The temperature dependence of microbial community respiration is amplified by changes in species interactions

Abstract

Respiratory release of CO2 by microorganisms is one of the main components of the global carbon cycle. However, there are large uncertainties regarding the effects of climate warming on the respiration of microbial communities, owing to a lack of mechanistic, empirically tested theory that incorporates dynamic species interactions. We present a general mathematical model which predicts that thermal sensitivity of microbial community respiration increases as species interactions change from competition to facilitation (for example, commensalism, cooperation and mutualism). This is because facilitation disproportionately increases positive feedback between the thermal sensitivities of species-level metabolic and biomass accumulation rates at warmer temperatures. We experimentally validate our theoretical predictions in a community of eight bacterial taxa and show that a shift from competition to facilitation, after a month of co-adaptation, caused a 60% increase in the thermal sensitivity of respiration relative to de novo assembled communities that had not co-adapted. We propose that rapid changes in species interactions can substantially change the temperature dependence of microbial community respiration, which should be accounted for in future climate–carbon cycle models.

Full text

Nature Microbiology | Volume 8 | February 2023 | 272–283 272
nature microbiology
Article https://doi.org/10.1038/s41564-022-01283-w
The temperature dependence of microbial
community respiration is amplified by
changes in species interactions
Francisca C. García 1,3,4, Tom Clegg 2,4, Daniel Barrios O’Neill1, Ruth Warield1,
Samraat Pawar 2 & Gabriel Yvon-Durocher 1
Respiratory release of CO2 by microorganisms is one of the main
components of the global carbon cycle. However, there are large
uncertainties regarding the eects of climate warming on the respiration
of microbial communities, owing to a lack of mechanistic, empirically
tested theory that incorporates dynamic species interactions. We present
a general mathematical model which predicts that thermal sensitivity of
microbial community respiration increases as species interactions change
from competition to facilitation (for example, commensalism, cooperation
and mutualism). This is because facilitation disproportionately increases
positive feedback between the thermal sensitivities of species-level
metabolic and biomass accumulation rates at warmer temperatures.
We experimentally validate our theoretical predictions in a community of
eight bacterial taxa and show that a shift from competition to facilitation,
after a month of co-adaptation, caused a 60% increase in the thermal
sensitivity of respiration relative to de novo assembled communities that
had not co-adapted. We propose that rapid changes in species interactions
can substantially change the temperature dependence of microbial
community respiration, which should be accounted for in future climate–
carbon cycle models.
Empirical data show that ecosystem-level respiration generally follows
an exponential-like relationship with temperature
1
. These findings have
led to concerns that climatic warming will increase carbon emissions
from the biosphere, increasing positive feedbacks in the carbon cycle,
ultimately accelerating the rate of planetary warming
2–5
. Microbes,
and in particular bacteria, by conservative estimates make up ~20% of
Earth’s total biomass
6
and, by decomposing organic matter, account
for a major fraction of the thermal response of ecosystem-level respira-
tion
2,7
. For example, bacterial contribution to ecosystem respiration is
estimated to be >50% in some ocean biomes7,8. Consequently, even small
changes in the thermal sensitivity of microbial community respiration
may have substantial impacts on future global warming projections
8,9
.
However, the response of microbial community respiration to tem-
perature changes remains a key uncertainty in climate–carbon cycle
projections for the coming century and is also an unresolved question
in microbial ecology2,10,11.
Published models of temperature responses of complex ecosys-
tems typically assume that thermal responses can be scaled up from the
individual level to the ecosystem level by a simple, weighted sum of the
temperature responses of component species’ populations
9,12–15
. These
models only focus on the direct effect of temperature on metabolism,
ignoring the effects of interactions among species. However, species
Received: 19 August 2021
Accepted: 2 November 2022
Published online: 2 February 2023
Check for updates
1Environment and Sustainability Institute, University of Exeter, Penryn, UK. 2Georgina Mace Centre, Department of Life Sciences, Imperial College London,
Silwood Park Campus, Ascot, UK. 3Present address: Red Sea Research Centre, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia.
4These authors contributed equally: Francisca C. García, Tom Clegg. e-mail: s.pawar@imperial.ac.uk; g.yvon-durocher@exeter.ac.uk

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Article https://doi.org/10.1038/s41564-022-01283-w
Eeco 
N
i󰁞0RiTCiTER󰅁iEC󰅁i

N
i󰁞0RiTCiT

(2)
where E
R,i
and E
C,i
are the thermal sensitivities (apparent activation
energies) of mass-specific respiration and biomass dynamics of the ith
species’ population, respectively. Equation (2) shows that Eeco is given
by the average thermal sensitivities of biomass dynamics and respira-
tion across all species (strains) in the system, weighted by each species’
total respiratory output, R
i
(T)C
i
(T). Note that equation (2) also contains
temperature-dependent terms reflecting the effects of biomass dynam-
ics, which results in a non-exponential thermal response of total eco-
system respiration (Fig. 1b). Next, we consider how Eeco (equation (2))
is affected by pairwise interspecific interactions. Below, we will con-
sider the potential effects of indirect and higher order interactions
(HOIs) (Supplementary Information). Assuming that interactions do
not affect species’ mass-specific respiration rate R
i
(that is, a single
interactions, such as predation, competition and facilitation, drive
population dynamics in all ecosystems, determining the amount and
distribution of biomass across species’ populations and ultimately total
ecosystem respiration and its response to changes in temperature
16–21
.
Thus, by failing to account for the effects of species interactions, cur-
rent models may not be able to predict the response of ecosystem
respiration to changing temperatures.
In microbial communities in particular, demographic processes
and population turnover occur over relatively short timescales and
the temperature dependence of community respiration most likely
reflect both the direct effect of temperature on individual metabo-
lism as well as its indirect effects through species interaction-driven
biomass dynamics. Microbial taxa interact in numerous ways, ranging
from competition for limiting abiotic resources, to facilitation through
cross-feeding on metabolic byproducts
18–20
. Microbial metabolic traits
are temperature-sensitive, so when temperatures change this alters
interaction-driven biomass dynamics and thus community-level respi-
ration
21
. For example, widespread facilitation might amplify the effects
of temperature by creating a positive feedback loop due to enhanced
metabolic and growth rates in warmer conditions. Conversely, if weak
or neutral interactions occur, such as when species partition resources,
their populations might become relatively decoupled, resulting in a
response of community respiration to temperature that is a simple
sum of the thermal responses of individual taxa weighted by their
respective population biomasses. In general, if species interactions are
strong, so will be the feedbacks between populations, amplifying the
(positive or negative) effects of temperature across the whole system.
Here, we investigated the role of biotic interactions in the temperature
dependence of community metabolism by combining theory with
laboratory experiments.
Results
Modelling the temperature dependence of microbial
community respiration
Our mathematical model links the effects of species-level metabo-
lism and interspecies interactions to the thermal response of
community-level (henceforth, synonymous with ‘ecosystem-level’)
respiration (Fig. 1). A fundamental premise of our model is that species
interactions act primarily to affect species’ biomasses and have a negli-
gible effect on individual-level respiration rate, which is constrained by
cellular enzyme kinetics and is therefore driven directly by environmen-
tal temperature. We also focus on the stages of community assembly
and dynamics before populations reach carrying capacity for two key
reasons. First, the bulk of community respiratory flux occurs when
resource availability is high; for example, spring blooms in seasonal
aquatic systems
22
and litter fall in soils
23
, during which populations
are in near-exponential growth. Second, environmental perturba-
tions and immigration events in natural microbial communities mean
that these communities are constantly perturbed from equilibrium
over time24,25.
Consider a community comprising N interacting species. This
community’s total temperature (T)-dependent respiration rate (Reco(T))
depends on the sum of contributions of each population’s total respi-
ration, which in turn can be expressed as the product of mass-specific
respiration (Ri(T)) and biomass (Ci(T)) of each population:
Reco T
N

