Journal of Animal Ecology 2009, 78, 1143–1151
doi: 10.1111/j.1365-2656.2009.01586.x
Testing a biological mechanism of the insurance
hypothesis in experimental aquatic communities
Daniel J. Leary and Owen L. Petchey*
Department of Animal and Plant Sciences, University of Sheffield, Western Bank, Sheffield, S10 2TN, UK
Summary
1. The insurance hypothesis predicts a stabilizing effect of increasing species richness on community and ecosystem properties. Difference among species’ responses to environmental fluctuations
provides a general mechanism for the hypothesis. Previous experimental investigations of the
insurance hypothesis have not examined this mechanism directly.
2. First, responses to temperature of four protist species were measured in laboratory microcosms.
For each species, we measured the response of intrinsic rate of increase (r) and carrying capacity
(K) to temperature.
3. Next, communities containing pairs of species were exposed to temperature fluctuations. Community biomass varied less when correlation in K between species (but not r) was more negative,
and this resulted from more negative covariances in population sizes, as predicted. Results were
contingent on species identity, with findings differing between analyses including or not including
communities containing one particular species.
4. These findings provide the clearest support to date for this mechanism of the insurance hypothesis. Biodiversity, in terms of differences in species’ responses to environmental fluctuations (i.e.
functional response diversity) stabilizes community dynamics.
Key-words: biodiversity, environmental fluctuations, insurance hypothesis, negative covariance,
stability, temporal variation
Introduction
High rates of extinctions have motivated renewed interest in
diversity–stability relationships (MacArthur 1955; May
1972; McCann 2000; Ives & Carpenter 2007). The multiple
meanings of diversity and stability make for many possible
‘diversity–stability’ questions (Pimm 1984; Grimm & Wissel
1997; Loreau et al. 2002). One question is how species richness affects the temporal variability of community properties,
such as total biomass, primary productivity and nutrient
cycling (Cottingham, Brown & Lennon 2001). This question
is important as variability in community properties will
impact the reliability of ecosystem services whose significance
includes environmental, socio-economic and conservation
values (Costanza et al. 1997; Daily 1997; Gaston & Spicer
2003). According to the insurance hypothesis, high species
richness should reduce temporal variability of community
properties by insuring them against the impact of environmental fluctuation (Yachi & Loreau 1999). Conversely, lower
levels of species richness may compromise the insurance
functions of biodiversity.
*Correspondence author. E-mail: o.petchey@sheffield.ac.uk
Numerous experiments have investigated the insurance
hypothesis by measuring how temporal variability of community and ecosystem properties vary among communities
that differ in the number of species they contain (see Cottingham et al. 2001 and Hooper et al. 2005 for reviews). Some
experiments support the hypothesis (Naeem et al. 1995;
Tilman 1996; McGrady-Steed, Harris & Morin 1997; Naeem
& Li 1997; McGrady-Steed & Morin 2000; Valone & Hoffman 2003; Dang, Chauvet & Gessner 2005; Steiner 2005;
Steiner et al. 2005; Tilman, Reich & Knops 2006; Vogt,
Romanuk & Kolasa 2006; Zhang & Zhang 2006; Bezemer &
van der Putten 2007; van Ruijven & Berendse 2007), while
others do not (Dodd et al. 1994; Wardle et al. 1999; Petchey
2000a; Petchey et al. 2002; Gonzalez & Descamps-Julien
2004; Morin & McGrady-Steed 2004).
Some studies have attempted to distinguish among the
multiple non-mutually exclusive and potentially non-independent biological and statistical mechanisms that could produce an insurance effect of biodiversity (e.g. Valone &
Hoffman 2003; Steiner 2005; Steiner et al. 2005; Vogt et al.
2006; Zhang & Zhang 2006). Biological mechanisms include
differences in how species respond to changes in environmental conditions, over-yielding and competition (Ives, Gross &
Klug 1999; Tilman 1999; Cottingham et al. 2001; Ives &
2009 The Authors. Journal compilation 2009 British Ecological Society
1144 D. J. Leary & O. L. Petchey
Hughes 2002). Different responses of species to environmental fluctuation may reduce temporal variability of ecosystem
properties by creating negative covariance between some
populations. Negative covariance causes fluctuations in some
populations’ biomass to be compensated for by opposite
direction fluctuations in the biomass of other populations
(Yachi & Loreau 1999). Over-yielding results from niche
differentiation or resource use complementarity between
species (Tilman, Lehman & Bristow 1998). When over-yielding
occurs, the magnitude of an ecosystem property increases
with species richness, reducing the impact of population variance on temporal variability of the ecosystem property
(Valone & Hoffman 2003). Competition impacts community
stability through its effect on population sizes, both separately and in concert with other biological factors. All else
being equal, competition will have a stabilizing influence by
leading to negative covariance between populations (Tilman
1999). However, mechanistic models of population and community dynamics suggest that while stronger competition
may increase negative covariance, it also tends to increase
species’ variance and therefore has little net effect on community stability (Ives et al. 1999).
