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Understanding and predicting physiological performance
of organisms in uctuating and multifactorial
environments
Apostolos-Manuel Koussoroplis, Sylvain Pincebourde, Alexander Wacker
To cite this version:
Apostolos-Manuel Koussoroplis, Sylvain Pincebourde, Alexander Wacker. Understanding and pre-
dicting physiological performance of organisms in uctuating and multifactorial environments. Eco-
logical monographs, Ecological Society of America, 2017, 87 (2), pp.178-197. �10.1002/ecm.1247�.
�hal-01693385�
178
CONCEPTS & SYNTHESIS
EMPHASIZING NEW IDEAS TO STIMULATE RESEARCH IN ECOLOGY
Understanding and predicting physiological performance of
organisms in fluctuating and multifactorial environments
Apostolos-MAnuel Koussoroplis,
1,3
sylvAin pincebourde,
2
And AlexAnder WAcKer
1
1
Theoretical Aquatic Ecology & Ecophysiology, Institute of Biochemistry and Biology, University of Potsdam,
Am Neuen Palais 10, Maulbeerallee 2, D-14469, Potsdam, Germany
2
Faculté des Sciences et Techniques, Institut de Recherche sur la Biologie de l’Insecte (IRBI, CNRS UMR 7261),
Université François Rabelais, 37200 Tours, France
Abstract. Understanding how variance in environmental factors affects physiological per-
formance, population growth, and persistence is central in ecology. Despite recent interest in
the effects of variance in single biological drivers, such as temperature, we have lacked a com-
prehensive framework for predicting how the variances and covariances between multiple en-
vironmental factors will affect physiological rates. Here, we integrate current theory on
variance effects with co- limitation theory into a single unified conceptual framework that has
general applicability. We show how the framework can be applied (1) to generate mathemati-
cally tractable predictions of the physiological effects of multiple fluctuating co- limiting fac-
tors, (2) to understand how each co- limiting factor contributes to these effects, and (3) to detect
mechanisms such as acclimation or physiological stress when they are at play. We show that
the statistical covariance of co- limiting factors, which has not been considered before, can be a
strong driver of physiological performance in various ecological contexts. Our framework can
provide powerful insights on how the global change- induced shifts in multiple environmental
factors affect the physiological performance of organisms.
Key words: co-limitation; covariance; eco-physiology; feeding rate; global change; multiple stressors;
nonlinear averaging; nutrients; scale transition; temperature; temporal ecology; variance.
introduction
Variation is the norm in nature. The natural envi-
ronment is heterogeneous across space, time, and scales.
Yet, ecologists mostly focus on the mean environmental
conditions as a predictor variable of the patterns and
processes they observed. There is, however, an increasing
recognition that the descriptors of natural heterogeneity,
such as the statistical variance and the probability distri-
bution of environmental conditions, explain many
important ecological phenomena (Benedetti- Cecchi et al.
2006). For example, understanding how variance influ-
ences organismal physiological performance is essential
for predicting the impacts of variable plant phytochem-
istry on herbivores (Underwood 2004, Hood and Sterner
2010, Wetzel et al. 2016) and increasing temperature
variation on ectotherms (Paaijmans et al. 2010, Estay
et al. 2014, Vasseur et al. 2014).
Environmental variation can be experienced at the pop-
ulation level, i.e., individuals or groups of individuals expe-
rience different values of a limiting factor depending on
their position in the landscape. However, quite often vari-
ation can also be experienced at the individual level, i.e., the
same individual faces changing values of a limiting factor
within its lifetime. Hence, the effects of the environmental
variation (e.g., temperature, light, pH, oxygen, food
quantity and quality) on physiological performance should
be analyzed at the scales relevant to individual organisms
(Potter et al. 2013). This variation can be spatial (e.g.,
movements within a thermally heterogeneous landscape)
and/or temporal (e.g., daily temperature fluctuations).
Even very small organisms such as spider mites (<1 mm)
moving across a single leaf can experience microhabitats
that differ by more than 10°C (Caillon et al. 2014).
Similarly, within an hour, understory plants or phyto-
plankton cells might experience changes in irradiance that
span from near darkness to oversaturating light (Ruel and
Ayres 1999, Litchman 2000, Retkute et al. 2015). Finally,
the food quantity and quality (essential nutrients, sec-
ondary metabolites) encountered by consumers during
Ecological Monographs, 87(2), 2017, pp. 178–197
© 2017 by the Ecological Society of America
Manuscript received 21 July 2016; revised 17 November 2016;
accepted 7 December 2016. Corresponding Editor: Aimée T.