i󰁞0
RiTCiT
(1)
This equation implies that temperature affects community respira-
tion by changing mass-specific respiration of individual populations,
by changing their biomasses, or by both (Fig. 1a). Next, we derive the
thermal sensitivity of Reco(T) (the magnitude of change of community
respiration to a unit change in temperature in log scale), which we
denote by an apparent activation energy, Eeco (Methods):
a
2.3
2.5
2.7
2.9
Reco R C×
Mass-specific
respiration Biomass
Increased
respiration
Increased
growth rates
Interactions
(amplification)
=
3.1
a < 0 a = 0 a > 0
Interaction
Eective
Eeco (Ev)
−2
0
2
4
6
5 10 15 20 25
Temperature (°C)
Ecosystem respiration (log(Reco))
Competition
Neutral
Facilitation
b
Fig. 1 | Species interactions affect the temperature sensitivity of microbial
community respiration. a, Temperature can act on community-level respiration
either by affecting individual metabolism directly (increasing respiration)
or by affecting the amount of biomass, which is determined by the effects of
temperature on growth rates and interactions between species. b, Prediction
of the relationship between temperature and community respiration under
different interaction structures. Respiration becomes more sensitive to
temperature change as interactions become more positive. Main plot shows
community respiration, log(Reco) normalized to a common Tref (15 °C) at three
levels of interaction strength across the community. Note that the curves
are nonlinear in log scale because the thermal sensitivity of community
respiration (the slope of log(Reco) versus temperature) is itself temperature
dependent (equation (2)) due to the nonlinear change in biomass dynamics with
temperature as explained in the main text. Inset plot shows the resultant effective
thermal sensitivity Eeco measured at Tref. See Methods for parameter values used
to generate these specific theoretical predictions.

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strain cell will have roughly the same respiration rate in the presence
or absence of interactions), we focus on how they affect the biomass
terms (Ci and EC,i) in equation (2). We show that the thermal sensitivity
of community-level respiration can be partitioned as follows (Methods)
Eeco 
aγ NCov wiaER󰅁iωiERω
(3)
where

a
is the average of the interaction coefficients between all
species pairs (aij),
γ
=dr
dT
(N−1)C0t
2
2
is the average thermal sensitivity of
time (t)-dependent biomass across all populations (driven by
temperature-dependent changes in average population growth
rate

r
),
w
ia
R
i
C
i
a
󰞍
N
i󰅗0RiCia
is the weighting of the ith species’ contribu-
tion (its normalized respiratory output) and
ω
i=dri
dT
(t+t
2
aiiC0,i
2)
is the
thermal sensitivity of its biomass at time t. The dependence of these
weights on
a
arises through the effects of species interactions on
population biomasses (
Ci(a)
).
Our equation (3) shows that the thermal sensitivity of community
respiration is determined by three components: (1) the effect of
averaged interspecies interactions (
aγ
), (2) the covariation between
species’ responses to interactions (via the weighting terms) and their
thermal sensitivities
NCov wiaER󰅁iωi
and (3) the average ther-
mal sensitivities of respiration and biomass growth (not accounting
for interactions) across species in the community
(
ER+ω
)
. When
interactions are, on average, neutral
(a=0)
the first of these terms is
zero and community sensitivity is dependent only on internal factors
affecting species’ population growth (growth rates and intraspecific
interactions in the 𝜔 and covariance term). When interactions are
non-neutral
(a≠0)
they will either amplify or dampen the sensitivity
of community respiration relative to this neutral case (Fig. 1b). More
facilitatory (positive) interactions will increase (amplify) thermal
sensitivity, while competitive interactions will result in a reduction
(dampening) in sensitivity (including intransitive competition; Sup-
plementary Information). In general, stronger interactions (greater
absolute values of
a
) will result in greater changes in community-level
sensitivity. This amplification or dampening happens because interac-
tions modulate the rate of change in biomass with temperature across
the community (altered rates of biomass accumulation), captured by
the γ term.
M9 + Glucose
~100
generations
48-h growth
Dilution
Adapted
M9 + Glucose Byproducts Byproducts
Byproducts
M9 + Glucose
Quantifying temperature sensitivity
Ancestral and adapted individual taxa and communities
Metabolic facilitation assay
de novo
de novo and adapted communities assay
Byproducts
M9 + Glucose
× 6 replicates
Community adaptation experiment
M9 + Glucose
Ancestral
Adapted
Inferring species interactions
Byproducts
M9 + Glucose
A + B
A
Ancestral and adapted individual taxa and pairs assay
20 °C
20 °C
15 °C
20 °C
25 °C
27.5 °C
30 °C
32.5 °C
35 °C
Fig. 2 | Experimental design. First, an artificial community was created using
eight bacterial taxa and replicated six times. Communities were transferred
every 48 h for 100 generations. After 100 generations, the adapted communities
comprised five taxa that were able to stably coexist and were retained for further
experimentation. The five bacterial taxa that comprised the adapted community
were also isolated and maintained in monoculture. We then compared the
adapted communities and the adapted strains with communities assembled from
the ancestral strains—termed de novo assembled communities—in subsequent
assays. Adapted and de novo communities and strains were incubated in
M9 + glucose until the glucose was depleted and the metabolic byproducts
were preserved in sterile conditions to create spent media. To quantify the
effect of community adaptation on species interactions, ancestral and adapted
taxa were incubated in M9 + glucose and the corresponding spent medium in
a metabolic facilitation assay (Methods). To quantify the effects of changes
in species interactions on the temperature sensitivity of respiration at taxon
and community levels (Methods), the de novo and adapted communities (and
individual strains) were incubated in M9 + glucose and spent media across a
temperature gradient and respiration rates measured. Finally, de novo and
adapted taxa in all pairwise combinations were incubated in M9 + glucose and the
spent media to quantify changes in pairwise species interactions. Figure created
with BioRender.com.

