M .W. Beck J. Exp. Mar. Biol. Ecol. 249 2000 29 –49
37
treatments are ranked at the different times and places trials for each contrast or comparison, and the likelihood that the rankings are randomly distributed among
treatments is assessed. In these tests, each site in each experiment was a separate trial i.e. each row in Appendix 1 represents a separate trial, and the responses to the
treatments were ranked within each trial for each of the a priori contrasts identified in assumption 1 and hypotheses 1–3. There was thus a maximum of 14 possible trials at
separate places and times Appendix 1.
2
Anderson’s Q was used to examine distributions of ranks in the contrasts one vs. three treatments when there were no tied ranks. In cases with tied ranks and for
comparisons e.g. high vs. control, binomial tests were used to combine results across experiments. If there was no difference in density or richness between treatments, each
treatment should be ranked first on average 50 of the time i.e. binomial p 5 q 5 0.5. When the binomial test was used for contrasts that involved the three low complexity
treatments with pits i.e. low vs. control, high vs. low, pits vs. pneumatophores, density and richness were averaged among the three treatments to condense the contrast to a
comparison of two groups. In trials with tied values, a tie was counted against the predictions i.e. in support of the null prediction if there was just one tie. When there
were two tied values, one value was counted in support of predictions and one against. In the analyses of the a priori contrasts for the individual species, a few trials were
dropped from consideration, because no individuals of that species were observed on any treatment in the trial. The number of omitted trials was noted on every occasion when
this procedure was done.
3. Results
The ANOVAs indicated that there were differences in density and to a lesser extent richness among the different sites and treatments Tables 2, 3. The three most common
species accounted for most of the density of gastropods on the treatments Fig. 4. The differences among sites were not surprising Fig. 4, because these sites were
haphazardly chosen. There were a few site by treatment interactions Tables 2, 3; these interactions generally occurred because of variation in the magnitude, but not direction,
of differences in treatments among sites. The differences among treatments were examined in the a priori contrasts.
3.1. Assumption 1: control vs. high and low complexity treatments In most cases, the results were consistent with the predictions of no difference
between control and complexity treatments. Total density was generally similar between control and high complexity treatments in the individual experiments Table 2, Fig. 5a.
When the data were combined across the different times and places, there was no significant difference in the ranking of density among trials Table 4, Appendix 1,
binomial P . 0.1. There was not a significant difference between the density of gastropods in control vs. low complexity treatments in most of the individual
experiments Table 2, Fig. 5a, but overall the density in the control treatments ranked
38
M .W
. Beck
J .
Exp .
Mar .
Biol .
Ecol .
249 2000
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49 Table 2
a
Comparisons of total density among treatments, sites, and shores in five separate experiments
a ANOVAs Experiment 1
Experiment 2 Experiment 3
Experiment 4 Experiment 5
Source df
MS F
Source df
MS F
Source df
MS F
df MS
F df
MS F
Treatment 3
0.53 0.82
Treatment 5Tr 4
4.62 7.74
Treatment 4
4.65 24.11
5 3.35
3.90 5
3.27 3.06
Residual 4
0.64 Shore
1 0.31
0.07 Site
2 2.10
13.65 2
1.49 7.68
2 2.54
11.61 Site Shore
2 4.59
33.01 Tr3Site
8 0.19
1.25 10
0.86 4.44
10 1.07
4.90
b b
Tr3Shore 4
0.60 2.42
Residual 15
0.15 17
0.19 14
0.22 Tr3SiteShore
8 0.25
1.77 Residual
20 0.14
b Summary of a priori contrasts of density among treatments
c c
Condition Experiment 1
Experiment 2 Experiment 3
Experiment 4 Experiment 5
Assumption 1 Low5Control
High5Control, No test
B112 — Control5High, Low All — Control5High, Low
Control.Low S1 — Control.High, Low
Hypothesis 1 No test
High.Low High.Low
All — High5Low All — High5Low
Hypothesis 2 WM5ND5NS
WM5ND5NS WM.NS,
All — WM5ND5NS B11S1 — WM5NS5ND
WM5ND, NS5ND B2 — NS.WM5ND
Hypothesis 3 No test
No test Pits.Pneumatophores
B112 — Pits5Pneumatophores B112 — Pits5Pneumatophores
S1 — Pits.Pneumatophores S1 — Pits.Pneumatophores
a
In the F-ratios, the mean squares for most terms are tested over the Residual. In experiment 2, Shore is tested over SiteShore, Treatment is tested over Treatment3Shore, which is tested over Treatment3SiteShore. In experiments 3–5, Treatment is tested over Treatment3Site.
b
Df reduced to account for replacement of missing replicates see text.
c
B1, Bare Island site 1; B2, Bare Island site 2; S1, Sutherland Point site 1; All, B1, B2, and S1.