The statistical mechanism relevant to the insurance
hypothesis – known as statistical averaging or the portfolio
effect – operates depending on two conditions (Doak et al.
1998; Tilman et al. 1998). First, as the number of species added
to a community increases, the biomass of individual species
decreases, as a result of density compensation. Second, if the
variance (r2) in the biomass of each species (i) scales with
mean (m) according to the power function ri = cmiz, where c
is a constant and z is a scaling factor, z must be greater than
one. When z is greater than one, reductions in biomass of each
population disproportionately decrease their variance.
The general approach that dominates efforts to understand which mechanisms are responsible involves decomposition of biomass dynamics into three statistical components:
summed variances, summed covariances and total biomass
(Tilman 1999; Lehman & Tilman 2000). Seven of the studies
which report an insurance effect and used this approach did
not find any relationship between species richness and covariance (Valone & Hoffman 2003; Steiner 2005; Steiner et al.
2005; Romanuk, Vogt & Kolasa 2006, 2009; Vogt et al. 2006;
Zhang & Zhang 2006). However, none of the biological processes that drive negative covariance were measured or
manipulated in these studies. Such phenomenological studies
of the insurance hypothesis will have much greater value
when supported by experimental manipulations designed to
detect the importance of different stabilizing or destabilizing
mechanisms, for example, by controlling and manipulating
the biological prerequisites for these mechanisms to occur
(Ives & Carpenter 2007).
Here we determine whether difference in species’ responses
to environmental variations provide a mechanism for the
insurance hypothesis. Our study system comprised laboratory microcosms containing aquatic micro-organisms
(ciliates and bacteria), which have short generation times
(12–24 hours approximately for ciliates, 2–6 hours approxi-
mately for bacteria; Fenchel 1987). Several previous studies
of the insurance hypothesis have used similar systems
(McGrady-Steed et al. 1997; Naeem & Li 1997) which allow
stringent control of environmental conditions and many generations of population dynamics to occur over a few weeks
(Lawler 1998; Jessup et al. 2004; Srivastava et al. 2004).
Observation of long-term population dynamics is vital for
testing the mechanisms of the insurance hypothesis; changes
in the size of populations which occur over multiple generations are explicit in the theories and mechanisms.
Environmental temperature is known to affect the
intrinsic rate of increase (r) and carrying capacity (K) of
ciliates (Fox & Morin 2001; Jiang & Morin 2004). Both
parameters have a unimodal relationship with temperature, and temperature can have a positive, negative or
neutral effect on a species’ r and K depending on the
species and the temperature range considered (Fox &
Morin 2001; Jiang & Morin 2004). This makes possible
two ways to manipulate the difference in responses to
temperature exhibited by species within a community: by
changing the identity of species and by altering the range
of temperatures used. Here, both approaches were used
to manipulate the difference in responses between species
in experimental communities containing two species. This
manipulates the component of biodiversity termed ‘functional response diversity’ (Dı́az & Cabido 2001). Holding
species richness constant prevented difference in species
responses to environmental fluctuation being confounded
by variation in species richness, and also prevented any
statistical averaging ⁄ the portfolio effect.
We tested the following predictions: communities containing species that respond more differently to environmental
fluctuation will be more stable, in terms of lower temporal
variability of total biomass and exhibit more negative covariance between population biomasses. Empirical support for
these predictions would indicate that biological differences
among species are an important mechanism responsible for
the stabilizing effects predicted by the insurance hypothesis.
Materials and methods
COMMUNITY ASSEMBLY AND MAINTENANCE
Aquatic communities were established using methods similar to
Lawler & Morin (1993). Microcosms were 200-mL glass jars
containing two wheat seeds and 100 mL of liquid medium covered
with aluminium foil. The medium was prepared from rainwater with
0Æ55 gL)1 of crushed protozoan pellet (Carolina Biological Supply,
Burlington, NC, USA) added to provide nutrients. The medium was
inoculated with three species of bacteria: Bacillus cereus (Frankland
and Frankland), Bacillus subtilus (Ehrenberg), and Serratia marcescens (Bizio). These grew for 24 hours before ciliates were added. Four
species of ciliates were used in the experiments: Colpidium striatum
(Stokes; hereafter referred to as Colpidium or C – mean cell mass
6Æ30 · 10)5 lg), Loxocephallus sp. (Eberhard; hereafter referred to
as Loxocephallus or L – 1Æ16 · 10)5 lg), Paramecium caudatum
(Ehrenberg; hereafter referred to as Paramecium or P –
6Æ70 · 10)5 lg) and Tetrahymena pyriformis (Ehrenberg; hereafter
referred to as Tetrahymena or T – 2Æ78 · 10)6 lg). Individuals of
2009 The Authors. Journal compilation 2009 British Ecological Society, Journal of Animal Ecology, 78, 1143–1151
Species’ responses and community stability 1145
Three replicates of each species were grown at each temperature (18,
20, 22, 24 and 26 C), for a total of 60 microcosms. About 50–100
individuals of each species were introduced to each microcosm. Adding a low density of each species ensured density-independent initial
growth. Population density was sampled daily throughout the period
of exponential growth until several data points at a similar density
had been obtained.