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In addition to this direct effect, interactions can also alter com-
munity sensitivity through the covariance term in equation (3)
(
Cov wiaER󰅁iωi
), which arises when species whose biomass is
strongly affected by interactions (those with more extreme
wi(a)
values) also tend to have higher temperature sensitivities of respiration
and biomass accumulation
(ER,i+ωi)
). Although there is no empirical
evidence of such relationships, it is possible that this pattern exists in
nature. For example, in microbial communities it is possible that tem-
perature and resource specialization are positively correlated such
that species with wide thermal niches (and low thermal sensitivities)
also tend to be more general in their resource use (and thus are more
affected by competition imposing a negative covariance structure).
The relative effect of interactions through this covariance term will
depend on the correlation between these two factors as well as the size
of their variation across the community (greater variation in thermal
sensitivity allows for more bias towards high sensitivity values).
It is important to note that our theory focuses on pairwise
interactions between populations and does not explicitly consider
the effects of indirect and higher order interactions, which can be
important for shaping structure and function in microbial communi-
ties26–28. In particular, indirect interactions in the form of intransitive
(rock-paper-scissor type) competitive loops can affect co-existence
and biomass dynamics in communities27,28. We tested the effect of
intransitive interactions on our theoretical predictions and found that
they had no qualitative effect on amplification of the community-level
thermal response (Methods; Supplementary Fig. 1). Our theoretical
predictions above also do not explicitly consider HOIs, where one or
more non-focal species modify the direct interaction between a pair of
species
26,27
. In general, we expect the effects of HOIs will be to alter, but
not qualitatively reverse, community-level amplification or dampening
(Supplementary Information). Future work focusing on HOIs is needed
to build a more accurate understanding of the effects of these interac-
tions on microbial community functioning and its thermal response.
Experimental microbial communities show an amplified
thermal sensitivity of respiration rate
We tested our theoretical predictions using experiments with com-
munities of aerobic, heterotrophic bacteria. We assembled replicated
(n = 6) communities of eight bacterial taxa (henceforth, ‘strains’) iso-
lated from geothermal streams in Iceland and incubated them in a
minimal, single carbon source medium (M9 + glucose) at ambient tem-
perature (20 °C) using serial transfers for ~100 generations (Methods;
Fig. 2). This experimental design exploited the tendency of bacterial
strains to increase facilitation by cross-feeding (exchanging metabolic
byproducts) when subject to resource limitation over time, producing
replicated communities with the same strains but different interaction
structures
29–31
. We henceforth refer to these as ‘adapted’ communities.
As a control, we also assembled replicated communities using the same
ancestral strains but incubated them for a much shorter period of 2 d,
thus limiting the time available for co-adaptation (Methods) (we refer to
these as ‘de novo communities’). In the adapted communities, biomass
dynamics stabilized after 16 d (seven transfers, ~50 generations), with
five of the eight strains that were originally combined persisting at a
relatively stable total abundances. At the end of the experiment, after
30 d (14 transfers, ~100 generations), we re-isolated the strains from
each of the communities. We assessed whether community adaptation
affected the thermal response of respiration for each of the five strains
along a broad temperature gradient (15–35 °C), for populations from
both the de novo and the adapted communities. We found no signifi-
cant difference in any of the parameters of the temperature response
of respiration between the ancestral isolates and the same strains
isolated from the adapted communities (Fig. 3a and Supplementary
Table 1), showing that the population-level temperature response of
mass-specific respiration remained unchanged following adaptation,
consistent with our theoretical assumption.
Our theory predicts that the thermal sensitivity of total commu-
nity respiration should be higher in the adapted communities, where
interactions were expected to have become less competitive (or more
cooperative or facilitatory), compared to de novo communities. To test
whether it was indeed facilitation through cross-feeding on metabolic
byproducts driving changes in interactions, we carried out community
respiration assays in both M9 + glucose and ‘spent’ media obtained by
allowing communities to grow until all the initial glucose was depleted
and only metabolic byproducts remained (Methods). If an increase
in metabolic facilitation is the main mechanism underlying changes
in species interactions, then we expected to see an amplification of
the thermal sensitivity of respiration in the adapted communities in
the spent media because the strains that comprise these communi
-
ties would have adapted to persisting on the metabolic byproducts,
whereas the de novo assembled communities would not. By contrast,
0.5
1.0
1.5
2.0
Adapted de novo
Treatment
Ea(eV)
−8
−4
0
4
a b c
15 20 25 30 35
Temperature (°C)
15 20 25 30 35
Temperature (°C)
15 20 25 30 35
Temperature (°C)
ln(rate (mgO2 l−1 h−1))
ln(rate (mgO2 l−1 h−1))
ln(rate (mgO2 l−1 h−1))
0.9
1.0
1.1
1.2
1.3
Adapted de novo
Treatment
−1
0
1
2
3
0.50
0.75
1.00
1.25
1.50
Adapted de novo
Treatment
−1
0
1
2
3
Ea(eV)
Ea(eV)
Fig. 3 | Microbial facilitation amplifies the temperature sensitivity of
community respiration. a–c, Temperature dependence of respiration at
the population level in M9 + glucose medium (a) and community level in
M9 + glucose (b) and spent medium (c). Colours denote whether populations
or communities are from the adapted (n = 6 biological replicates) (red) or de
novo (n = 6 technical replicates) community isolates (black). Inset plots show
the distribution of thermal sensitivities (E, activation energy) for each treatment
where box plots depict the median (centre line) and the first and third quartiles
(lower and upper bounds). Whiskers extend to 1.5× the interquartile range (IQR,
the distance between the first and third quartiles). The solid lines represent the
average temperature sensitivity estimated by fitting the Sharpe–Schoolfield
equation using nonlinear mixed effects models (Methods).