M .W
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Exp .
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Biol .
Ecol .
249 2000
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49
39 Table 3
a
Comparisons of richness among treatments, sites, and shores in the five experiments
a ANOVAs Experiment 1
Experiment 2 Experiment 3
Experiment 4 Experiment 5
Source df
MS F
Source df
MS F
Source df
MS F
df MS
F df
MS F
Treatment 3
0.0 0.0
Treatment 5Tr 4
2.54 3.03
Treatment 4
5.08 12.45
5 2.05
2.32 5
5.31 6.42
Residual 4
0.5 Shore
1 0.03
0.00 Site
2 7.03
8.44 2
0.58 1.00
2 1.69
6.10 Site Shore
2 5.63
11.84 Tr3Site
8 0.41
0.49 10
0.88 1.51
10 0.83
2.98
b b
Tr3Shore 4
0.84 1.03
Residual 15
0.83 17
0.58 14
0.28 Tr3SiteShore
8 0.81
1.71 Residual
20 0.48
b Summary of a priori contrasts of richness among treatments
c c
Condition Experiment 1
Experiment 2 Experiment 3
Experiment 4 Experiment 5
Assumption 1 Low5Control
High5Control, No test
High5Control, B1 — High.Control
Control5Low Control5Low
B2, S1 — High5Control All — Low5Control
Hypothesis 1 No test
High5Low High5Low
High5Low B1 — High.Low
B2, S1 — High5Low Hypothesis 2
WM5ND5NS WM5ND5NS
WM5ND5NS WM5ND5NS
B1, S1 — WM5ND5NS B2 — NS.WM5ND
Hypothesis 3 No test
No test Pits.Pneumatophores
Pits5Pneumatophores B1 — Pits5Pneumatophores
B2,S1 — Pits.Pneumatophores
a
The mean squares in the F-ratios are the same as in Table 2.
b
Df reduced to account for replacement of missing replicates see text.
c
B1, Bare Island site 1; B2, Bare Island site 2; S1, Sutherland Point site 1; All, B1, B2, and S1.
40 M
.W. Beck J. Exp. Mar. Biol. Ecol. 249 2000 29 –49
Fig. 4. Total density of gastropods by species, treatment and site. Sites differed in total density and in the relative abundance of individual species. These values are pooled across all five experiments. Sutherland Point
site 2 is not included because it was only used in one experiment. The Low column is the average density on the three low complexity treatments with pits. Pneum5treatment with pneumatophores. Error bars indicate one
standard error for total density.
M .W. Beck J. Exp. Mar. Biol. Ecol. 249 2000 29 –49
41
Fig. 5. Density and richness of gastropods by treatment and experiment. Data were averaged first within sites before calculating the average and standard error among sites. The value is the mean11 S.E. Data from
experiment 1 are not included, because only one site was used in the experiment. Lines underneath the bars indicate results of tests when data are combined across all experiments. Treatments on the same solid line are
statistically similar. Pneum5treatment with pneumatophores.
first in most trials above densities on all three low complexity treatments Table 4,
2
Appendix 1, Q 5 14.09, df 5 3, P , 0.01. Species richness was similar between control and complexity treatments in most
experiments Table 3, Fig. 5b. When the data were combined across the different times and places they were statistically similar Table 4, high . control in five of ten trials,
binomial P . 0.1; low . control in four of 11 trials, binomial P . 0.1. Of the three most abundant species, the densities of A
. porcata and B. nanum were
42
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J .
Exp .
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Biol .
Ecol .