Classen.
3
E-mail: apostolos.koussoroplis@uni-potsdam.de
May 2017 179PERFORMANCE IN FLUCTUATING ENVIRONMENTS
ConCepts & synthesis
their lifetime can also be highly variable (Park et al. 2004,
Simpson and Raubenheimer 2012). Even consumers for-
aging within individual plants experience substantial vari-
ation in nutritional quality (Orians and Jones 2001). A
growing body of experimental and theoretical work
demonstrates that there is much to be gained in the study
of the sources and consequences of the variation experi-
enced by individual organisms (Dowd et al. 2015,
Pincebourde et al. 2016).
To date however, studies on variation mostly con-
sidered single environmental factors, and to a large extent
only temperature, thus largely ignoring the fact that
organismal performance can be simultaneously co-
limited by several factors. Here, co- limitation is defined
(see the glossary in Box 1 for definitions) in its broadest
sense: when the combination of simultaneous or sequential
changes in several biotic or abiotic factors has a different
effect on organismal performance response (e.g., vital
rates such as growth, maturation, fertility, survival) than
the effects of changing each factor alone. To cite only a
few examples, such co- limitations have been repeatedly
shown for light and temperature on plants (Edwards et al.
2016), temperature and nutrients (Cross et al. 2015), or
various combinations of nutrients (Harpole et al. 2011,
Sperfeld et al. 2016) on autotrophs and heterotrophs.
Co- limitation of physiological performance does not
necessarily involve two distinct factors (e.g., light and
temperature), but can also involve the same factor in dif-
ferent contexts (e.g., temperature during immersion and
emersion in intertidal organisms; Pincebourde et al.
2012). Interestingly, co- limitation can involve a fluctu-
ating factor and the temporal scale at which the factor
fluctuates as co- limiting factor (Kingsolver and Woods
2016). Despite accumulating evidence on the importance
of co- limitation on physiological performance of
organisms, a conceptual framework of how organisms
can be affected by environmental variation in their co-
limiting factors is still missing (Gunderson et al. 2016).
Yet, such a framework is essential for addressing the
pressing issue of the potential effects of the multiple
drivers of ecological change on organisms (Darling and
Côté 2008, Jackson et al. 2016).
Our objective here is to introduce a conceptual
framework in physiological ecology that motivates and
guides the study of the role of multifactorial environ-
mental variation. The framework (Fig. 1) extends recent
theory on the consequences of the thermal variation expe-
rienced by individual organisms (Dowd et al. 2015) to any
combination of variable factors that might simultaneously
limit performance. In the first part of the paper, we propose
a novel integration of theory on nonlinear averaging in
biological systems (Chesson 2012, Denny and Benedetti-
Cecchi 2012, Dowd et al. 2015), co- limitation theory con-
cepts (Harpole et al. 2011, Sperfeld et al. 2016), and
Box 1. Glossary.
Additivity: When the effect of simultaneous or sequential changes in several biotic or abiotic factors equals
the sum of the effects of changing each factor alone.
Antagonism: When the effect of simultaneous or sequential changes in several biotic or abiotic factors is
smaller than the sum of the effects of changing each factor alone.
Co- limitation: When the simultaneous or sequential changes in several biotic or abiotic factors have a
different effect on performance than the effects of changing each factor alone.
Covariance effect: Sensitivity of the performance to the covariance of the co- limiting factors in a variable
environment.
Cross- dependence: When the level of one of the co- limiting factors determines the shape (i.e., the position
of the maxima, minima, inflexion, and/or half- saturation points along the limiting factor axis) of the response
to the other factor.
Effect partitioning (scale transition [ST] theory): Mathematical partition of the ST term that allows the
quantification of the individual contributions of the variances of each co- limiting factor as well as that of
their covariance.
Integrated performance (ST theory): Predicted performance in a variable environment. Symbolized by
f(x)
.
Mean- field (ST theory): Biological response (here, organismal performance) in a constant environment.
Symbolized by
f(
x)
.
Scale transition theory: A mathematical upscaling “recipe” stemming from recognition that biological response
functions are typically nonlinear and that the interaction of these nonlinearities with spatial or temporal
variation distorts the prediction of large- scale patterns from small- scale patterns.
Scale transition term (ST theory): The mathematical correction to add to the mean- field in order to predict
the integrated performance.
Static performance curve: The common practice of experimentally generating a curve describing the perfor-
mance of an organism as a function of a limiting factor under constant conditions. While several factor levels
are tested, the level of the factor experienced by individual organisms over the experiment is kept constant.
