Metabolic ecology

Authors


Summary

  1. Ecological theory that is grounded in metabolic currencies and constraints offers the potential to link ecological outcomes to biophysical processes across multiple scales of organization.
  2. The metabolic theory of ecology (MTE) has emphasized the potential for metabolism to serve as a unified theory of ecology, while focusing primarily on the size and temperature dependence of whole-organism metabolic rates.
  3. Generalizing metabolic ecology requires extending beyond prediction and application of standardized metabolic rates to theory focused on how energy moves through ecological systems.
  4. A bibliometric and network analysis of recent metabolic ecology literature reveals a research network characterized by major clusters focused on MTE, foraging theory, bioenergetics, trophic status, and generalized patterns and predictions.
  5. This generalized research network, which we refer to as metabolic ecology, can be considered to include the scaling, temperature and stoichiometric models forming the core of MTE, as well as bioenergetic equations, foraging theory, life-history allocation models, consumer–resource equations, food web theory and energy-based macroecology models that are frequently employed in ecological literature.
  6. We conclude with six points we believe to be important to the advancement and integration of metabolic ecology, including nomination of a second fundamental equation, complementary to the first fundamental equation offered by the MTE.

Introduction

One way to think of an animal is as an energy processor: it acquires energy from its environment and allocates this energy among maintenance, growth, and reproduction, with the end result that a portion of the ingested energy is converted into (somatic or reproductive) biomass (Yodzis & Innes 1992).

Thinking about animals in this way is attractive because it serves to link environmental conditions to ecological and life-history outcomes, via explicit and quantifiable physiological processes governed by physical laws defining the conservation and loss of energy. Even better, the approach extends beyond the scales of organismal biology rather well – cells and organelles can be usefully thought of as energy processors, as can populations, species and ecosystems. As summarized recently by Brown, Sibly & Kodric-Brown (2012), ‘Ecology is fundamentally metabolic and we can look to metabolism as the mechanistic basis for a unifying theory of ecology’.

Most recent attention related to the metabolic unification of ecology has focused on the metabolic theory of ecology (MTE), as summarized by Brown et al. (2004). Brown et al.'s (2004) definition of metabolism and suggested application to ecology is notably broad:

Metabolism is the biological processing of energy and materials. Organisms take up energetic and material resources from the environment, convert them into other forms within their bodies, allocate them to the fitness-enhancing processes of survival, growth, and reproduction, and excrete altered forms back into the environment. Metabolism therefore determines the demands that organisms place on their environment for all resources, and simultaneously sets powerful constraints on allocation of resources to all components of fitness. The overall rate of these processes, the metabolic rate, sets the pace of life. It determines the rates of almost all biological activities.

Yet, much of the attention generated by MTE has focused, in particular, on the form and mechanistic basis of the relationship between body size, temperature and metabolic rate. The mechanisms and parameters that define the size and temperature dependence of metabolic rates are clearly important and controversial (see Maino et al. 2014), but here, we seek to make a distinction between this focus and the broader application of metabolic theory in ecology. As is readily acknowledged by MTE proponents (Brown, Sibly & Kodric-Brown 2012), conceiving metabolic theory as either a single fundamental equation or as one or a few processes responsible for many broadscale ecological patterns constrains how much of ecology can use metabolic theory as its foundation. Clearly, ecology is a broad field of study, and the biological processing of energy and materials is a complex and composite phenomenon with highly diversified inputs, regulatory controls and outcomes. Thus, ecology and metabolism intersect in many ways, which are likely to be beyond the reach of a single equation or a few parameterized processes.

Brown et al. (2004) suggest that ‘metabolic theory may provide a conceptual foundation for much of ecology, just as genetic theory provides a foundation for much of evolutionary biology’. One of the successes of genetic theory is the diversity of theoretical approaches, and models that have been developed and applied. A Web of Science (v.5.9. Thomson Reuters) search on genetic* + theor* + evol* identifies more than 12 000 publications between 2005 and 2012. Considering only the 10 most-cited papers within this 12 000 publication set, genetic theory can be seen to focus on genome dynamics, phylogenetic inference, game theory and the regulation of gene expression. There is no one fundamental genetic equation, but rather a wide array of genetic models, ranging from simple to complex, with differing inputs and outputs, and divergent areas of application, loosely connected to each other through the shared conceptual foundation of heritable variation.