Intrinsic rate of increase (r) for each population was the slope of
the regression of ln(Nt) on t where: ln is natural log and Nt is
the population density at time t, during the period of exponential
growth (Fox & Morin 2001). The period of exponential growth was
identified for each replicate separately by visual inspection of the
population dynamics (Fox & Morin 2001). Apart from Colpidium at
24 and 26 C, the r2 values of the regressions were 0Æ79 in one case
and otherwise >0Æ90, indicating that exponential growth occurs during the selected period (Supporting Information, Fig. S1).
Carrying capacity (K) was the highest population biomass for each
population. Longer experiments and or over-compensatory dynamics could, in theory, affect this measurement method. Results were,
however, qualitatively identical when carrying capacity was the mean
of the highest two or three values.
Theoretical models of the insurance hypothesis most often assume
that values of r and K do not differ greatly between species (Yachi &
Loreau 1999; Ives & Hughes 2002). To test this assumption, we
modelled the effect of species identity and temperature on r and K
with species identity as a categorical variable and temperature (linear,
quadratic and cubic variables) as a continuous variable. Values of K
were log10-transformed to meet model assumptions.
QUANTIFYING DIFFERENCES BETWEEN SPECIES’
RESPONSES TO TEMPERATURE
The single-species responses to temperature were used to calculate
a measure of the difference in the response of pairs of species to
environmental fluctuations (i.e. functional response diversity). A
Pearson’s correlation coefficient was calculated for each combination of r and log10(K), species pair (CL, CP, CT, LP, LT, PT) and
temperature range (18–22, 20–24 and 22–26 C), giving 18 correlations for each of r and K. Three temperature ranges allowed for tests
of effects within species compositions. Overlapping temperature
ranges were because of logistical constraints.
(a)
4
Intrinsic rate of increase (r)
SINGLE-SPECIES RESPONSES TO TEMPERATURE
Each correlation coefficient describes the difference in species
responses to temperature on a scale of +1 to )1. Positive values indicate two species that respond in a similar way and negative values
that they respond differently. Because there were three replicates of
each species at each temperature, the average correlation for all nine
possible pairs was calculated for each species pair and temperature
range.
We wished to test if correlations between r of two species (and
between K of two species) varied among the species pairs and temperature ranges (e.g. Figs 1b and 2b). Two-way anova is an inappropriate model for this data. The overlapping temperature ranges result in
some r and some K values being used more than once in the subsequent analyses and such non-independence invalidates P-values in
parametric models. We therefore used the bootstrap approach
(Manly 1997) to test whether patterns were different from a random
expectation. This involved randomizing the values of r (or K) among
the microcosms, calculating the correlations, and then calculating the
random value of a test statistic (e.g. F-value, slope or correlation,
depending on the specific analysis), and repeating this process 1000
times to produce a distribution of random values of the test statistic.
Tetrahymena
Loxocephalus
Colpidium
Paramecium
3
2
1
0
18
20
22
24
26
Temperature (°C)
(b)
Correlation in intrinsic rates of increase
these species grow, die, respire, compete for bacteria and influence
many ecosystem processes such as decomposition rate, community
respiration and invasion resistance (McGrady-Steed et al. 1997).
Microcosms were maintained at five different temperatures; 18,
20, 22, 24 and 26 C. Microcosms at 18 C were placed in an incubator, those at 20 C on a work surface in a controlled temperature
(CT) room and those at 22–26 C in separate water baths in the
20 C CT room. Microcosms were arranged randomly in each location and kept in the dark.
To estimate ciliate abundance, the medium in each microcosm was
homogenized with a Pasteur pipette and a small volume (c. 0Æ33 mL)
was removed. The number of cells was counted under a dissecting
microscope, with dilution as necessary. Abundance was converted
into biomass per millilitre by multiplying density per millilitre by the
mean cell mass of each species. Mean cell mass was calculated by
inserting cell dimensions measured from 10 cells of each species into
the formula of an appropriate geometric shape (Wetzel & Likens
1991) and assuming 1 mL = 1 g.