Synergy: When the effect of simultaneous or sequential changes in several biotic or abiotic factors is larger
than the sum of the effects of changing each factor alone.
180 APOSTOLOS- MANUEL KOUSSOROPLIS ET AL.
ConCepts & synthesis
Ecological Monographs
Vol. 87, No. 2
phenotypic plasticity of the responses to variance
(Kingsolver and Woods 2016, Sinclair et al. 2016). After
presenting the mathematical framework for predicting the
effect of multifactorial variation and its utility for parti-
tioning the contribution of each factor (effect partitioning;
Fig. 1, Box 1), we focus on the contribution of the
covariance between factors (covariance effect; Fig. 1),
which remains virtually unconsidered in eco- physiology
(Pincebourde et al. 2012, Koussoroplis and Wacker 2016).
The mathematical framework has to be viewed as a null-
model based on certain assumptions on the physiology of
the organisms, which when violated, lead to deviations
from predictions. We review the broad categories of such
deviations and provide a novel synthetic view of how these
deviations relate to the temporal scale at which variance
manifests (time dependence; Fig. 1). We propose this syn-
thesis as a diagnostic tool for identifying the specific phys-
iological mechanisms causing the deviation.
In the second part of the paper, we present two appli-
cation examples of our conceptual framework. In the first
example, we explore a novel question: How does the
complexity of the interaction between co- limiting factors
(cross-dependence) modulate the way different statistical
moments of the experienced environment affect physio-
logical performance? The second example illustrates how
the problem of coincidence of environmental stressors can
be reformulated within our framework and the novel
insights to be gained from that. In both examples, the
covariance between co- limiting factors is predicted to be an
important driver of physiological performance. We con-
clude by discussing how our framework can conceptually
advance global change research and identify the necessary
future theoretical and methodological directions.
theory And concepts
Nonlinearity of physiological responses
and environmental variance
One of the main mechanisms through which organ-
ismal performance is affected by environmental variation
is the nonlinearity that characterizes most of the physio-
logical responses to the various environmental factors
(Ruel and Ayres 1999). For example, temperature perfor-
mance curves (TPC) are generally characterized by an
exponential increase at low temperatures, a transition to
a peak at an optimal temperature, followed by a rapid
decline in performance at higher temperatures. In ther-
mally variable environments, the nonlinearities of the
TPC lead to disproportionate effects of cool and warm
events on performance. Because of Jensen’s inequality
(Jensen 1906), the integrated performance over a period
of thermal variability increases (concave upward part of
the TPC) or decreases performance (concave downward
part of the TPC) relative to that predicted by mean tem-
perature (Ruel and Ayres 1999).
The quantification of these increases or decreases can be
achieved using mean- field approaches (Morozov and
Poggiale 2012), which are the core of the scale transition
(ST) theory. This theory focuses on the changes in the equa-
tions for population dynamics as the spatial or temporal
scale enlarges (Chesson 2012). There is however a formi-
dable opportunity to apply the concepts of this theory to
other levels of biological organization such as the physio-
logical level (Denny and Benedetti- Cecchi 2012). Such an
“eco- physiological” ST framework has been recently
developed (Box 2) for organisms limited by a single factor
(temperature), allowing important theoretical insights on
the effects of thermal variability on ectotherms (Dowd
et al. 2015). However, despite the fact that the vital rates of
organisms can be limited by multiple environmental factors
simultaneously, current theory does not include
co- limitation. Here, we address this theoretical gap.
Accounting for multiple co- limiting factors
and partitioning their effects
A strength of the ST mathematical framework is that
it can be extended to include as many co- limiting factors
Fig. 1. Conceptual diagram of the structure of this paper.
The diagram shows the place of our eco- physiological,
multifactorial, scale transition (ST) framework in the literature
and the ideas and concepts that it integrates. The main novel
methods and concepts that our framework contributes are
illustrated through two examples.
Scale Transition (ST) theory
(e.g., Chesson 2012)
[Populations-Communities, multi-factorial]
Eco-physiological ST framework
(Denny and Benedetti-Cecchi 2012; Dowd et al. 2015)
[Physiological level; uni-factorial]
Multi-factorial eco-physiological
ST framework
Background
Effect
partitioning
Time
dependence
Applications
Covariance
effect
Methods and Concepts
Multi-factorial
dependence of
performance
Physiological
adaptation to
variance
Non-linear averaging in
biological systems
Conceptual framework
Integration
Example 1
Exploring the role of cross-
dependence between
co-limiting factors
Example 2
Revisiting the effects
of thermal stress
coincidence
May 2017 181PERFORMANCE IN FLUCTUATING ENVIRONMENTS
ConCepts & synthesis
Box 2. Using scale transition (ST) theory for predicting physiological
performance in fluctuating unifactorial environments.