Likewise, if metabolic theory is envisioned, not as a single and controversial fundamental equation, but as any and all ecological theory using the biological processing of energy and materials as its conceptual foundation, then much more ecology comes into play. But realizing this potential requires awareness and integration of theory that captures a more diverse set of metabolic constraints and consequences in animal ecology. Fortunately, there is a deep and diversified foundation of energetic and metabolic theory in ecology, including contributions from many of the most influential ecologists of the 20th century. Lotka's (1922) speculation that ‘Natural selection tends to make the energy flux through the system a maximum, so far as compatible with the constraints to which the system is subject’ was later advanced and formalized as the maximum power principle by Odum & Pinkerton (1955). Elton (1927) considered ‘supplies of energy’ as the basis of food chains, and Lindeman's (1942) trophic-dynamic models are organized around ‘the transfer of energy from one part of the ecosystem to another’. Fisher (1930) wondered about ‘what circumstances in the life history and the environment would render profitable the diversion of a greater or lesser share of the available resources towards reproduction’. Hutchinson (1941) envisioned open-water biological communities as ‘machines causing a detour in the degradation of radiant energy from the sun’. MacArthur & Pianka (1966) modelled optimal diet breadth based on the principle of maximizing energy gain per unit time. Andrewartha & Birch's (1984) ‘theory of environment’ considers that an animal's environment is defined, first and foremost, by components directly affecting its accumulation or configuration of matter and energy.

Thus, our intent in initiating this Journal of Animal Ecology Special Feature and in producing this introductory manuscript was to consider metabolic ecology in all its diversity. In particular, we were curious how various metabolic and energetic principles are being incorporated into recent theory focused at various scales of organization within animal ecology, including but not limited to the MTE. What are the key metabolic constraints and currencies used to model the behavioural decisions of individual animals, the trophic interactions of consumers and resources, and the interaction strengths and nutrient cycles of whole food webs? How easily can all of these currencies and constraints be related to each other? Accordingly, we invited contributed articles from researchers active across the ecological hierarchy, with research foci ranging from individual behaviour to whole ecosystems, and asked them to take a broad-brush look at how metabolism functions as a currency and a constraint within their research area. As a preface to these special feature papers, we provide a systematic review and bibliometric analysis of recent animal ecology papers with a focus on metabolism and energy. This literature review and analysis offer an organizational framework for metabolic ecology, highlighting clusters of research focus and literature citation that define current research on metabolic currencies and constraints in animal ecology. We situate the six contributed papers in relation to this organization and conclude with a discussion of six major challenges that we believe to be important to the future of metabolic ecology.

Materials and methods

To assess areas of research emphasis in relation to metabolic ecology, we completed a Web of Science (v.5.9 Thomson Reuters, New York, US) literature search and analysed identified references using Science Mapping Analysis software Tool (SciMAT), an open-source science mapping software tool for bibliometric networks (Cobo et al. 2012). We conducted two searches, one using topic keywords metabo* + theor* + ecolog* (hereafter referred to as the metabolic theory search) including years 2005–2012, and the other using energ* + model* + ecolog* + animal* (hereafter referred to as the energy model search) including years 2005–2012. Topic searches cover complete Web of Science records, including titles, abstracts, author key words and Web of Science ‘KeyWords Plus’. Articles identified by the metabolic theory search were predominated by contributions advancing or evaluating the MTE as described by Brown et al. (2004), because of the perfect correspondence of the terms in our keyword search with the MTE title. The energy model search was intended to avoid this word correspondence while including terms that would relate to metabolism and theory within an ecological domain. The term animal* was included in the energy model search to narrow the focus to energy in biological systems, in general, and animals, in particular. Thus, while energy and energetics are not fully synonymous with metabolism, and theory is not fully synonymous with models or modelling, the energy model search successfully identified a broader literature of pertinence to metabolic ecology.