249 2000
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49 Table 4
Summary of results when data were combined across experiments: non-parametric comparisons of assumption and hypotheses 1–3 Condition
Variable Density:
Richness Density
All species A
. porcata B
. nanum C
. tramoserica Assumption 1
Control5High, Control.Low Control5High, Low
Control5High, Low Control5High, Low
Control.High, Low Hypothesis 1
High.Low High.Low
High.Low High.Low
High5Low Hypothesis 2
WM.ND, WM5NS, NS5ND WM5NS5ND
WM5NS5ND WM5NS5ND
WM5NS5ND Hypothesis 3
Pits.Pneumatophores Pits.Pneumatophores
Pits5Pneumatophores Pits.Pneumatophores
Pits.Pneumatophores
M .W. Beck J. Exp. Mar. Biol. Ecol. 249 2000 29 –49
43
similar between complexity and control treatments, but the density of C . tramoserica
was not Table 4, Fig. 5c–e. The density of A . porcata was similar between the control
and the complexity treatments high . control in six of ten trials, binomial P . 0.1; low . control in three of 11 trials, binomial P . 0.1 as was the density of B
. nanum high . control in two of six trials after four all-zero trials dropped, binomial P . 0.1;
low . control in four of eight trials after three all-zero trials dropped, binomial P . 0.1. The density of C
. tramoserica was, however, significantly greater in the control treatment than on the complexity treatments when the responses were combined across
experiments high . control in zero of ten trials, P , 0.001; low . control in one of 11 trials, P , 0.01. Inferences about the effects of treatments on C
. tramoserica must be regarded with caution, because they may not accurately reflect the effects of habitat
structure on this species in unmanipulated habitats. 3.2. Hypothesis 1: high vs. low complexity treatments
Total density of gastropods was greater on high than on low complexity treatments at all times and places. When the data were examined for each experiment, the ANOVAs
indicated significant differences between high and low complexity treatments only in experiments 2 and 3 Table 2, Fig. 5a. When the data were combined across
experiments, the density of gastropods on the high complexity treatment was ranked first above the densities on the three low complexity treatments in all 13 trials; a result that is
2
highly unlikely to occur by chance Table 4, Appendix 1, Q 5 39, df 5 3, P , 0.001. Species richness was greater on the high than low complexity treatments at most times
and places Table 3, Fig. 5b. There was, however, only one statistically significant difference among these treatments when the data were analyzed for each experiment
Table 3. When the responses to treatments were combined across experiments, richness was greater on the high complexity treatment than on the low complexity treatments in
ten of 13 trials Table 4, binomial P , 0.05.
Of the three most abundant species, the densities of A . porcata and B. nanum were
affected by complexity, but the density of C . tramoserica was not Table 4, Fig. 5c–e.
When the data were combined across the experiments, the densities of A . porcata and B.
nanum were significantly greater on high than on low complexity treatments after four all-zero trials were dropped A
. porcata — high . low in nine of nine trials, binomial P , 0.01; B
. nanum — high . low in eight of nine trials, binomial P , 0.05. The density of C
. tramoserica was not affected by complexity high . low in five of 13 trials, P . 0.1.
3.3. Hypothesis 2: comparison of indices among low complexity treatments There were few significant differences in density among the three low complexity
treatments Tables 2, 4, Fig. 5a, and thus D was not significantly better than other indices at predicting responses of gastropods to complexity. The ANOVAs revealed only
three significant differences in total density among these treatments Table 2b. When the data were combined across experiments, the density of gastropods on the WM
treatment was greater than on the ND treatment in most trials Appendix 1, binomial
44 M
.W. Beck J. Exp. Mar. Biol. Ecol. 249 2000 29 –49
P , 0.01. There were no significant differences in rankings of density among trials between WM and NS treatments or NS and ND treatments Table 4, binomial P . 0.05
for both Appendix 1. The ANOVAs revealed only two significant differences in richness among the three
low complexity treatments Table 3, Fig. 5b. When the data were combined across the experiments, there were no significant differences in richness among the three low
complexity treatments Table 4. There were also no significant differences in the density of any of the three most
abundant species on the low complexity treatments when the results were combined across experiments Table 4, Fig. 5c–e.
3.4. Hypothesis 3: pits vs. pneumatophores Total density was greater on treatments with pits than on treatments with
pneumatophores at most times and places Table 2, Fig. 5a. The ANOVAs for the individual experiments indicated that there were significant differences in total density
between these treatments at most times and places Table 2b. When the data were combined across experiments, the density of gastropods was greater on treatments with
pits in seven of eight trials Table 4, Appendix 1, binomial P , 0.05.
Richness was greater on treatments with pits than on treatments with pneumatophores at all times and places. The ANOVAs indicated that richness was significantly greater on
treatments with pits at most times and places Table 3, Fig. 5b. When the responses to treatments were combined across experiments, richness was greater on treatments with
pits in eight of eight trials Table 4, binomial P , 0.01.
Of the three most abundant species, the densities of B . nanum and C. tramoserica
were significantly
greater on
treatments with
pits than
on treatments
with pneumatophores Table 4, Fig. 5d,e; B
. nanum — pits . pneumatophores in six of six trials after two all-zero trials dropped, binomial P , 0.05; C
. tramoserica — pits . pneumatophores in seven of eight trials, P , 0.05. The density of A
. porcata was not significantly different between treatments with pits vs. pneumatophores Table 4, Fig.
5c; pits . pneumatophores in four of six trials after two all-zero trials dropped, P . 0.1.
4. Discussion