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in the M9 + glucose medium, populations would be able to indepen-
dently access glucose, relatively free from exploitative or interference
competition (as the assays were carried out at low densities in the expo-
nential phase of growth) leading to neutral interactions. Therefore,
on the basis of our theory which predicts a relatively small amplifica-
tion effect when interactions are weak, for communities incubated in
M9 + glucose medium, we expect comparable temperature sensitivities
between the population level and community level in both de novo and
adapted treatments.
Consistent with our predictions, we found that the average tem-
perature sensitivity of respiration was statistically indistinguishable
between the de novo and adapted communities measured in M9 + glu-
cose (Fig. 3b and Supplementary Table 2). Furthermore, the apparent
activation energy of respiration at both population level and commu-
nity level in the M9 + glucose medium (where interactions are expected
to be weak) were indistinguishable (species, 1.01 eV ± 0.19; community,
1.04 eV ± 0.17), as predicted by equation (3) for near-neutral inter-
actions. In contrast, when we quantified the temperature response
of community respiration in spent media, as predicted, we found a
marked and statistically significant increase in the thermal sensitivity
of respiration compared to that of de novo communities (Fig. 3c and
Supplementary Table 2), with the activation energy of the adapted
community in the spent medium (1.4 eV ± 0.40) 40% higher than the
average population-level activation energy. To eliminate the possibil-
ity that the observed amplification of community respiration was
driven by changes in per capita, mass-specific respiration rates of the
strains instead of interaction-driven biomass dynamics, we compared
the thermal sensitivity of per capita respiration (mgO2 h−1 cell−1) and
biomass accumulation (Methods) between the de novo and adapted
communities. We found that the thermal sensitivity of per capita respi
-
ration was indeed statistically indistinguishable between the de novo
and adapted communities (Fig. 4a,b and Supplementary Table 3),
while that of biomass accumulation was significantly higher in the
latter when communities were incubated in spent media (Fig. 4c,d and
Supplementary Table 4).
The amplification in thermal sensitivity is driven by a
shift from competition to facilitation during community
adaptation
Next, we confirmed that interactions had indeed become more facilita-
tory (or less competitive) in the adapted relative to the de novo com-
munities through two additional experiments. First, we looked at how
the asymptotic biomasses of the communities and the individual strains
(the carrying capacity, K) changed following adaptation. If interactions
between populations had become more facilitatory, we expected to see
higher biomass attained in these communities due to more efficient use
of limiting resources. When each taxon was grown in monoculture on
the M9 + glucose medium for 72 h at 20 °C, we saw no statistically sig-
nificant effect of treatment on K before and after adaptation (P = 0.56;
Supplementary Fig. 2 and Table 5). However, when the same test was
performed with communities, K was significantly higher in the adapted
communities (Fig. 5a M9 + glucose medium and Supplementary
Table 6). To further investigate these effects, we repeated the experi-
ment but this time incubated the communities in spent media. We
found that the adapted communities reached higher K compared to the
de novo assembled communities in the spent media (Fig. 5a and Sup-
plementary Table 6). Furthermore, the K attained by the adapted com-
munities in the spent media was even higher than they attained in the
M9 + glucose medium. Thus, co-adaptation between strains increased
the biomass production efficiency of the community for the given set
of resources. Because we observed an increase in community-level
performance of the adapted communities in M9 + glucose medium
and spent media, it is likely that the facilitatory (or less competitive)
interactions persist in M9 + glucose, albeit with a smaller impact on
community biomass because, on average, each strain’s population
relies less on metabolic byproducts in resource-rich media.
−24
−23
−22
15
a b
c d
20 25 30 35
Temperature (°C)
15 20 25 30 35
15 20 25 30 35 15 20 25 30 35
Temperature (°C)
Temperature (°C) Temperature (°C)
ln(rate (mgO2 Cell−1 h−1))
ln(rate (mgO2 Cell−1 h−1))
−24
−23
−22
−21
−20
−19
−8
−7
−6
−5
−4
−8
−7
−6
−5
−4
37.538.038.539.039.540.0
Inverse temperature (eV−1)
37.538.038.539.039.540.0
Inverse temperature (eV−1)
ln (biomass (OD600))
ln (biomass (OD600))
Fig. 4 | Temperature dependence of respiration per cell and community
biomass. a,b, Temperature dependence of respiration per cell (ln respiration rate
(mgO2 cell−1 h−1)) for de novo assembled (black) and adapted (red) communities
in M9 + glucose medium (a) and spent media (b). Parameter estimates are given
in Supplementary Table 3. c,d, Temperature dependence of community biomass
(ln(OD600)) for the de novo assembled (black) and adapted (red) communities in
M9 + glucose medium (c) and spent media (d). Bright coloured points represent
the exponential part of the temperature dependence and transparent points
represent the biomass estimates beyond the maximum which were not included
in the estimate of the temperature sensitivity. Parameter estimates are given in
Supplementary Table 4.

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We then experimentally quantified the change in direction and
magnitude of pairwise species interactions after adaptation. We grew
isolates of each strain individually, and in all possible pairwise combina-
tions of strains, before and after adaptation for up to 72 h (depending
upon when they reached carrying capacity) at 20 °C in M9 + glucose
and the spent media. We then estimated the mean of the pairwise
interaction strengths using a measure based on the comparison of
growth rates in monocultures versus paired cultures (Methods; Sup-
plementary Fig. 3). When grown in M9 + glucose medium, interactions
predominantly shifted towards positive values following adaptation,
indicating a shift from competition to facilitation (Fig. 5b). When the
same experiment was attempted in monoculture in spent media, many
of the isolates did not grow despite the whole communities being able
to coexist under these conditions. This indicates that the resource
environment that emerges from the metabolic byproducts in multispe-
cies communities is essential for the co-adapted populations to grow.
The metabolic byproducts of just a single community member are
insufficient to enable persistence. This point can be made more exact
by analysing the Lotka–Volterra equations (Methods). Our experimen-
tal results showed that the population growth of monocultures in spent
media was negative, such that growth, plus the effects of density
dependence, were negative, that is,
ri−aiiCi<0
. The joint population
growth is still negative in paired cultures because the effect of positive
pairwise interactions is still not enough to allow persistence. In con-
trast, the whole community’s growth is positive where all interspecies
interactions are present, that is,
ri−aiiCi+NaC >0
. Taking both these
constraints into account, it follows that the net effect of interactions
must be positive to outweigh the negative intrinsic growth rates and
that
a>0
in the assembled communities, consistent with our estimates
of the pairwise interaction coefficients. We note that it was not possible
to estimate each of the pair of (potentially asymmetric) interaction
coefficients between any two strains in paired culture in our experi-
mental system because this would have required us to track the relative
abundance of each taxon over time. Importantly, our prediction that
a shift towards positive species interactions amplifies the thermal
sensitivity of community respiration pertains to the overall average of
interaction strengths in the community, for which an estimate of the
mean interaction strength between pairs of strains is sufficient.
Finally, we tested the possibility that a change in the interaction
structure to favour populations with higher thermal sensitivity (meaning
an increase in the covariance term
Cov wiaER󰅁iωi
in equation (3)
was responsible for the amplification of community respiration by
examining the relationship between the population-level thermal
sensitivity values and estimated interaction coefficients. We found no
relationship between these two features (Supplementary Fig. 4), either
before or after adaptation, indicating that the covariance term con-
tributed relatively little to the overall temperature sensitivity of com-
munity respiration. That is, the increase in thermal sensitivity of
community respiration cannot be explained by an increase in the ten-
dency for interactions to positively affect populations with high ther-
mal sensitivity.
Discussion
In summary, our theoretical and empirical results provide compel-
ling evidence that a shift from competition to facilitation results in
positive population dynamical feedbacks that ultimately amplify the
thermal sensitivity of community-level respiration rate by increasing
total biomass. This amplification occurs in a predictable way and can
be quantified through a general relationship between the magnitude
and direction of average interaction strength in the community and
the thermal sensitivity of its respiration that we have derived here.
Our finding that changes in the direction and strength of microbial
species interactions can so profoundly alter the temperature sensi-
tivity of community-level respiration, has far-reaching implications
given the substantial contributions that microbial communities make
to ecosystem functioning in aquatic and terrestrial environments.
Microbial communities tend to have either competitive or cooperative
interactions across space
20
or over time (during community assem-
bly for example30,32). This implies that microbial communities can
either dampen or amplify the effects of temperature change on carbon
cycling. For example, changes in interaction structure over time due
to longer term assembly and turnover dynamics could mean that the
M9 + Glucose Spent media
Adapted de novo Adapted de novo
0.04
0.08
0.12
0.16
Treatment
Carrying capacity (K)
a
2 20
20 23
18 20
15 20
2 23
15 23
18 23
2 15
15 18
2 18
−0.5 0 0.5 1.0
Change in interactions
Taxa pair
b
Fig. 5 | Emergence of facilitation in experimental microbial communities.
a, Carrying capacity of the adapted (n = 6 biological replicates for each medium
treatment) and de novo (n = 6 technical replicates for each medium treatment)
assembled communities grown in either M9 + glucose or spent media for 72 h at
20 °C (Supplementary Table 6). Box plots depict the median (centre line) and the
first and third quartiles (lower and upper bounds). Whiskers extend to 1.5× IQR
(the distance between the first and third quartiles). b, Change in interaction
strength between pairwise combinations of strains from the de novo to adapted
communities in the M9 + glucose. Each row shows the average and 95%
bootstrapped confidence intervals of the estimated change in interactions for
each pair of strains. Negative values indicate that interactions have become more
competitive, while positive values indicate that interactions have become more
facilitatory. The interactions become predominantly more facilitatory (70% of
the cases), with
a
changing from −0.07 in the de novo to 0.065 in the adapted
communities.