1·0
0·5
0·0
–0·5
18–22 °C
20–24 °C
22–26 °C
–1·0
CL
CP
CT
LP
LT
PT
Species pair
Fig. 1. (a) Response of intrinsic rate of increase (r, per day) to temperature and species identity. Each data point is from a separate singlespecies population. Solid lines are the predictions of a regression
model with species identity as a categorical explanatory variable and
linear, quadratic and cubic continuous temperature variables (also
see Table 1). (b) Value of correlation coefficients for correlations of r
between pairs of species. Correlations were calculated for three different temperature ranges. Error bars are ± 1 SE. Species pair codes
refer to the species’ initial letters: C, Colpidium; L, Loxocephallus;
P, Paramecium; T, Tetrahymena.
2009 The Authors. Journal compilation 2009 British Ecological Society, Journal of Animal Ecology, 78, 1143–1151
1146 D. J. Leary & O. L. Petchey
with correlation as the continuous explanatory variable and species
pair as the categorical explanatory variable, because of the dependencies between correlation values (caused by overlapping temperature
ranges). Instead we used two randomization tests, one to test for
effects within species pairs, and another to test the combined effect of
differences within and among species pairs. To test for effects within
species pairs the r (or K) values were randomized only within species
pairs, whereas values were randomized irrespective of species pair to
test for the combined effect. The test statistic in both cases was the
slope of the relationship. If the observed slope was in the upper or
lower 2Æ5% of the distribution of slopes produced from the randomized data, we concluded that the observed slopes were significantly
different from the random.
In three microcosms (two replicates of the PT species pair in the
20–24 C temperature range and one replicate from the PT species
pair in the 22–26 C temperature range), either one or both of the
populations were not counted within a day. Responses for these
microcosms were therefore calculated from time series of 25 rather
than 26 data points.
To test for a significant interaction between species pair and temperature range, values of r (or K) were randomized only within species
and the test statistic was the interaction term’s F-value. The P-value
is given by comparing the distribution of randomized F-values with
the real F-value. This approach solves the problem of non-independence by including the dependencies between data points in the test
statistic distribution.
COMMUNITY RESPONSES TO TEMPERATURE
Communities containing all pairings of the four ciliate species (CP,
CL, CT, LP, LT, PT) were assembled and cycled through one of three
temperature ranges, 18–22, 20–24 and 22–26 C. Each combination
of species pair and temperature range was replicated thrice, for a total
of 54 microcosms. Temperature was fluctuated by moving communities between temperatures in 2 C increments every four days. A complete cycle of temperature fluctuation was low, medium, high,
medium, low (e.g. 18, 20, 22, 20 and 18 C). Four days corresponds
to 5–10 generations of the ciliates used in this experiment. Microcosms were cycled through each temperature range thrice over the
52-day duration of the experiment.
Population density was sampled every two days starting the day
after community assembly, producing time series with 26 data points.
As a precaution against extinctions, 1 mL of stock (c. 100–1000 individuals) of each species was added to each community every four
days. For the duration of the experiment, all species coexisted and
maintained population sizes of at least 100,000 individuals, suggesting that this immigration had little effect on dynamics. To maintain
nutrient levels, 10% of the medium within each microcosm was
replaced every four days with sterile nutrient medium.
Five components of community-level dynamics were calculated: (i)
temporal variability of total biomass; (ii) summed covariance of population biomasses; (iii) correlation between population biomasses;
(iv) summed variance of population biomasses; and (v) temporal
mean of total biomass. Temporal variability of total community biomass is the inverse of temporal stability and was measured by summing the biomass per millilitre of the two species at each sampling
interval and calculating the coefficient of variation (CV) through
time. CV measures temporal variability scaled to the mean (Gaston
& McArdle 1994) and has been used in previous experimental studies
investigating insurance hypothesis, and is comparable with measures
used in theoretical studies.
The effects of correlation between species’ r and K were investigated separately for each of these five components of community
dynamics. Again, we could not use a parametric test such as ancova,
Results
SINGLE-SPECIES RESPONSES TO TEMPERATURE
Temperature had strong and consistent effects on the intrinsic rate of increase (r) that differed among the four species
(Fig. 1a). The growth rate of Paramecium and Loxocephallus
increased continuously from 18 C to 26 C (Fig. 1a). The
growth rate of Tetrahymena reached a maximum at 22–24 C
and the growth rate of Colpidium decreased from 20 C to
26 C (Fig. 1a). These differences among species caused a significant interaction between species’ identity and linear, quadratic and cubic temperature in a linear model (Table 1;
Supporting Information, Fig. S2). The quadratic and cubic
interaction terms indicate that not only do species differ in
how they respond to temperature, but the nature of the differences depends on the temperatures considered. Colpidium
was the only species to exhibit any evidence of near-lethal
effects of temperature, as it did not show net growth in one
replicate at 24 C and all the three replicates at 26 C.
Temperature also had a significant effect on log10-carrying
capacity (K) that differed among the four species (Fig. 2a).