We then completed a bibliometric network analysis on both article sets using scimat (v.1.1.0; Cobo et al. 2012). Individual articles (nodes) were associated with each other (links) based on shared literature cited using the formula:

display math

with strong links among articles that cite similar literature and weak links among articles citing distinct literature. Basing the network on literature cited rather than, for example, shared key words or shared authorship was intended to reflect the literature base, and thereby the conceptual foundations, from which each article arose. Each network was then imported into gephi (v.0.8.1; Bastian, Heymann & Jacomy 2009), an open-source network visualization and manipulation software, to perform link-based modularity analysis and identify major clusters defined by a high similarity of literature cited. For each network analysis, we report the range of link values (reflective of shared literature cited with a maximum value of 1 for two papers with 100% shared citations) and the modularity coefficient (with high values reflecting well-defined clusters with many strong within-cluster links and very few ‘odd’ links to other nodes outside the cluster).

We assessed the topical focus of the two networks and their five largest clusters (i.e. the five clusters that included the most articles) using a word cloud analysis (Wordle; Feinberg 2009) of word frequency in titles, in which font size reflects title word frequency. Here, we focused on titles alone (rather than the title, abstract and key word searches used to identify relevant literature) to reduce the total number of words included in the analysis and to prioritize title words chosen by authors to be most representative of their article's focus and contribution. The literature cited by articles in each network and in each cluster was also tabulated, and the most frequently cited literature across each network and within each cluster was used as a second descriptor. We used two measures of literature cited within each cluster: the rank order of citation frequency (CR; with 1st indicating the most-cited reference within the cluster) and the citation's cluster specificity (Cs), calculated as the times cited within cluster divided by times cited across network. Thus, Cs = 1·0 indicates the paper is cited within the cluster, but nowhere else in the network and Cs = 0·5 indicates half of the papers' network wide citations occur within the focal cluster. Cluster titles were selected semisubjectively based on word-use frequency apparent in the cluster's wordle as well as the titles and content of particular cited sources that were important in differentiating the clusters (i.e. those with high CR and CS scores).

Results

The metabolic theory search (metabo* + theor* + ecolog*) identified 560 articles published between 2005 and 2012. Title word use within these articles was predominated by terms included in our search (e.g. 81 uses of metabolic, 81 uses of theory and 66 uses of ecology), as well as scaling (52), temperature (36), species (36), size (33), body (32), model (32), rate (31), energy (29), food (27) and growth (26; Fig. 1). The reference most frequently cited by these 560 articles was Brown et al. (2004), with over 40% of articles citing this single reference. After Brown et al. (2004), the 29 next most-cited references were related to Brown et al. (2004); either via similar authors (e.g. Gillooly et al. 2001, 23%; West, Brown & Enquist 1997, 22%), a shared focus on allometry (e.g. Peters 1983, 15%; Kleiber 1932, 9%; Reich et al. 2006, 6%), temperature (e.g. Clarke 2004, 5%) or stoichiometry (e.g. Sterner & Elser 2002, 7%), or by being presented as a test or review of models and predictions summarized in Brown et al. (2004) (e.g. Dodds, Rothman & Weitz 2001, 8%; Glazier 2005, 8%; Kozlowski & Konarzewski 2004, 7%). The two most frequently cited references lacking a direct linkage to Brown et al. (2004) are Felsenstein's (1985) description of independent contrasts for multispecies comparisons (36th most-cited reference, cited by 4% of papers in the set), and Currie et al.'s (2004) test of climate-based hypothesis for large-scale diversity gradients (rank 38th, cited by 4%).

Figure 1.

Network analysis of 560 articles located through a metabolic theory search (metabo* + theor* + ecolog*) for years 2005–2012. Network nodes are individual publications, and node connectivity is based on shared literature cited. The top left word frequency analysis (wordle) is representative of title word use across the entire network. The remaining six wordles are representative of title word use within six major clusters present within the network.

The metabolic theory network had link values ranging from 0 to 0·294, and 25 clusters were identified with a modularity coefficient of 0·164, reflective of a network that is strongly linked overall, in part, because it is comprised of clusters that are weakly differentiated from each other. Thus, this network can be envisioned as one large, well-connected network comprised of overlapping clusters. The largest six clusters (two clusters were tied for fifth largest, so we included both in subsequent analyses) included 92% of the article set, representing weakly differentiated subdivisions of metabolic theory research (Fig. 1), including clusters focused on temperature and diversity (127 articles), scaling (112 articles), trophic interactions (92 articles), evolutionary trade-offs and interactions (81 articles), plant ecology (52 articles) and socio-ecological systems (52 articles). Three key citations for each of the six clusters are summarized in Table 1.