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Article https://doi.org/10.1038/s41564-022-01283-w
same microbial community would switch between states that dampen
(when competition dominates, at early stages of community assembly)
and amplify (with facilitation dominates, in later states of community
assembly) the sensitivity of ecosystem functioning to temperature
change. In particular, microbe-mediated decomposition of organic
matter, which is the main contributor to CO2 and CH4 fluxes in the
carbon cycle, depends on facilitation among taxonomically diverse
consortia of bacteria and archaea. Indeed, our finding that weaken-
ing of competition and strengthening of facilitation amplifies the
temperature sensitivity of community metabolism may help to explain
the relatively high thermal sensitivity seen in syntrophic methanogenic
microbial communities33.
Methods
Deriving the thermal sensitivity of ecosystem respiration
For a given ecosystem (henceforth, synonymous with a bacterial com-
munity), total temperature-dependent respiratory carbon flux, R
eco
(T)
can be expressed as the sum of the products of species (strain)-level
mass-specific respiration rates R
i
(T) and biomasses C
i
(T) (equation (1)).
We are interested in the thermal sensitivity of ecosystem respiration,
Eeco:
Eeco =
dlog (R
eco
(T))
dT
.
(4)
Using the fact that
dlog(R
eco
(T))
dT
=
1
Reco(T)dR
eco
(T)
dT
and substituting equa-
tion (1) in equation (4), we get:
Eeco 
d
dT
N
i󰁞0RiTCiT

N
i󰁞0RiTCiT

N
i󰁞0
dR
i
T
dTCiT
dC
i
T
dTRiT

N
i󰁞0RiTCiT

Using the general definition
E
x=
dlog(x(T))
dT
, this simplifies to
equation (2). The equation (2) shows that the thermal sensitivity of
ecosystem respiration is given by the average of the sensitivities of
biomass and respiration to temperature across the community,
weighted by the respiratory output of each species. We can further
explore this by defining
w′
i≡
R
i
(T)C
i
(T)
∑
N
i=0Ri(T)Ci(T)
(effectively, a normalized
weighting parameter) which lets us write Eeco as:
Eeco 
N

i󰁞0
w󰅄
iEC󰅁iER󰅁iNERECNCov w󰅄
iEC󰅁iER󰅁i
(5)
where
EC
and
ER
are the average thermal sensitivities of biomass and
respiration across all N species in the community (defined as
E=
1
N
∑
N
i
E
i
).
Expressing E
eco
in this way shows that it depends on both the average
sensitivities across the community and the covariance between the
weightings (the relative contribution of each species to total respira-
tion) and the thermal sensitivities of individual species. Note that this
partitioning of total ecosystem function into the contributions of the
average effect across populations and the specific structure of their
contributions and biomass (the covariance term) is the same as that
used in the Price equation which has been previously applied to under-
stand ecosystem function and the effects of species loss34.
Next, we consider how interspecies interactions affect the thermal
sensitivity of ecosystem respiration. Because species interactions
are expected to change species’ biomasses much more rapidly than
respiration rates (which change at much longer, macro-evolutionary
timescales
35
), we focus on the effects of interactions on the biomass
components of equation (2) (the C
i
and E
C,i
). To model these effects,
we use the generalized Lotka–Volterra (GLV) model:
1
C
i
dC
i
dt
=ri(T)−aiiCi+
N
∑
i≠j
aijCj
(6)
Here, r
i
(T) is the (temperature dependent) intrinsic growth rate
of the ith species, a
ij
the strength of the effect of the jth species on
the ith one (positive or negative) and aii the strength of (negative)
intraspecific density dependence. For an arbitrary structure of species
interactions (signs and strengths of the a
ij
), it is impossible to meaning-
fully determine how interaction structure affects species’ biomasses.
Therefore, next, we derive an approximate relationship with the aim
to quantitatively predict the response of biomass in the early stages of
community assembly as follows.
First, we derive a mean-field approximation36,37 of the GLV model
(equation (6)). We use the definition of the average interaction expe-
rienced by a focal species,
aij
C
i≠j
=
1
N
∑
N
i≠j
a
ij
C
j
to write the interspecies
interactions term in equation (6) as:
N
∑
i≠j
aijCj=(N−1)aij Ci≠j
Assuming the system is large (N is large) and the difference
between
Cj≠i
and
C
(exclusion of the ith species has little effect on
C
),
we express the interaction term as:
N

i󰝷j
aijCjN1aC N1Cov aij Cj
Assuming that the effect of any single interaction on a species’
biomass is small, we can take the covariance term to be negligible,
yielding the mean-field approximation of the GLV (equation (6)) model:
1
Ci
dC
i
dt
≈ri(T)−aiiCi+(N−1)aC
(7)
Although this approximation relies on the assumption of large
community size, we show that our results hold qualitatively even in
small communities (Supplementary Fig. 5).
Next, we need to solve this system of equations representing
an ecosystem for the C
i
, to determine the (temperature-dependent)
effects of species interaction structure on population biomasses, C
i
.
We use a Taylor-series expansion around t = 0 to get an approximate
expression for C
i
in the early stage of community assembly in terms of
average interaction strength a. We start by considering log biomass
as a function of time, log(C
i
(t)), which can be approximated around
t = 0 giving:
log Citlog Ci0
t
Ci0
dC
i
t
dtt󰁞0
t2
2Ci0
2d2Cit
dt
2t󰁞0Ci0d2Cit
dt
2t󰁞0
(8)
We use equation (8) to get the second-order derivatives (by taking
the time derivative again). This in turn requires an expression for
d
C
dt
,
which we obtain using the Taylor-series approximation of the average
of a function of uncorrelated random variables xi,…,xN,
fx1xNfx1xN1
2
N

i󰁞1
σ2
iδ
2
f
δx
2
i

Combined, these give an expression for the ith species’ log bio-
mass at time t:
log Cita
2
N󰁝1
2
t2C
2
0
2
N󰁝1t2σ2
C0
2
aN󰁝1t2rC0
2N1tC0N󰁝1C0aiit2C0
2N󰁝1aiit2C2
0
2N󰁝1aiit2σC2
0
2
log C0C2
0a2
iit2
2
C0aiiriTt2
2
C0aiitriTt
(9)