The carrying capacity of Tetrahymena, Loxocephallus and
Table 1. Summary of the statistical significance of effects of temperature and species identity on intrinsic rate of increase (r) and carrying
capacity [log10(K)]. Also see figures in Supporting Information
r
Species identity (Spp.ID)
Temperature (Temp.)
Temperature2 (Temp.2)
Temperature3 (Temp.3)
Spp.ID · Temp.
Spp.ID · Temp.2
Spp.ID · Temp.3
Error
K
F-value
P
F- value
P
716Æ8
131Æ1
7Æ88
0Æ68
120Æ8
7Æ3
4Æ0
<2Æ2 · 10)16
8Æ8 · 10)15
0Æ0074
0Æ41
<2Æ2 · 10)16
0Æ00044
0Æ014
9Æ8
3Æ1
7Æ8
0Æ47
3Æ2
5Æ6
0Æ32
<2Æ2 · 10)16
5Æ1 · 10)6
4Æ6 · 10)5
0Æ30
2Æ3 · 10)10
5Æ1 · 10)7
0Æ26
2009 The Authors. Journal compilation 2009 British Ecological Society, Journal of Animal Ecology, 78, 1143–1151
Species’ responses and community stability 1147
(a)
that were caused by the lack of Colpidium growth in the high
(24–26 C) temperature range.
Mean values of correlation between species’ K ranged from
about )0Æ4 to +0Æ9 (Fig. 2b), and there was a significant
interaction effect of species pair and temperature range (randomization test, P = 0Æ008). The very low carrying capacity
of Colpidium at 26 C contributed to some of the strong positive correlations (Fig. 2b; pairs CL and CT).
Carrying capacity [log10(K)]
4
3
2
Tetrahymena
Loxocephalus
Colpidium
Paramecium
1
COMMUNITY RESPONSES TO TEMPERATURE
18
20
22
24
Temperature (°C)
26
Correlation in carrying capacities
(b)
1·0
0·5
0·0
–0·5
–1·0
18–22 °C
20–24 °C
22–26 °C
CL
CP
CT
LP
LT
PT
Species pair
Fig. 2. (a) Response of carrying capacity (K) to temperature and species identity. (b) Values of correlation coefficients for correlations of
log10(K) between pairs of species. All other details are as in Fig. 1.
Paramecium were relatively constant across the temperature
range, while that of Colpidium decreased from 22 C to
26 C. Across the entire temperature range, a regression
model indicated a significant interaction between species
identity and linear and quadratic temperatures (Table 1;
Supporting Information, Fig. S3). This significant interaction
was partly because of the decrease in the carrying capacity of
Colpidium at higher temperatures. Removal of Colpidium
from the analysis results in stronger and significant quadratic
and cubic terms. Thus, differences exist among the other
three species in how r and K respond to temperature, as well
as in comparison with Colpidium.
QUANTIFYING DIFFERENCES BETWEEN SPECIES’
RESPONSES TO TEMPERATURE
Different species pairings and temperature ranges created different correlations for both r and K (Figs 1b and 2b). Mean
values of correlation between species’ r varied from close to
)1Æ0 to close to +1Æ0 (Fig. 1b), and there was a significant
interaction between species pair and temperature range (randomization test, P < 0Æ001). In general, correlations were
less positive and more negative in the higher temperature
ranges, but the magnitude of this effect differed greatly
among species pairs. The species pairs containing Colpidium
(CL, CP, CT) contained some strong negative correlations
The qualitatively different responses of Colpidium to temperature, lack of growth of Colpidium in some high-temperature
microcosms and the consequent lack of fit of the regression
model used to estimate r values, led us to conduct all analyses
with or without Colpidium data (pairs CL, CP and CT).
None of the five components of community dynamics were
significantly associated with correlation in growth rate (without Colpdium Fig. 3a–e; with Colpidium Fig. 4a–e; Table 2).
All randomization-based P-values were greater than 0Æ05
except the within CL (Fig. 4c, e) and LP communities
(Fig. 3b, e).
There were significant associations between three of the
components of community dynamics and the correlation in
carrying capacity (without Colpidium Fig. 3f–j; Table 2).
Communities containing species whose carrying capacities
responded more similarly to temperature fluctuations were
less stable (i.e. higher CV; Fig. 3f), had more positive covariances (Fig. 3g) and greater correlation between population
sizes (Fig. 3h). The overall relationships (including variation
within and among species pairs) were all significant at
P < 0Æ05 and those for CV and covariance were significant
at P < 0Æ01. There were no significant relationships within
any species pair. In the presence of communities containing
Colpidium, there were no statistically significant relationships.