Table 1. The scope of metabolic ecology as defined by the conceptual focus of well-cited papers within research clusters. Rows represent five major clusters of the metabolic ecology research network (1–5) and six subclusters from within the MTE and MTE-related cluster (1a–f). See Fig. 3 for additional explanation and presentation of clusters. Citation patterns of selected papers are indicated by CR, the rank order of citation frequency (with 1st indicating the most-cited reference within a cluster) and Cs, the citation's cluster specificity (with Cs = 1·0 indicating the paper is cited within the cluster but nowhere else in the network and Cs = 0·5 indicating half of the papers' network wide citations occur within the focal cluster). Papers were selected based on these citation scores and the extent to which they highlighted cluster-defining conceptual foci
  1. MTE, metabolic theory of ecology.

1. MTE+
1a. Scaling

Kleiber (1932) (Cr = 7th, Cs = 0·73)

¾ Power relationship between body size and metabolic rate

Peters (1983) (Cr = 5th, Cs = 0·58)

General allometry of morphological, biological, and ecological traits

West, Brown & Enquist (1997) (Cr = 1st, Cs = 0·57)

¾ Power metabolic scaling derived from a general model assuming minimization of energy dissipation in fractal networks of branching tubes

1b. Diversity

Wright (1983) (Cr = 18th, Cs = 0·93)

Diversity as a function of area and energy available in the environment

Rohde (1992) (Cr = 12th, Cs = 0·94)

Diversity as a function of evolutionary speed, which is a function temperature

Allen, Brown & Gillooly (2002) (Cr = 3rd, Cs = 0·68)

Diversity as a function of metabolism and evolutionary speed

1c. Trophic interactions

Elton (1927) (Cr = 12th, Cs = 0·77)

Energy flows between carnivores, herbivores and plants

Yodzis & Innes (1992) (Cr = 11th, Cs = 0·55)

Energy-explicit consumer–resource equations

Brose, Williams & Martinez (2006) (Cr = 5th, Cs = 1·0)

Extended Yodzis & Innes (1992) equations to N-species webs. Referred to elsewhere as the Allometric Trophic Network (ATN) model

1d. Evolutionary trade-offs and interactions

(Pearl 1928) (Cr = 4th, Cs = 0·5)

The rate of living and life span

Sheldon & Verhulst (1996) (Cr = t5th, Cs = 0·83)

Immunity, reproductive effort and longevity

Strauss et al. (2002) (Cr = t5th, Cs = 0·83)

Resistance to herbivory and optimal defence theory

1e. Plant ecology

McMahon & Kronauer (1976) (Cr = 26th, Cs = 0·89)

Tree branching patterns maintaining structural support

Niklas (1994) (Cr = 16th, Cs = 0·67)

General allometric scaling in plants

West, Brown & Enquist (1999) (Cr = 1st, Cs = 0·73)

¾ Power scaling of plant metabolism derived from a general model assuming minimization of energy dissipation in branched vascular systems

1f. Socio-ecological systems

Odum (1971) (Cr = 16th, Cs = 0·86)

Diverse content, including the maximum power principle emphasizing the prioritization of power over efficiency

Foster (1999) (Cr = 1st, Cs = 1·0)

Marx's concept of metabolic rift created when resource demands of social metabolism exceed the resource supply generated by the metabolism of natural systems

Clark & York (2005) (Cr = 2nd, Cs = 1·0)

Metabolic rift concept applied to greenhouse gas emissions and sequestration

2. Foraging theory

Charnov (1976) (Cr = t4th, Cs = 1·0)

Marginal value theorem for energy gain optimization by central place foragers

Stephens & Krebs (1986) (Cr = 1st, Cs = 1·0)

Optimal foraging theory, including information constraints and risk sensitivity

Houston & McNamara (1999) (Cr = 3rd, Cs = 0·78)

Behavioural decisions, with a focus on dynamic optimization, state dependency and predation

3. Patterns-inference-prediction

MacArthur & MacArthur (1961) (Cr = t3rd, Cs = 1·0)

Diversity as a function of habitat configuration

Tilman et al. (2001) (Cr = t3rd, Cs = 1·0)

Forecasting environmental impacts based on current use and future growth

Burnham & Anderson (2002) (Cr = 1st, Cs = 0·71)

Model support as a function of simplicity and likelihood

4. Bioenergetics

Kleiber (1975) (Cr = t2nd, Cs = 1·0)