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We can take the derivative of equation (9) with respect to tempera-
ture to get an expression for EC,i:
EC󰅁iaN󰁝1C0t
2
2
drT
dTtt
2
aiiC0
2driT
dT
aγ ωi(10)
Where
γ
N󰁝1C0t
2
2
drT
dT
and
ωi
dr
i
T
dT
t
t2a
ii
C
0
2
are constants repre-
senting the temperature dependence of average biomass growth across
the whole system and the biomass growth of species i, respectively.
Finally, substituting equation (10) back into equation (5) gives an
expression for the thermal sensitivity of respiration across the whole
system (same as equation (3)):
Eeco 
N

i󰁞0
w󰅄
iaaγ ωiER󰅁i
ay NCov w󰅄
i
aE
R󰅁i
ω
i
E
R
ω
Supplementary Fig. 6 shows that this approximation adequately
captures the qualitative effects of interactions on thermal sensitivity
of ecosystem respiration. Thus, as explained in the main text, the above
equation predicts that E
eco
will depend only on internal factors affecting
species’ population growth (growth rates and intraspecific interac-
tions) when
a=0
(competitive and facilitatory interactions balance
each other) and, relative to this, it will be dampened if
a<0
(competi-
tive interactions dominate) and amplified if
a>0
(facilitatory interac-
tions dominate).
Generating speciic predictions. To generate specific predictions on
the basis of this theory, we parameterized equation (9) with randomly
generated communities of n = 50 to obtain biomass estimates in the
early stages of assembly (t = 3.0), setting C(0) = 0.01. We consider
this time frame as it corresponds to the experimental setup. For each
such synthetic community we multiplied these biomass estimates by
mass-specific respiration R and summed over all populations to get the
total ecosystem respiration R
eco
(Fig. 1b). This process was repeated at
different fixed temperatures from 5 to 25 °C. We used a modified Boltz-
mann–Arrhenius equation to represent the temperature dependence
of growth r and respiration R rates,
BTB0e
󰁝E1
kT 󰁝1
kTref 
where B0 is a normalization constant, E is the temperature sensitivity,
k is the Boltzmann constant and T and Tref are the temperature and
reference temperature (set to 15 °C), respectively. For both r and R,
we sampled the B0 and E values from normal distributions such that B0
∼N(1,0.1) and E ∼N(0.6,0.1). We considered three types of community
interaction structures—competitive, neutral and facilitatory—by set-
ting a = −0.02, 0 and 0.02, respectively. Intraspecific interactions were
all set to a
ii
= −10. We calculated E
eco
by using the same parameters in
equation (3) to generate the values in the inset plot of Fig. 1b.
Isolation and identification of bacterial taxa
The experiment was conducted with eight bacterial taxa isolated from
a geothermal valley in Iceland (Supplementary Table 7). These were
isolated from biofilm samples collected from the surface of rocks
in May 2016–May 2017 in Hvergerdi Valley, 45 km east of Reykjavik,
Iceland. Samples were immediately frozen upon collection with 17%
glycerol and transported at −20 °C for further processing in the labo-
ratory. Upon return to the laboratory, samples were thawed at 20 °C
and prepared by serial dilution and plating 10 µl onto R2A agar plates
(Oxoid Ltd) with sterile glass beads. Plates were incubated at a range of
temperatures between 15 and 25 °C for 5–10 d. The resulting colonies
were distinguished by morphology, picked and placed into 200 µl
lysogeny broth (LB) and incubated for 48 h. To preserve the library of
taxa, samples were then centrifuged, the supernatant was removed
and the pellet was resuspended in mix of LB and 17% glycerol before
being frozen at −80 °C.
Isolates were assigned taxonomy using 16S polymerase chain
reaction (PCR) followed by Sanger sequencing within the 16S ribo-
somal RNA gene. A master-mix solution was prepared using 7.2 µl of
DNA free water, 0.4 µl 27 forward primer, 0.4 µl 1,492 reverse primer
and 10 µl of Taq polymerase per sample. To create a template solu-
tion, 2 µl of sample 100× diluted in DNA free water was added to 18 µl
of master-mix solution. Samples were then placed in a thermal cycler
(Applied Biosystems Veriti Thermal Cycler). This procedure included
one cycle at 94 °C for 4 min, 35 cycles at 94, 48 and 72 °C for 1 min, 30 s
and 2 min, respectively, and finally, one cycle at 72 °C for 8 min. The PCR
product was cleaned up using exonuclease I and Antartic phosphatase
and high-quality samples were Sanger sequenced using the 27 F, 1,492 R
primers (Core Genomic Facility, University of Sheffield). Sequences
were trimmed in Genious (v.6.1.8) removing the base pairs (bp) from the
5ʹ end and trimming the 3ʹ end to a maximum length of 1,000 bp. Using
Mothur v.1.39.5 (ref. 38), sequences longer than 974 bp were aligned to
the Silva.Bacteria. Taxonomic identities were assigned using the RDP
trainset 9 032012 as a reference database (Supplementary Table 7).
Morphology was assessed visually to allow recognition of each taxon
when mixed in an experimental community.
Community adaptation experiment
We assembled replicated communities with the eight bacteria taxa.
Stock cultures were first grown in LB medium at 20 °C overnight to
establish a dense, healthy culture and then standardized to a common
biomass density in M9 medium with 0.2% glucose. We used this minimal
growth medium because it has a single, defined and easily quantifiable
carbon source. A ‘community stock’ solution was built by adding 100 µl
of each taxon. Then, a 40 µl aliquot of the community stock solution
was added to 5,000 µl of M9 medium + 0.2% glucose and incubated at
20 °C in glass vials for 48 h. We used six replicates and two blanks to
check for medium contamination. We transferred each community
every 48 h by diluting 40 µl of the community in 5,000 µl of fresh
medium. Each transfer encompassed both exponential and stationary
(typically reached within 24 h) phases of the growth cycle. Preliminary
experiments revealed that >95% of the glucose was depleted after
24 h. Consequently, the duration of each transfer encompassed both
resource-replete conditions where glucose was abundant and periods
where glucose was scarce. In the resource-scarce periods, persistence
of strains was expected to be strongly dependent on their ability to use
recycled carbon in the form of metabolic byproducts (cross-feeding).
Each community was passaged 14 times (30 d, ~100 generations) in this
manner over the course of the experiment. Optical density (OD
600
)
of the community was measured at every transfer using a Thermo
Fisher Scientific Multiskan Sky Microplate Spectrophotometer at
600 nm. Each community was also plated on R2A agar once a week to
ensure they remained uncontaminated. At the end of the experiment,
each community was plated and individual taxa isolated, identified
and stored at −80 °C for downstream analysis. We henceforth refer
to these replicate communities, established from a common pool of
taxa and then incubated across multiple generations under intermit-
tent resource-depleted conditions, as ‘adapted’. For comparison, we
assembled six replicated communities with the same eight taxa in the
same conditions as the adapted communities without transferring (pas-
saging) them several times. We refer to these communities as ‘de novo’.
Metabolic facilitation assay
To investigate whether metabolic facilitation emerged in each com-
munity we carried out an assay to quantify levels of total biomass
production in conditions where the only available resources were
metabolic byproducts generated during its assembly (spent media).