Discussion
A core mechanism of the insurance hypothesis of biodiversity
is stabilizing effects of compensatory dynamics of species
with different responses to environmental variation (Ives
et al. 1999). In our experiment and consistent with predictions, communities containing species which responded more
differently to environmental fluctuations had lower temporal
variability of total biomass, and more negative covariance
between populations (Fig. 3f, g). Results also indicated that
species identity played an important role. Colpidium exhibited a qualitatively different response to temperature, with
lack of growth at higher temperatures. When communities
containing Colpidium were included in analyses, the results
were non-significant. These findings provide evidence that
species with different responses to environmental variation
can contribute a stabilizing force through their effect on
population covariances, but also that species identities play
an important role in whether this stabilizing effect is
observed.
2009 The Authors. Journal compilation 2009 British Ecological Society, Journal of Animal Ecology, 78, 1143–1151
1148 D. J. Leary & O. L. Petchey
0·4
0·3
0·5
5e–05
–5e–05
0·0
–1·0 –0·5
0·0
0·5
1·0
Intrinsic growth rate correlation
(g)
0·6
0·5
0·4
0·3
(h)
(i)
0·5
5e–05
–5e–05
Sum of variances
Summed covariances
0·7
0e+00
–1·0 –0·5
0·0
0·5
1·0
Intrinsic growth rate correlation
–1·0 –0·5
0·0
0·5
1·0
Intrinsic growth rate correlation
Correlation
CV of population biomass
(f)
0·0
8e–04
4e–04
–0·5
0·2
–1·0 –0·5
0·0
0·5
1·0
Carrying capacity correlation
–1·0 –0·5
0·0
0·5
1·0
Carrying capacity correlation
4e–04
–0·5
0·2
–1·0 –0·5
0·0
0·5
1·0
Intrinsic growth rate correlation
8e–04
0e+00
–1·0 –0·5
0·0
0·5
1·0
Carrying capacity correlation
–1·0 –0·5
0·0
0·5
1·0
Carrying capacity correlation
(e)
Mean total population biomass
0·5
(d)
Sum of variances
0·6
(c)
Correlation
0·7
18–22 °C
20–24 °C
22–26 °C
0·040
0·030
0·020
0·010
–1·0 –0·5
0·0
0·5
1·0
Intrinsic growth rate correlation
(j)
Mean total population biomass
(b)
LP
LT
PT
Summed covariances
CV of population biomass
(a)
0·040
0·030
0·020
0·010
–1·0 –0·5
0·0
0·5
1·0
Carrying capacity correlation
Fig. 3. Associations between correlations of species’ responses to temperature change on five components of community dynamics. The top row
(a–e) contains associations with correlation in species’ intrinsic rate of increase (r). The bottom row (f–j) contains associations with correlations
in species’ carrying capacities (K). Solid lines indicate a relationship significant at P < 0Æ01; dashed lines, significant at P < 0Æ05; and dotted
lines, P > 0Æ05. Black lines show the overall relationship (ignoring species pair) while the grey lines show the within-pair relationships. Species
pair codes refer to the species’ initial letter: L, Loxocephallus; P, Paramecium; T, Tetrahymena. Biomass units are milligrams per millilitre.
0·4
0·3
0·2
–1·0 –0·5
0·0
0·5
1·0
Intrinsic growth rate correlation
(f)
0·006
0·5
4e–04
2e–04
0e+00
0·0
–0·5
–2e–04
–1·0 –0·5
0·0
0·5
1·0
Intrinsic growth rate correlation
(g)
(i)
0·4
0·3
0·2
–1·0 –0·5
0·0
0·5
1·0
Carrying capacity correlation
0·5
4e–04
2e–04
0e+00
–2e–04
–1·0 –0·5
0·0
0·5
1·0
Carrying capacity correlation
Sum of variances
0·5
0·006
Correlation
0·6
Summed covariances
CV of population biomass
6e–04
0·7
0·002
0·000
–1·0 –0·5
0·0
0·5
1·0
Intrinsic growth rate correlation
–1·0 –0·5
0·0
0·5
1·0
Intrinsic growth rate correlation
(h)
0·004
0·0
–0·5
–1·0 –0·5
0·0
0·5
1·0
Carrying capacity correlation
0·004
0·002
0·000
–1·0 –0·5
0·0
0·5
1·0
Carrying capacity correlation
(e)
Mean total population biomass
0·5
(d)
Sum of variances
0·6
(c)
6e–04
Correlation
0·7
18–22 °C
20–24 °C
22–26 °C
0·08
0·06
0·04
0·02
–1·0 –0·5
0·0
0·5
1·0
Intrinsic growth rate correlation
(j)
Mean total population biomass
(b)
CL
CT
LP
LT
PT
Summed covariances
CV of population biomass
(a)
0·08
0·06
0·04
0·02
–1·0 –0·5
0·0
0·5
1·0
Carrying capacity correlation
Fig. 4. Associations between correlations of species’ responses to temperature change on five components of community dynamics. The top row
(a–e) contains associations with correlation in species’ intrinsic rate of increase (r). The bottom row (f–j) contains associations with correlations
in species’ carrying capacities (K). Solid lines indicate a relationship significant at P < 0Æ01; dashed lines, significant at P < 0Æ05; and dotted
lines, P > 0Æ05. Black lines show the overall relationship (ignoring species pair) while the grey lines show the within-pair relationships. Species
pair codes refer to the species’ initial letter: C, Colpidium, L, Loxocephallus, P, Paramecium, T, Tetrahymena. Biomass units are milligrams per
millilitre.