Diverse content including an expression of the first law of thermodynamics relating decrease in chemical energy to heat, work and other forms of energy

Schmidt-Nielsen (1997) (Cr = 1st, Cs = 1·0)

Diverse content including metabolic heat production in relation to heat loss via conduction, convection and radiation and heat storage

Alexander (2003) (Cr = t2nd, Cs = 0·80)

Diverse content including the energy cost of transport in relation to power, mass and velocity

5. Isotopes-diet-trophic status

DeNiro & Epstein (1978, 1981) (Cr = 2nd, Cs = 1·0; Cr = 1st, Cs = 1·0)

Isotopic fractionation between diet and consumer

Minagawa & Wada (1984) (Cr = 6th, Cs = 1·0)

Trophic position deduced from diet composition and fractionation constants

McCutchan et al. (2003) (Cr = 3rd, Cs = 1·0)

Variability in fractionation constants related to dietary protein composition, tissue-to-tissue variation, and sample preparation

The energy model search (energ* + model* + ecolog* + animal*) identified 257 articles published between 2005 and 2012. Title word use within these articles was predominated by terms included in our search (e.g. 25 uses of energy, 21 uses of ecological and 19 uses of model), as well as body (15), metabolic (15), foraging (14), scaling (13), food (13), theory (12), size (12), habitat (12), thermal (11) and temperature (11; Fig. 2). The reference most frequently cited by these 257 articles was again Brown et al. (2004), but only 13% of articles cited this reference. Other references that were highly cited by this article set, but not by the metabolic ecology article set, included Stephens & Krebs (1986) foraging theory book, Burnham & Anderson's (2002) model selection and multimodel inference guide, Nagy, Girard & Brown's (1999) field metabolic rate review, and McNab's (2002) book on the physiological ecology of vertebrates.

Figure 2.

Network analysis of 257 articles located through an energy model search (energ* + model* + ecolog* + animal*) for years 2005–2012. Network nodes and connectivity are as described for Fig. 1. The top left word frequency analysis (wordle) is representative of title word use across the entire network. The remaining five wordles are representative of title word use within five major clusters present within the network.

The energy model network had link values ranging from 0 to 0·086, and 32 clusters were identified with a modularity coefficient of 0·468, reflective of a network that is weakly linked overall, in part, because it is comprised of clusters that are well differentiated from each other. Thus, this network can be envisioned as multiple, distinct clusters that are weakly connected with each other, leading to a loosely connected overall network. The largest five clusters included 77% of the energy model article set and represented major subdivisions of energy model research (Fig. 2), including clusters focused on metabolic theory (57 articles), foraging theory (53 articles), patterns, prediction and inference (37 articles), bioenergetics (30 articles) and isotopes, diets, and trophic status (22 articles). Three key citations for each of the five clusters are summarized in Table 1.

Discussion

The network analysis identifies six research clusters within a MTE-dominated literature (Fig. 1) and embeds MTE-dominated literature within a larger body of energy and metabolism-related research (Fig. 2). We refer to this larger network of research as metabolic ecology (see also Brown, Sibly & Kodric-Brown 2012). So considered, metabolic ecology is a loosely connected but highly clustered network of ecological research that uses metabolism as a conceptual foundation, whereas MTE is a very productive, well-cited and well-connected cluster within the metabolic ecology network. However, even the MTE-dominated portion of this cluster extends well beyond the fundamental MTE equation (predicting metabolic rate as a function of body size and temperature) to diverse research foci including trophic interactions, evolutionary trade-offs and socio-ecological systems.

Metabolic ecology can thus be considered to include the scaling, temperature and stoichiometric models forming the core of MTE, as well as bioenergetic equations, foraging theory, life-history allocation models, consumer–resource equations, food web theory and energy-based macroecology models that are frequently employed in ecological literature. Socio-ecological models oriented around Marx's theory of metabolic rift were identified as an additional cluster within the metabolic ecology network. Although most contemporary papers within this socio-ecological cluster are weakly linked to the rest of the network, a shared influence of classic ecological literature, including Lotka (1922) and Odum (1971), combined with recent extensions of MTE to socio-ecological systems (Brown et al. 2011; Hamilton, Burger & Walker 2012), offers avenues of future integration. Isotope-based studies of trophic status form another cluster of metabolic ecology research that is more isolated than expected given obvious potential linkage to bioenergetic and consumer–resource models (Harvey et al. 2002; Pecquerie et al. 2010).