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We hypothesized that, if the development of metabolic facilitation were
to drive species interactions to be more positive in communities where
the constituent members had been grown together under resource
limitation, then we should observe enhanced biomass production in
the adapted compared to the de novo communities, when both were
grown in spent media. This is because metabolic facilitation should
enable better growth on the metabolic byproducts of community
members. For this, the de novo and adapted communities were each
inoculated into 5 ml of M9 medium + 0.2% glucose and incubated at
20 °C until the glucose level in the medium fell below detection limit
(typically, 48 h).
A Glucose GO Assay Kit (Sigma) was used to monitor the level of
glucose in the medium. The samples were then centrifuged at 1,421g
(3,000 rpm) for 10 min. We refer to spent medium as the resulting
medium containing species metabolites without any other carbon
source. The spent media were filter-sterilized and stored at 4 °C. The
de novo communities were then regrown in the spent media extracted
from their own (shorter) incubation. Each unique adapted community
was regrown in its own spent medium. Biomass was measured every
4 h as optical density using a Thermo Fisher Scientific Multiskan Sky
Microplate Spectrophotometer at 600 nm.
The community-level carrying capacity was quantified by fitting
the logistic growth model to the resulting time series using nonlinear
least squares regression using the R package nlsLoop (following ref.
39
).
At the single-taxon level, we used an analysis of variance (ANOVA) to
test for significant differences in carrying capacity among treatments
(ancestral or adapted) (Supplementary Table 5). At the community
level, we also used an ANOVA to test whether carrying capacity differed
significantly between treatments (adapted or de novo), media sources
(M9 + glucose or spent media) or their interaction (Supplementary
Table 6).
Quantifying the temperature sensitivity of respiration
We characterized the thermal response curves for respiration at
the taxon level for both the ancestral and adapted strains (isolated
from the adapted communities). The isolates were grown overnight
in LB medium from −80 °C freezer stocks, then transferred into M9
medium + 0.2% glucose and acclimated in incubators at nine tempera-
tures (15, 20, 25, 27.5, 30, 32.5, 35, 40 and 45 °C) for 24 h. The incubation
time was selected on the basis of the time the isolates take to reach car-
rying capacity. After acclimation, biomass was estimated by measuring
optical density using a Thermo Fisher Scientific Multiskan Sky Micro-
plate Spectrophotometer at 600 nm and then standardized at the same
optical density (OD
600
= 0.05). A 4 ml aliquot of each sample was added
into 46 ml of fresh M9 media. We used six technical replicates of each
taxon for each treatment (de novo and adapted) and took the average
as our estimate of respiration rate. All measurements were made while
the isolates were in the exponential phase of growth.
At the community level, we measured the temperature sensitivity
of respiration for the adapted and de novo assembled communities.
The de novo isolates were grown in LB medium overnight immediately
after coming out of the −80 °C freezer, then transferred into either M9
medium with 0.2% glucose or the spent medium containing only meta-
bolic byproducts. Each of the six adapted communities (six biological
replicates) was transferred directly to fresh M9 medium with 0.2% glu-
cose or the corresponding spent medium. All samples were acclimated
in the appropriate assay media (either M9 + glucose or spent media)
in Percival incubators at seven temperatures (15, 20, 25, 27.5, 30, 32.5
and 35 °C) for 24 h. After acclimation, samples were standardized to
the same biomass (OD600 = 0.05). The de novo communities were then
assembled by adding 800 µl of each ancestral isolate into 46 ml of the
corresponding media (M9 + glucose or spent media). Each de novo
community was replicated six times. For the adapted communities, we
added 522 µl of each replicate community into 6 ml of the correspond-
ing media (M9 + glucose or spent media).
Respiration rate measurements. Respiration was measured as oxy-
gen consumption using an array of ten SensorDish Readers (SDR,
PreSens GmbH). Each plate reader can analyse 24 samples, meaning
the array of ten allowed us to measure 240 samples simultaneously.
The PreSens system was calibrated using a two-point calibration at
each measurement temperature. A 0% oxygen saturation was defined
using a solution of 1% (w/w) sodium sulfite and 100% oxygen satura-
tion used air-saturated water. In each well, we placed a 5 ml vial with
the sample to be measured. The vials were slightly overfilled so that
no air was trapped within the vials as the lids were closed. The equip-
ment was then run in parallel at the nine temperatures (see above)
and we measured the concentration of dissolved oxygen every min-
ute for ∼4 h. The rate of respiration was derived from the slope of a
linear regression of oxygen concentration against time (mgO2 l−1 h−1).
To estimate respiration per cell, a 200 µl aliquot for each treatment,
medium and replicate was sampled after measuring the respiration
rate to quantify bacterial abundance. Samples were fixed with para-
formaldehyde and glutaraldehyde (P + G) 1% final concentration and
kept in the −80 °C freezer. Samples were stained using SYBRTM Gold
nucleic acid stain and analysed using the BD Accuri C6 flow cytometer
in low flow rate. Total community respiration (mgO
2
l
−1
h
−1
) was divided
by the total bacterial abundance (cell l−1) to obtain the respiration
per cell.
Biomass estimates. To estimate community biomass, a 200 µl aliquot
for each temperature, treatment, medium and replicate was sampled
after community respiration rate measurements were completed. The
samples were then analysed in a Thermo Fisher Scientific Multiskan
Sky Microplate Spectrophotometer standard plate reader at 600 nm
to obtain the total bacterial biomass in OD600. A blank containing the
medium without any bacterial cells was also analysed to correct the
data by subtracting the blank to the sample value.
Model itting. We fitted the four parameter Sharpe–Schoolfield equa-
tion to the respiration rate data measured along the thermal gradient
to calculate thermal sensitivity (see ref. 40). At taxon level, we fitted
the Sharpe–Schoolfield model to the rate data using nonlinear mixed
effects models in the nlme package in R. We modelled species as a ran-
dom effect and treatment (ancestor or adapted) as a fixed effect on each
parameter. Model selection started with the most complex possible
model, including fixed effects on all parameters and then proceeded
by removing treatment effects on each of the parameters. At the com-
munity level, we fit the Sharpe–Schoofield model separately to each
medium (M9 + glucose and spent media) using nonlinear mixed effects
models in the nlme R package. We modelled replicate as a random effect
and treatment (de novo or adapted) as a fixed effect on each parameter
in the Sharpe–Schoolfield equation. With both analyses, model selec-
tion started with the most complex possible model, including fixed
effects on all parameters and then proceeded by removing treatment
effects on each of the parameters. We used likelihood ratio tests for
model comparisons (Supplementary Tables 1–3).
The temperature dependence of total biomass was quantified
using the Arrhenius equation by applying a linear mixed effects model
to the natural logarithm of total biomass along the exponential part
of the thermal response (15–25 °C). We used only the exponential part
of the thermal response curve as total biomass did not follow a typi-
cal unimodal shape, which precluded fitting the Sharpe–Schoolfield
equation.
ln NN0Ea
1
kT

(11)
Where N is community biomass (ln (OD600), N0 is the rate constant, Ea
is the activation energy, k is Boltzmann’s constant (8.62 × 10−5 eV K−1)
and T is the absolute temperature in °C.

