Appendix S1
Species’ traits predict the effects of disturbance and productivity on diversity
Nick M. Haddad, Marcel Holyoak, Tawny M. Mata, Kendi F. Davies, Brett A.
Melbourne, and Kim Preston
Supplementary Material
Methods for determining species traits
Intrinsic growth rate, r, and carrying capacity, K
We determined the intrinsic growth rate, r, and the carrying capacity, K, for each species
at high and low nutrient levels as described in the main text. Figure S1 shows data from
that experiment, including best fit models that support logistic growth. Estimates were
generated for each of 5 replicates of high and low nutrient treatments. In each case,
logistic growth was supported over exponential or theta-logistic growth. The final
estimates of r and K were the average of the values generated from the 5 replicates. For
one bottle of Paramecium bursaria and one bottle of Spirostomum ambiguum, we could
not obtain an estimate. For high nutrient treatments used to predict disturbance responses
in the main text, species differed in r (n=38, F = 68.16, p<0.001, with Colpidium sp. >
Cyclidium sp. = P. aurelia > Euglena gracilis = S. ambiguum > Euplotes aediculatus =
Coleps sp. = P. bursaria), and in ln(K) (n=38, F = 187.88, p<0.001, with E. gracilis >
Cyclidium sp. > P. bursaria > Colpidium sp. = E. aediculatus = P. aurelia > Coleps sp >
S. ambiguum).
Haddad et al., Supplementary Material, Page 1
Dispersal rank
The dispersal experiment was conducted in two 1-day blocks, using fresh multispecies
communities on each day. To obtain multispecies communities, we mixed subcultures of
individual species that were old enough to have reached their equilibrium density into
one large culture. Communities contained 12 species each day, and among the 2 days
included all 8 species that we considered in this paper. We homogenized and sampled
this large culture twice to measure starting densities of individual species by counting the
individuals of each species in ten weighed droplets. If at least 20 individuals of each
species were not found in the original droplets, we continued to add more volume until
we reached 20. Initial densities (#/ml) were, in Day 1: Coleps sp. = 1.2, Colpidium sp. =
2, Cyclidium sp. = 1210, Euglena gracilis = 6.5, Euplotes aediculatus = 0.933,
Paramecium aurelia = 20; and in Day 2: Coleps sp. = 3.33, Colpidium sp. = 260,
Cyclidium sp. = 158, E. aediculatus = 60, P. aurelia = 51, P. bursaria = 122, S.
ambiguum = 0.4.
We measured dispersal in 24 replicates of 2 bottles connected by silicone rubber tubing
that was 13 cm long and 0.635 cm internal diameter. To complete the final count of
dispersing individuals in a timely manner, we conducted 14 replicate dispersal trials on
day 1 and 20 on day 2. Source bottles received 100 ml of the mixed species stock
cultures. The recipient bottles were filled with 100 ml of sterile nutrient medium, rather
than bacteria-rich nutrient medium, to encourage the organisms to move in search of
food. Beginning 5 hours later (that is, before reproduction could happen for most
Haddad et al., Supplementary Material, Page 2
species), we started randomly sampling the non-inoculated bottles. We homogenized and
then surveyed the liquid until we counted at least eight individuals of each species. If 8
individuals were not found, as was the case for some of the poor dispersers, we surveyed
all 100 ml of liquid in the bottle.
We determined dispersal rank in the same way that Cadotte (2006) calculated rank from
his measure of colonization, although our measure of dispersal was different. We first
divided the number of individuals in the recipient bottle by the number in the source
bottle to obtain a proportion that dispersed. We then ranked this proportion for each trial.
Finally, we averaged the ranking among trials to determine dispersal rank for a species.
When a species was tested in both days, we also averaged the dispersal rank across days.
Dispersal ranks are reported in Table 1 of the main text. Dispersal rank was highly
correlated with intrinsic growth rate (Table S1). Because this was a non-spatial
experiment, we used intrinsic growth rate in analysis.
Colonization rank
Colonization ranks were available for 6 of our 8 species from Cadotte, et al. (2006). The
ranks of Cadotte et al. (2006) were measured in a similar experimental setup to ours, with
the response being the time to colonization of a more distant bottle. Like dispersal rank,
colonization rank was correlated with intrinsic growth rate and dispersal rank.
Furthermore, because we did not have colonization ranks for all species, we did not use
colonization rank in analysis.