Theoretical principles
In its ecophysiological version (Dowd et al. 2015), ST theory (Chesson et al. 2005) predicts that the
physiological performance in a variable environment is expressed as the sum of the performance under the
average yet constant environment (the mean-field) and a correction term (the ST) that accounts for the effect
of environmental variance on performance. For a performance function, g, (or any other vital rate function
contributing to organismal fitness) depending on the abundance of a resource, R, the ST can be written as
a second- order Taylor expansion around the mean resource value:
where
g(R)
is the integrated performance under variable R conditions and
g(
R)
is the growth expected on
the averaged resource over the considered time period,
R
.
g
′′
(
R)
is the second derivative of g and quantifies
the nonlinearity of the performance function measured at
R
. The variance around
R
is
𝜎
2
R
. Note that
g
′′
(
R) > 0
for concave upward functions, and
g
′′
(
R) < 0
for concave downward functions, thus explaining the positive
or negative effects of environmental variance, respectively. For linear functions,
g
��
(
R)
=
0
thus leading to
g(R)
=
g(
R)
(no variance effect).
Applications and links to ecological concepts
Scale transition theory is increasingly applied to thermal biology (recently reviewed by Dowd et al. 2015).
For example, it can been used to explain (1) why ectotherm’s body temperature preferences should lie below
the temperatures that optimize physiological performance (Martin and Huey 2008), (2) why ectotherms fitness
should be more vulnerable to changes in temperature variance rather than to averaged climate warming (Vasseur
et al. 2014), and (3) why temperature variance has to be accounted for when determining the climatic ranges
for the development (Blanford et al. 2013) and the transmission (Paaijmans et al. 2010) of pathogens.
Scale transition theory can also be used to translate risk sensitivity of foraging behavior into long- term
energetic gain (Smallwood 1996, Matassa and Trussell 2014). In the context of resource- dependent growth,
ST theory can be related to resource- and growth-integration, two important concepts of resource- limited
growth in variable environments (Litchman 2000, Sterner and Schwalbach 2001, Hood and Sterner 2010).
Growth integrators readily respond to resource abundance changes, producing synchrony between growth
and resource fluctuations. The resulting long- term growth rate is the mean of the growth expected for
each value the resource takes, thus the
g(R)
term of Eq. 1. Alternatively, resource integrators are able to
store resources, thus buffering the resource fluctuations and, by consequence growth fluctuations, around
their mean values (Fujiwara et al. 2003). Hence, the integrated growth on variable resources departs from
the predicted
g(R)
and converges toward the growth predicted by the mean resource level
g(
R)
depending
on the strength of the storage buffering effect (reserve effect).
Scale transition theory can be applied to both spatial and temporal variations. Rather than quantifying the
integrated performance through time of an individual in a variable environment, ST can be used to describe
the instantaneous performance of a population of individuals distributed in a heterogeneous landscape. The two
applications can be combined to estimate the time- integrated physiological performance of the population.
Limitations
Scale transition theory is a highly valuable theoretical tool for understanding the effects of environmental
variation on physiological performance, the mean- variance interaction, and in its multifactorial version (see text:
Accounting for multiple co-limitng factors and partitioning their effects), for partitioning variance and covariance
effects. However, the ST equation is accurate only when σ
x
is small. For temperature performance curves
(TPCs) for instance, it is accurate only when the range of temperature is small compared to the overall breadth
of the TPC. For numerically accurate predictions at larger variances,
g(x)
must be calculated using
where
P
(x;
𝜇
x
,
𝜎
2
x
)
is the probability density function of the distribution of the limiting factor x (Vasseur et al.
2014). The equation can be solved analytically for Gaussian distributions. For more complex distributions,
g(x)
must be calculated from numerical simulation in which x are drawn at random from the distribution.
For each drawn x, a g(x) is calculated to produce the arithmetic average
g(x)
. Also, in its current version,
ST theory is based on performance functions that do not account for multiple limiting factors or some
physiological phenomena thereby reducing the accuracy of the predictions under some circumstances (see
Box 3: Time-scale-dependent effects).
(B1)
Integrated
performance
g(R) ≈
mean- field
g(
R) +
scale transiton
1
2
g
��
(
R)
2
R
g
(x) =
g(𝜇
x
,𝜎
2
x
) =
∫
P(x;𝜇
x
,𝜎
2
x
)g(x)
dx