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We modelled replicate as a random effect on the intercept and
treatment (de novo or adapted) as a fixed effect on both the intercept
and the slope (Ea); estimates are given in Supplementary Table 4.
Inferring species interactions
To quantify how long-term coculture altered the nature and strength of
biotic interactions we use an approach based on the difference in exper-
imentally observed growth rates when strains are grown individually
versus when they are grown in pairs. In brief, our approach involves two
stages. First, using the microcosm experiments, we estimate growth
rate for each strain individually and in all pairwise combinations. We
then use these to estimate the direction and magnitude of interactions
based on a model of population growth detailed below.
To measure growth rates for both pairs and individual strains,
we grew isolates of each taxon before and after adaptation at 20 °C in
M9 + glucose in monoculture, as well as in all possible pairwise com
-
binations of taxa. For each incubation, we measured OD
600
every hour
until each pair reached carrying capacity. Depending on the species
and treatment this incubation time could vary between 24 and 72 h.
We then repeated the experiment using the spent media (see section
on Metabolic facilitation assay, above). This second set of experiments
was focused on growing each taxon in the metabolites of the others in
all pairwise combinations. First, we grew the five original isolates in
LB medium. All taxon abundances were standardized at OD600 = 0.1
diluted into M9 + glucose. We then inoculated 40 µl of each taxon’s
population into 5 ml of M9 medium with 0.2% glucose, in 5 ml vials.
We incubated each vial until there was no detectable glucose remain-
ing. The cells were separated from the spent medium by centrifuging
in 15 ml Falcon tubes at 3,000 rpm for 10 min and the spent medium
was filter-sterilized and stored at 4 °C. We used the same protocol with
the adapted isolates to obtain a spent medium with their metabolic
byproducts. Subsequent experiments with the ancestral or adapted
isolates used the corresponding spent medium. We inoculated each of
the five taxa in M9 + glucose medium and in the spent media of the five
taxa in all pairwise combinations at 10% v/v in a 384-well plate. All taxa
were standardized at OD600 = 0.05 before being inoculated to 90 µl of
M9 + glucose or spent medium. The plate was incubated in a Thermo
Fisher Scientific Multiskan Sky Microplate Spectrophotometer plate
reader at 20 °C and OD600 was measured every hour until carrying
capacity was reached. To obtain estimates of growth rates (r, h
−1
) from
both experiments we fit both logistic and exponential growth models
to the OD
600
data from the first 20 h. This time limit was chosen because
it encompassed the growth phase (either before populations reached
carrying capacity or started to decline) across all strains and pairs. The
growth estimate was taken from the best-fitting model as indicated
by the lowest Akaike information criterion for each strain or pair and
treatment combination.
We used the growth rates obtained from these experiments to
estimate pairwise interaction coefficients using a method based on
the difference in growth rates when strains are grown in pairs or in
monoculture. This method is similar to that previously used to assess
the nature of interactions in bacterial communities
29,39
(Supplementary
Information) and is derived as follows.
First, consider the growth of a pair of strains x1 and x2 in isolation,
which can be modelled by the growth equations:
dx
1
dt
=r1x1and
dx
2
dt
=r2x2,
where r1 and r2 are the mass-specific growth rate and x1 and x2 are the
biomass of each population. Note that we omit the intraspecific den-
sity dependence terms here as we are interested in the early stages of
population growth within which the experimental observations were
made. At these timescales the effects of density dependence will be
of the order O(C2) and thus smaller than the effects of actual growth
rates, allowing them to be left out of the growth equation. In practice,
any deviations from the true maximal growth rate caused by density
dependence in the experiments will be captured in the effective growth
rate we measure.
When both strains are grown together, the additional interaction
terms a
12
and a
21
need to be introduced to capture the effect of interac-
tions between the two species:
dx
1
dt
=r1x1+a21x1x2and
dx
2
dt
=r1x2+a12x1x2
Next, we write the equations for the growth of the total biomass
of the pair, xtot, as:
dx
tot
dt
=
dx
1
dt
+
dx
2
dt
=r1x1+r2x2+(a12 +a21)x1x2
(12)
which we can also approximate in the early stages of the pair’s assembly
using a single effective growth rate which incorporates the effects of
both intrinsic population growth and interactions from equation (12).
This is done in terms of the total biomass of the pair x
tot
which is the only
quantity observable in the experimental data:
dx
tot
dt
≈rtotxtot .
(13)
Combining equations (12) and (13) thus gives:
rtotxtot =r1x1+r2x2+(a12 +a21 )x1x2
allowing us to solve for the total interaction strength:
atot =a12 +a21 =
r
tot
x
tot
−r
1
x
1
−r
2
x
2
x1x2
.
(14)
The equation (4) defines a line of solutions on which the values
of a12 and a21 can lie.
Taking into account that at the beginning of the experiment each
strain is at equal abundance, that is
x1=x2=
1
2
x
tot
and
x1x2=
1
4
x
2
tot
, we
can write the total interaction strength as:
atot =a12 +a21 =
2r
tot
−(r
1
+r
2
)
1
2
xtot .
(15)
The equation (15) shows how the total interaction strength is given
by the deviation of the total paired growth from the null-case with no
interactions (given by the sum of the individual strain growth rates in
monoculture). If the pair grows at a lower rate than expected from their
growth in monoculture, then we infer that the interaction between
them is competitive and vice versa. Note that the use of the biomasses
at t = 0 here is not to say that biomasses of strains are constant over
time but rather that the relative contributions of the growth rates of
the individual strains to the null, non-interacting case is equal. In this
way, the biomasses are only used to correctly weigh the individual
monoculture growth rates in the null model. The change in biomass
over time is captured in the growth rate terms and we do not assume
that the biomasses are constant.
To derive an estimate of the individual pairwise interaction coef-
ficients we next consider the case where interactions are symmetric
a12 = a21 = α letting us write:
α=
2r
tot
−(r
1
+r
2
)
xtot
.
Note that this assumption is the same as considering the average
interaction strength of the pair:
a
=
a
12
+a
21
2
=
2α
2
=
α
. Therefore, as such,
the symmetry of interaction coefficients does not affect our inference

Nature Microbiology | Volume 8 | February 2023 | 272–283 282
Article https://doi.org/10.1038/s41564-022-01283-w
of the overall average interaction strength across the community. To
calculate asymmetric interactions, one would require data on the rela-
tive abundances of strains when grown together, over time.
As the total abundance is held constant across all the experiments,
the x
tot
term in the denominator acts as a single scaling term across
all interaction estimates and can thus be dropped giving the final
expression:
α=2rtot −(r1+r2).(16)
To apply equation (16) to our data, we use a bootstrapping proce-
dure to account for variation in growth rate estimates amongst repli-
cates. Specifically, taking the data from the growth curve experiments,
we sample each of the parameters from equation (16) with replacement
across the replicates 10,000 times and calculate α for each taxon pair.
This gives a distribution of estimates of α for each pair as shown in Fig. 5.
Data availability
All data to reproduce our results are at https://doi.org/10.5281/
zenodo.7105128.
Code availability
All code to reproduce our results are at https://doi.org/10.5281/
zenodo.7105128.
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Acknowledgements
This work was supported by a European Research Council Starting
Grant awarded to G.Y.-D. (ERC StG 677278 TEMPDEP). T.C. was
supported by the QMEE CDT, funded by NERC grant no. NE/P012345/1.
S.P. was funded by Leverhulme Fellowship RF-2020-653\2 and UK
national NERC grants NE/M020843/1 and NE/S000348/1.
Author contributions
G.Y.-D. and S.P. conceived the study. F.C.G. and G.Y.-D. designed
the laboratory experiments. F.C.G., R.W. and D.B.O. carried out
the laboratory experiments. T.C. and S.P. developed the theory.
All authors conducted the analysis of the experimental data and
wrote the manuscript.
Competing interests
The authors declare no competing interests.
Additional information
Supplementary information The online version
contains supplementary material available at
https://doi.org/10.1038/s41564-022-01283-w.
Correspondence and requests for materials should be addressed
to Samraat Pawar or Gabriel Yvon-Durocher.
Peer review information Nature Microbiology thanks the anonymous
reviewers for their contribution to the peer review of this work.
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