Haddad et al., Supplementary Material, Page 3
Spreading speed and diffusion coefficient
Because we were concerned that dispersal rank and colonization rank were not identical,
and that dispersal rank was not significantly correlated with competitive rank, as Cadotte,
et al. (2006) found with a similar group of protozoans (Table S1), we used the spreading
speed as another metric of colonization using data we had for all of our species. The
spreading speed is closely related to the measure of colonization used by Cadotte et al
(2006). The spreading speed combines intrinsic growth rate and the diffusion coefficient
into one metric and is equal to 2*(r*D)0.5 (e.g., Okubo & Levin 2002). Cadotte, et al.
(2006) also recognized that colonization is related to dispersal and population growth. In
our experiment, we assumed dispersal between two patches (i,j) was governed by
dN i
 D N j  N i 
dt
yielding the diffusion coefficient:
D
1  2 N 2 t  
 (1)
ln 1 
2t 
N1 0 
where t is the time of the trial, N1(0) is the starting density in the source bottle, and N2(t)
is the final density in the recipient bottle. D and spreading speed were correlated with
intrinsic growth rate, and because this was a non-spatial experiment, we used intrinsic
growth rate in analysis.
Competitive rank
Independent of Cadotte, et al. (2006), we had conducted a similar competition experiment
using pairwise comparisons of the subset of species used in this paper. Between Cadotte
Haddad et al., Supplementary Material, Page 4
et al. (2006) and our experiment, we evaluated competitive rankings of all species used in
analysis of species responses to disturbance in this paper. We first describe our
competition experiment, and then how we scaled the two experiments to obtain one
ranking.
The outcome of competition among eight paired species was assayed in a fully crossed
design. Species used were Rotifer sp., Paramecium aurelia, Coleps sp., Euglena gracilis,
Paramecium caudatum, Euplotes aediculatus, Cyclidium sp., and Uronema sp.
Treatments consisted of bottles containing standard nutrient media, as in the main
experiment, with two wheat seeds to provide a slow release of nutrients. There were 4
replicates of each species pair and each single species for a total of 144 bottles.
Approximately 30 individuals of each species were added to initiate the experiment.
Densities of species were sampled after 4 weeks, sufficiently long for equilibrium
densities to be reached, using the methods described for the main experiment.
We defined competitive effect as the effect of an individual on another individual,
whether of the same or a different species. We quantified competitive effect as the
reduction in per capita growth rate caused by an individual. To calculate pairwise
competitive effects, we used a two species Lotka-Volterra model, which at equilibrium is
1 dN iP*
 ri 1   ii N iP*   ij N Pj*   0
P*
Ni
dt
(2)
where N iP* is the density of species i at equilibrium when grown in "pair" culture (i.e.
with species j), and ij is the interspecific interaction coefficient (the per capita effect of
Haddad et al., Supplementary Material, Page 5
species j on species i). We used this model because the population growth of our study
microorganisms is best represented in continuous time. Solving for ij gives the
following equation:
 ij 
1   ii N iP*  N iS*  N iP*  1
 P*
 
N Pj*
N iS*

 Nj
(3)
where ii is the intraspecific interaction coefficient and is equal to the reciprocal of the
equilibrium density in single species culture, ii = 1/NiS*. Equation 3 shows that the
interspecific competitive effect of species j is quantified as the per capita contribution of
species j to the proportional reduction in the equilibrium density of species i in pair
culture compared to single-species culture. When the sign of the interaction coefficient is
negative, the effect is facilitative.
For each replicate, we used the final densities to calculate ii for single species cultures
and ij for all pairwise species combinations. We defined competitive ability, C, of a
species as the combination of its average competitive effect in the community, and its
average competitive response (ability to withstand competition), as follows
Cj 
1

 ij   ji 
n i
i

(4)
where the first summation is the effect, the second summation is the response, and n is
the number of species. Negative C indicates poor competitive ability, whereas positive C
indicates good competitive ability. Zero C indicates that the net competitive ability of the
species is neutral. Equation 4 shows that species with the poorest competitive ability
have a facilitative effect on other species but also suffer from their competitive effects.
Haddad et al., Supplementary Material, Page 6
Conversely, species with the best competitive ability strongly compete with other species
but are also facilitated by them. Our measure of competitive ability is similar to Mouquet
et al. (2004) and Cadotte et al. (2006) in that both effect and response contribute to
overall competitive ability. Mouquet et al. (2004) used the relative yield of a single
generational step. However, compared to their system of annual plants with a discrete
time process, relative yield was not appropriate for our system in which competitive
effect is continuous and incremental in time. Cadotte et al. (2006) calculated competitive
ability from long term persistence data. For example, the effect of species j on i was
considered to be high if i often went extinct in the presence of species j. Our measure
more finely defines the competitive ability of each species by directly estimating per
capita interaction coefficients, and has the advantage of shorter culture times.