Some previous experimental manipulations of biodiversity
have found no relationship between species richness and the
temporal variability of community properties (Dodd et al.
1994; Tilman 1996; Wardle et al. 1999; Petchey 2000a; Petchey et al. 2002; Gonzalez & Descamps-Julien 2004; Morin &
McGrady-Steed 2004). Our results provide one possible
explanation. Unless the environment varies, and does so in a
range across which species responses to environmental conditions differ, an insurance effect may not occur. Therefore,
unless we know more about the responses of species to environmental variation, studies finding no evidence can be diffi-
cult to interpret as evidence for the general lack of such an
effect. Another environmental characteristic that could be
important to the functioning of insurance effects is the temporal scale and pattern of environmental variation. Ideally,
investigations of insurance effects of biodiversity would
include variation in the frequency and other characteristics of
environmental variation (e.g. Petchey 2000b; Dang et al.
2009).
Other studies demonstrate a significant stabilizing effect of
species richness (Tilman 1996; McGrady-Steed et al. 1997;
Naeem & Li 1997; McGrady-Steed & Morin 2000; Valone &
2009 The Authors. Journal compilation 2009 British Ecological Society, Journal of Animal Ecology, 78, 1143–1151
Species’ responses and community stability 1149
Table 2. Summary statistics for relationships between the five community-level response variables and the two species-level predictor variables,
for data sets including or excluding Colpidium
Analyses excluding Colpidium
Explanatory variable
Response variable
Slope
r correlation
Coefficient of variation
Covariances
Correlations
Variances
Biomasses
Coefficient of variation
Covariances
Correlations
Variances
Biomasses
)0Æ10
)2Æ30 ·
)0Æ238
1Æ00 ·
0Æ01
0Æ26
1Æ10 ·
0Æ84
7Æ77 ·
)0Æ004
K correlation
10)5
10)4
10)4
10)5
Hoffman 2003; Steiner 2005; Steiner et al. 2005; Vogt et al.
2006; Zhang & Zhang 2006; Bezemer et al., 2007; van Ruijven
& Berendse 2007). In some of these, increased species richness
had no detectable effect on covariance (Valone & Hoffman
2003; Steiner 2005; Steiner et al. 2005; Vogt et al. 2006; Zhang
& Zhang 2006). Similarly, there appears to be a limited negative covariance among population fluctuations in natural
communities (Houlahan et al. 2008; Valone & Barber 2008;
Winfree & Kremen 2009). The implications of these findings
for insurance hypothesis are difficult to be known, however.
Calculating total covariance over many species can hide
potentially important stabilizing pairs of species and give
very limited information about biological mechanisms. This
point was made very clearly in table 4 of Schluter (1984),
where competition, predation, mutualism and no interaction
can each result in positive, negative or no association between
species abundances. Schluter concluded that there is no necessary correspondence between ‘variance tests’ (Schluter’s
method for detecting community-wide covariance) and any
ecological process. Any test of the insurance hypothesis will
have much greater value when supported by experimental
manipulations designed to detect the importance of different
stabilizing or destabilizing mechanisms.
Theoretical models suggest that different responses to
environmental variability should have a net stabilizing effect
(Ives et al. 1999; Ives & Hughes 2002). Such models often
assume that species make an equal per capita contribution to
total community biomass, have the same average r and K and
the same competitive ability, that is, per capita effect on each
other’s biomass (e.g. Ives & Hughes 2002). These conditions
result in a relatively even distribution of biomass between
species when averaged through time (Doak et al. 1998;
Schwartz et al. 2000). In our experiment, species exhibited
difference in per capita contributions to community biomass
of up to an order of magnitude difference. Values of r and K
differed between species, and it is possible that the strength of
competition varied. These factors resulted in an uneven distribution of total biomass between species in our experiment;
dominance by one species was particularly marked in communities which contained Tetrahymena, with Tetrahymena
Analyses including Colpidium
r2
P
Slope
r2
P
0Æ06
0Æ04
0Æ06
0Æ03
0Æ10
0Æ17
0Æ33
0Æ24
0Æ00
0Æ10
0Æ36
0Æ39
0Æ44
0Æ42
0Æ38
0Æ01
0Æ003
0Æ04
0Æ40
0Æ38
)0Æ02
)5Æ60 · 10)5
)0Æ03
)0Æ001
)0Æ02
0Æ07
2Æ0 · 10)4
0Æ57
0Æ001
0Æ03
0Æ01
0Æ06
0Æ00
0Æ19
0Æ35
0Æ03
0Æ21
0Æ15
0Æ08
0Æ20
0Æ43
0Æ41
0Æ46
0Æ34
0Æ29
0Æ18
0Æ06
0Æ09
0Æ18
0Æ08
contributing little towards total biomass. The models also
assume that a species’ competitive ability is not a function of
the environment, whereas it is possible that the strength of
competition was affected by temperature in our experiment.
