0.01
3.66
3.53
2
1
2
0.940
0.056
0.171
0.92
1.98
1.33
2
1
2
0.632
0.160
0.514
0.33
Tree
Size
Height
Height:Size
0.01
Simpson’s diversity
(1-D)
Tree
Size
Height
Height:Size
<0.01
NMDS axis 1
Tree
Size
Height
Height:Size
0.05
Tree
Size
Height
Height:Size
0.06
NMDS axis 2
6.88
0.06
7.50
var.
Figure S4: Scatterplot matrix of the exogeneous and endogenous variables. A scatterplot
matrix of the 3 experimental exogenous (predictor) and 8 endogenous (response) variables
used in the Structural Equation Models (Text S5; Figure S5).
Blakely & Didham Mechanistic drivers of ecosystem-size effects
Figure S5: Full Structural Equation Models. The a priori multivariate hypotheses used in
structural equation modeling to test the direct and indirect network of causal factors that
influence (a) aquatic insect species richness, and (b) community composition (represented by
non-metric multidimensional scaling, NMDS, axes 1 and 2) in water-filled tree-hole
microcosms. Arrows point from predictor to response variables.
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Blakely & Didham Mechanistic drivers of ecosystem-size effects
Supporting results
Table S2: Aquatic insect species inhabiting water-filled tree-hole microcosms. Aquatic
insects inhabiting experimental water-filled tree-hole microcosms of three different sizes,
near the ground and in the canopy, after 12 months colonization from January 2005–2006.
Microcosm volumes: Small = 0.56 L, Medium = 1.54 L, Large = 3.07 L.
Ground
Canopy
Microcosm size: Small Medium Large Small Medium Large Total
Coleoptera
Scirtidae
Scirtidae sp.
3
2
0
1
0
0
6
Diptera
Chironomidae
Tanypodinae
Monopelopia sp.
658
3,050 3,323
1,829
5,306 4,495 18,661
Chironominae
Chironomidae sp.1
23
40
34
17
7
32
153
Orthocladiinae
Limnophyes vestitus
60
3
2
26
0
6
97
Gymnometriocnemis ?lobifer 5
0
0
0
0
0
5
Culicidae
Maorigoeldia argyropus
45
61 1,692
17
16
541
2,372
Syrphidae
Eristalis tenax
32
182
17
89
165
1
486
Tipulidae
Limoniinae sp.1
11
7
15
12
36
100
181
Limoniinae sp.2
10
1
0
0
0
0
11
Anisopodidae
Sylvicola fenestralis
45
49
1
16
0
1
112
Psychodidae
Psychoda penicillata
56
21
0
15
4
0
96
Psychoda formosa
27
14
0
0
0
0
41
Muscidae
Muscidae sp.
0
0
0
0
5
0
5
Ceratopogonidae
Forcipomyia sp.
4
0
0
0
0
0
4
Ceratopogoniinae sp.
0
0
0
1
0
0
1
Total
979
3,430 5,539
2,023
5,084 5,176 22,231
Number of microcosms
17
20
19
17
16
19
108
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Blakely & Didham Mechanistic drivers of ecosystem-size effects
Table S3: Pearson’s correlation results. t values and their significance for post-hoc
Pearson’s correlations between the first two axes from a non-metric multidimensional scaling
(NMDS) ordination and six most abundant aquatic species (statistical analyses are described
fully in Text S2). df = 106. * = P < 0.05, ** = P < 0.01, *** = P < 0.001.
Monopelopia sp.
Maorigoeldia argyropus
Eristalis tenax
Limoniinae sp.1
Chironomidae sp.1
Sylvicola fenestralis
NMDS axis 1
4.574***
0.157
-0.670
1.211
-1.230
-2.640**
NMDS axis 2
1.430
-1.096
-0.319
-4.135***
0.691
-2.022*
Figure S6: Habitat quality variables in microcosms. Mean (± 1SE) (a) pH, (b)
conductivity (µS25 cm-1), (c) water temperature (°C), (d) dissolved oxygen (mg l-1), (e) total
resource (g dry weight), and (f) resource concentration (g l-1 dry weight) measured after 12
months in water-filled tree-hole microcosms of three different sizes in the canopy (open
circles) and at ground-level (closed circles).
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Blakely & Didham Mechanistic drivers of ecosystem-size effects
Figure S7: Non metric multidimensional scaling ordination of insect communities in
microcosms. Non-metric multidimensional scaling (NMDS) ordination graphically
illustrating the relationship among the aquatic insect communities inhabiting small (560 ml;
circles, n = 34), medium (1540 ml; squares, n = 36), and large (3070 ml; triangles, n = 38)
water-filled tree-hole microcosms located at ground-level (2–4 m, filled symbols) and in the
canopy (16–18 m, open symbols) within continuous mixed broadleaf-podocarp temperate
rainforest. The NMDS was based on a Bray-Curtis matrix of dissimilarities using square-root
transformed abundance data, and the first two NMDS ordination axes gave a good
representation of the actual community dissimilarities among the 108 microcosms (stress =
0.14). The addition of a third axis did not markedly improve the stress value (0.11). Note that
the axes are scaled identically so that microcosms closest together are more similar in species
composition than those further apart.
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Blakely & Didham Mechanistic drivers of ecosystem-size effects
Figure S8: Species richness in natural tree holes. In natural systems, species richness
frequently increases with ecosystem size. We found this to be the case when we surveyed 25
randomly selected water-filled and very damp tree holes on red beech (Nothofagus fusca)
trees in Orikaka Ecological Area, Buller District, New Zealand, in April 2009. A linear
mixed-effects (LME) model, tested with maximum likelihood and model simplification
(Crawley 2007), where tree identity was treated as a random factor to control for
pseudoreplication (i.e., multiple holes were sampled on each of 16 trees), showed that lntransformed aquatic insect species richness was positively, linearly related to tree-hole size
(ln-transformed tree-hole volume, cm3). The equation for the fitted is: ln(y) = -0.07 +
0.22.ln(x), and the slope of the line was significantly different from zero: χ2 = 6.91, d.f. = 1, P
= 0.008. Note that the axes are plotted on logarithmic scales.
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Blakely & Didham Mechanistic drivers of ecosystem-size effects
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14