To obtain a ranking of the competitive ability of each species, we calculated Cj for one
replicate set of single and pairwise cultures, and ranked the species from 1 to 8 from
worst to best competitor. To estimate the mean and confidence limits for the rank of
competitive ability, we used a bootstrap procedure. We first resampled the final density
data to construct four new replicate data sets. In this resampling, individual trials for
single or pairwise species could be drawn from any of the four original replicates. For
each new replicate, we calculated one complete set of ijs, effects, responses, Cjs, and
ranks. We then calculated the mean of the four replicates. We drew 10000 bootstrap sets
of four replicates. We took the 2.5 and 97.5 percentiles from the bootstrap distribution of
the means to determine the 95% confidence limits for the mean competitive rank. The
bootstrap estimates are given in Tables S2 and S3.
Haddad et al., Supplementary Material, Page 7
As in Cadotte, et al. (2006), competitive ranks were highly variable. However, ranks
from the two studies were similarly ordered (Fig. S2). Thus, we rescaled the rankings
from Cadotte, et al. (2006), using the 3 overlapping species among the two studies.
Rescaling was necessary because ranks were based on different species numbers.
Rescaling was accomplished by, first, conducting orthogonal regression to obtain the
relationship: competitive rank = -11.85 + 2.15*(Cadotte et al. (2006) rank) and, second,
averaging ranks of species that overlapped among the two studies. Unlike Cadotte, et al
(2006), our measure of competitive rank was not significantly correlated with dispersal
rank, so both variables could be safely included in analysis of effects of species traits on
response to disturbance. We should note that we used fewer species in our experiment
than Cadotte, et al. (2006), and with more species, given the trend we observed, there
may have been a significant, negative relationship between competition and dispersal
ranks.
Correlations among variables
Because of correlations between variables (Table S1), we used three variables in analysis,
intrinsic growth rate, ln(K), and competitive rank. The intrinsic growth rate was related
to every variable measuring dispersal or colonization. We used intrinsic growth rate in
analysis because this was a non-spatial experiment. Ln(K) and cell size were also highly
correlated, so we retained ln(K) because it had more ecological relevance in the context
of this experiment. Finally, competitive rank was not correlated with any other variable
we used in analysis. Pragmatically, having a reduced set of explanatory variables was
Haddad et al., Supplementary Material, Page 8
reasonable given that our sample size in species trait analysis was 8 (one for each
species).
Regression analysis
We used the three variables in multiple regression analysis. Each regression started with
all three variables, intrinsic growth rate, ln(K), and competitive rank (weighted by the
difference between the max and min of the 95%CI of competitive rank to account for
variation in that variable). Variables were eliminated through backward elimination
multiple regression if P>0.20. Results of regression analyses are presented in Tables S4S6. We note that there are interdependencies among how traits predict responses by
disturbance type that are not accounted for in analysis. We did not conduct a full analysis
with interactions because 1) our sample size is 8 so it is not possible to include many
factors and interactions, and 2) intrinsic growth rate is the dominant predictor in all cases,
which would not change in a more complicated analysis.
Haddad et al., Supplementary Material, Page 9
Table S1. Correlations among traits. (Pearsons correlation coefficient) italics indicate
p<0.05, bold typeface indicates p<0.01
Variable
Ln(cell
size)
r
Ln(r)
Ln(K)
Dispers
al rank
D
Spreading speed
Colonization rank
Ln(cell size)
-0.41
r
Ln(r)
Ln(K)
Dispersal rank
D
Spreading
speed
Colonization
rank (Cadotte)
Competitive
rank
-0.46
0.97
-0.85
0.18
0.20
-0.50
0.95
0.93
0.30
-0.03
0.80
0.70
-0.09
0.83
-0.11
0.87
0.78
-0.05
0.89
0.99
-0.58
0.80
0.82
-0.10
0.80
0.78
0.77
0.24
-0.63
-0.58
-0.06
-0.61
-0.68
-0.67
-0.89
Table S2. Mean interaction coefficients (ij), mean competitive effects, and mean
competitive responses of eight species estimated by bootstrap resampling. Table cells are
the effect of species j (columns) on species i (rows). Negative values indicate facilitation.
Rotifer sp.
P. aurelia
Coleps sp.
E. gracilis
P. caudatum
E. aediculatus
Uronema sp.
Cyclidium sp.
Comp effect
Rotifer
sp.