With these differences between the general theoretical models
and the conditions of this experiment, it is perhaps surprising
that our results match the general theoretical predictions.
One explanation is that the stabilizing effect of differential
species responses is relatively strong, compared with other
processes such as changes in interaction strength with temperature. A deeper understanding of the results of this experiment requires, for example, an accurate dynamic model of
the experimental system.
Contrary to the differences in responses of carrying capacity to temperature, differences in species’ intrinsic rate of
increase to temperature were not associated with community-level variability or covariance, or any other component
of community dynamics (Fig. 3a–e). While our data are not
ideal for understanding this difference, because of the different distributions of correlation values for intrinsic growth
rates and for carrying capacity, they argue for caution when
assessing the importance of this mechanism of insurance
hypothesis. Lack of evidence for insurance hypothesis could
result from measuring inappropriate aspects of species
responses to environmental variation. One solution to this
problem is a closer coupling of empirical observations with
theoretical models of community dynamics. For example, a
theoretical model could test whether our intuitive explanation about the lack of effect of r is a mathematically sound
explanation of the quantitative patterns in community
dynamics. Fischer, Frost & Ives (2001) successfully coupled
autoregressive models and data to show that compensatory
dynamics occurred within functional groups of zooplankton
if species responded differentially to acidification. Conversely, they found that synchronous dynamics occurred
within functional groups of species that responded similarly
to environmental variation. Their work shows that careful
coupling of model and data can provide important insights
into the drivers of community stability in natural and diverse
ecosystems.
2009 The Authors. Journal compilation 2009 British Ecological Society, Journal of Animal Ecology, 78, 1143–1151
1150 D. J. Leary & O. L. Petchey
According to the insurance hypothesis, high species richness within communities decreases the temporal variability
of community properties, potentially increasing the reliability
of the provision of ecosystem services (Naeem 1998; Yachi &
Loreau 1999). While this idea has gained prominence, investigations have focused on statistical and phenomenological
approaches to dissecting the mechanisms responsible (e.g.
Doak et al. 1998; McGrady-Steed & Morin 2000; Steiner
et al. 2005). Our experiment shows that a stabilizing mechanism – difference in species responses to environmental fluctuations – operates by increasing negative covariance
between population abundances and that this leads to greater
stability of community dynamics. The approach that we have
taken is to study and record information about individual
species and to use that information to make predictions at
the community level. This is similar in concept to measuring
the functional characteristics of species and using them to
predict community- and ecosystem-level features (e.g. Petchey & Gaston 2006). We measured the response to the environment of species characteristics likely to impact
community-level properties; the term ‘response functional
trait’ describes such traits, and the term ‘functional response
diversity’, the diversity of such traits. Integrating studies of
the insurance effect of biodiversity with the concept of
response functional diversity may allow our general method
to transfer to real and diverse ecological systems, and ultimately aid in understanding how biodiversity loss may compromise the sustainable delivery of ecosystem services.
Acknowledgements
D.J. Leary was funded by a NERC Studentship; O.L. Petchey was
funded by a Royal Society University Research Fellowship. Tamara
Romanuk, Sara Blanchard and various anonymous reviewers helped
with the previous versions of this paper.
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Received 2 March 2009; accepted 4 June 2009
Handling Editor: Guy Woodward
Supporting Information
Additional supporting information may be found in the online version of this article.
Fig. S1. Single-species population dynamics used to estimate
intrinsic rate of increase (r) and carrying capacity (K). Grey-filled
symbols indicate those used to calculate r. The r2 value is the
regression of population size in time and is given for each of the
three replicates.
Fig. S2. Residual plots of the linear model of response of intrinsic
growth rate to temperature. Also see Table 1 and Fig. 1a.
Fig. S3. Residual plots of the linear model of response of carrying
capacity to temperature. Also see Table 1 and Fig. 2a. Low fitted values are for Colpidium, and suggested checking for robustness of
results to the presence ⁄ absence in the data set of Colpidium.
Please note: Wiley-Blackwell are not responsible for the content or
functionality of any supporting information supplied by the authors.
Any queries (other than missing material) should be directed to the
corresponding author for the article.
2009 The Authors. Journal compilation 2009 British Ecological Society, Journal of Animal Ecology, 78, 1143–1151