0.00187
-0.00146
0.0007
-0.04063
-0.00176
-0.0004
-0.00437
0.00159
-0.00556
Paramecium
aurelia
0.00115
0.00333
0.00048
-0.01134
0.00678
0.00395
-0.00228
-0.00017
0.00024
Coleps sp.
-0.11883
-1.62874
0.04324
0.01939
-0.01494
0.52281
-0.47764
0.00234
-0.20655
Euglena
gracilis
8.6x10-7
0.00021
-0.02742
0.00067
0.00142
0.00016
-0.00088
-0.00041
-0.00328
Paramecium
bursaria.
0.00256
0.02031
-0.00858
-0.00733
0.0052
-0.05365
-0.00526
-0.00119
-0.00599
Euplotes
aediculatus
-0.0027
0.23823
0.26251
0.02759
0.03059
0.02481
0.02038
0.18224
0.09795
Haddad et al., Supplementary Material, Page 10
Uronema
sp.
0.00016
0.0005
-0.00032
-0.0004
0.00012
-0.06923
0.00137
-0.0003
-0.00851
Cyclidium
sp.
0.00041
0.00016
0.00234
0.00032
-0.00004
0.03565
-0.00094
0.00081
0.00484
Comp.
Resp.
-0.01442
-0.17093
0.03412
-0.00147
0.00342
0.05801
-0.0587
0.02311
Table S3. Mean competitive ability and mean competitive rank of eight species estimated
by bootstrap resampling. Negative values indicate poor competitive ability.
Species
Rotifer sp.
Paramecium aurelia
Coleps sp.
Euglena gracilis
Paramecium caudatum
Euplotes aediculatus
Uronema sp.
Cyclidium sp.
Competitive ability
0.00887
0.17117
-0.24066
-0.00182
-0.00876
0.03955
0.05019
-0.01827
Competitive rank
4.637
5.362
2.438
4.144
4.100
5.936
5.961
3.421
Table S4. Traits that predict species response to disturbance intensity. Ln(K) and
competitive rank were eliminated in backward multiple regression.
Source
Model
Error
Corrected Total
df
1
6
7
Sum of Squares
0.00004462
0.00002977
0.00007439
Parameter
estimate
-0.01179
0.004
Standard
error
0.00146
0.00133
F
8.99
P
0.02
t
-8.05
3.00
P
0.001
0.02
R2 = 0.60
Variable
Intercept
Intrinsic growth rate
Table S5. Traits that predict species response to disturbance frequency. Competitive
rank was eliminated in backward multiple regression.
Source
Model
Error
Corrected Total
df
2
5
7
Sum of Squares
0.1536
0.07029
0.22389
Parameter
estimate
-0.00163
-0.18841
0.02967
Standard
error
0.12764
0.06029
0.01775
F
5.46
P
0.055
t
-0.01
-3.12
1.67
P
0.99
0.03
0.16
R2 = 0.69
Variable
Intercept
ln(r)
ln(K)
Haddad et al., Supplementary Material, Page 11
Table S6. Traits that predict species response to disturbance effects on nutrient loss.
Ln(K) was eliminated in backward multiple regression.
Source
Model
Error
Corrected Total
df
2
5
7
Sum of Squares
0.64116
0.04216
0.70662
Parameter
estimate
-0.21252
0.28153
0.02155
Standard
error
0.05959
0.04216
0.007
F
24.49
P
0.003
t
-3.57
6.68
3.08
P
0.02
0.001
0.03
R2 = 0.91
Variable
Intercept
Intrinsic growth rate
Competitive rank
Haddad et al., Supplementary Material, Page 12
Figure S1. Relationship between population size and growth rate for each species (A-H)
studied in the disturbance experiment. Points show growth rates from 5 replicates each
for high and low nutrient microcosms. Lines show the best fit estimates derived for r and
K. Although we show all points from high and low nutrient treatments, r and K were
determined separately for each microcosm and then averaged to generate the best fit line.
Figure S2. Rescaled means and 95% confidence intervals of competitive ranks obtained
from this and Cadotte et al’s (2006) studies. Filled symbols are for species shared among
the two studies that were used to rescale ranks.
Figure S3. Effects of disturbance intensity, frequency, and impacts on nutrient loss on
the density of each species (A-H). Numbers within bars are the proportion of replicates
(out of 10 total) in which the species persisted.
Haddad et al., Supplementary Material, Page 13
0.8
Low nutrients
High nutrients
Predicted low
Predicted high
Log(Nt+1/Nt)/
(time interval)^0.5
0.6
0.4
0.2
B) Colpidium sp.
2
1
0
0
50
100
150
200
-0.2
0
0
-0.4
200
400
600
800
-1
-0.6
-2
-0.8
Log(Nt+1/Nt)/
(time interval)^0.5
3
3
C) Cyclidium sp.
2.5
2.5
2
2
1.5
1.5
1
1
0.5
0.5
0
D) Euglena gracilis
0
0
1000
2000
3000
4000
5000
-0.5
0
40000
80000
120000
160000
-0.5
0.6
E) Euplotes aediculatus
F) Paramecium aurelia
1.5
Log(Nt+1/Nt)/
(time interval)^0.5
0.3
1.2
0
0
100
200
300
400
500 0.9
-0.3
0.6
-0.6
0.3
-0.9
0
0
-1.2
100
200
300
400
-0.3
0.65
G) Paramecium bursaria
1.4
H) Spirostomum ambiguum
0.45
Log(Nt+1/Nt)/
(time interval)^0.5
Figure S1
3
A) Coleps sp.
0.9
0.25
0.4
0.05
-0.15
0
150
300
450
600
750
900
-0.1 0
Haddad
et al., Supplementary
14
Density Material, Page
-0.35
-0.6
10
20
Density
30
40
Figure S2
Haddad et al.
Euplotes
P.aurelia
Euglena
Cyclidium
Coleps
Cadotte et al. (2006)
P.bursaria
P.aurelia
Spirostomum
Euplotes
Coleps
Colpidium
-5
0
5
Mean rank
Haddad et al., Supplementary Material, Page 15
10
Figure S3
1000
A) Coleps sp.
Intensity=50%
Intensity=98%
Intensity=89%
Density
100
High Nutrients
Low Nutreints
10
1
0.1
0.01
1.0
Control
10000
0.9
1.0
0.9
Low
0.9
0.2
High
0.8
Low
0.0
1.0
High
0.2
0.0
0.1
Low
0.0
High
B) Colpidium sp.
Density
1000
100
10
1
0.1
0.01
1.0
Control
10000
1.0
0.9
1.0
Low
1.0
High
1.0
1.0
Low
1.0
0.8
0.9
High
0.6
Low
1.0
0.1
High
C) Cyclidium sp.
Density
1000
100
10
1
0.1
0.01
1.0
Control
10000
1.0
1.0
1.0
Low
1.0
High
1.0
0.9
0.9
Low
0.1
High
1.0
0.2
0.4
Low
0.0
High
D) Euglena gracilis
Density
1000
100
10
1
0.1
0.01
1.0
Control
0.9
1.0
0.8
Low
0.9
High
Frequency
0.7
0.5
0.0
Low
0.1
High
Frequency
Haddad et al., Supplementary Material, Page 16
0.1
0.2
0.2
Low
0.0
High
Frequency
Figure S3 (cont.)
100
E) Euplotes aediculatus
Intensity=89%
Intensity=50%
Intensity=98%
Density
10
High Nutrients
Low Nutrients
1
0.1
0.01
1.0
1.0
Control
1000
0.8
0.7
Low
0.9
0.8
High
0.9
0.0
Low
0.0
High
0.2
0.0
0.0
Low
0.0
High
F) Paramecium aurelia
Density
100
10
1
0.1
0.01
1.0
1.0
Control
1000
1.0
1.0
Low
1.0
1.0
1.0
High
1.0
Low
0.8
1.0
High
0.4
1.0
Low
0.0
High
G) Paramecium bursaria
Density
100
10
1
0.1
0.01
1.0
Control
Density
10
1.0
1.0
1.0
Low
1.0
1.0
High
1.0
0.0
Low
0.0
1.0
High
0.8
0.0
Low
0.0
High
H) Spirostomum ambiguum
1
0.1
0.01
0.8
Control
0.7
0.4
0.2
Low
0.1
High
Frequency
0.1
0.0
0.0
Low
0.0
High
Frequency
Haddad et al., Supplementary Material, Page 17
0.0
0.0
0.0
Low
0.0
High
Frequency
Literature Cited
Cadotte M.W., Mai D.V., Jantz S., Collins M.D., Keele M. & Drake J.A. (2006). On
testing the competition-colonization trade-off in a multispecies assemblage. The
American Naturalist, 168.
Mouquet N., Leadley P., Meriguet J. & Loreau M. (2004). Immigration and local
competition in herbaceous plant communities: a three-year seed-sowing
experiment. Oikos, 104, 77-90.
Okubo A. & Levin S.A. (2002). Diffusion and ecological problems: modern perspectives.
Springer-Verlag, New York.
Haddad et al., Supplementary Material, Page 18