All six special feature articles, published in this issue, integrate concepts, modelling approaches and literature from multiple clusters within the metabolic ecology network to address key ecological questions situated at different scales of organization. Maino et al. (2014) start by showing that constraints involved in the storage and use of assimilated resources generate the same metabolic scaling relationships as (Brown et al. 2004) derive from transport networks. This compelling alternative, derived from Dynamic Energy Budget (DEB) theory (Kooijman 2010), highlights a larger set of general biophysical constraints operating at the interface of metabolic ecology and scaling relationships. Houston & McNamara (2014) remind us of the importance of behaviour and individual flexibility in ecological interactions. In particular, they review the role of metabolism and energetic status in behavioural decisions and routines, and describe how energy gain, predation and somatic damage can be combined into a single currency framework. Buckley et al. & DeLong et al. (2014) relate metabolism to population-level phenomena. DeLong et al. (2014) focus on density-dependent metabolism while Buckley et al. (2014) consider species differences in energetic status across an environmental gradient. Finally, Reuman et al. and Dell et al. (2014) focus on whole competitive communities and trophic interactions, respectively, with a shared focus on the temperature dependence of metabolism and related processes. Despite diversified points of emphasis, all of these special feature articles draw on literature and approaches from multiple research clusters within the metabolic ecology network (Fig. 3), highlighting how diversified metabolic ecology approaches can be combined in novel ways to address important ecological questions.

Figure 3.

Schematic of the metabolic ecology research network, comprised of six clusters (top) identified through the metabolic theory search (Fig. 1) and five clusters (bottom) identified through the energy model search (Fig. 2). Because one of the five bottom clusters overlapped extensively with the metabolic theory search, which yielded mainly metabolic theory of ecology (MTE) and MTE-related papers, this cluster is labelled MTE and situated in the middle of the network generated by the metabolic theory search. So envisioned, metabolic ecology (abbreviated ME in the bottom network) is comprised of five loosely connected clusters, one of which is dominated by MTE and MTE-related research, which further subdivides into six, weakly differentiated clusters. The clusters and linkages emphasized by the six special feature papers are illustrated by the smaller panels on the left and right of the main schematic. In these panels, text size, box line weight and darkness of connecting lines reflect correspondence between the literature cited by special feature papers, relative to the clusters identified in our literature-wide bibliometric analysis. Despite differing areas of emphasis, all special feature papers draw on literature and theory distributed across the metabolic ecology network.

We conclude this paper with the below six points we believe to be important to the advancement and integration of metabolic ecology.

Metabolism or energy or heat or work or power or efficiency or resources – what's in a word, what's in a variable?

As ecologists, we often get away with making rather loose associations between the concepts and quantities related to metabolism, energy, heat, work, power, efficiency and resources. A bioenergetic equation focused on the distribution of ingested energy among urinary and faecal output, growth, reproduction and maintenance has clear analogies to a life-history model focused on the allocation of assimilated resources to survival and reproduction. A measure of the metabolic rate of a homeotherm based on gas exchange will often yield a result that is broadly comparable to a measure based on heat production. Sometimes, it is enough to treat these as broadly analogous and conceptually linked. But, when it comes time to directly compare measured traits or parameterize a model, much more precision will usually be required. We are unable to review here all of the ways that metabolism, energy, heat, work, etc., can be measured, and how these measures are related and different. Thus, we direct readers to a few of the many detailed treatments of metabolism, energy and related concepts (e.g. Kleiber 1975; Robbins 1993; Kooijman 2000; McNab 2002) and encourage caution and reflection when equating measurements and units used in different areas of metabolic ecology. Sometimes, it will be simply a matter of unit conversion (e.g. 1 cal = 4·184 J, 1 J s−1 = 1 W, mlO2 can be converted to cal if the respiratory quotient is known or can be assumed; Robbins 1993), but more often than not researchers will be faced with differing methodological standards, conventions and limitations, as well as implicit assumptions regarding the processes and forms of variation that should be included and excluded from measurements. For example, the cost of growth and maturation is included in the respiration term within DEB theory (Kooijman 2010) but separated from maintenance costs in many other frameworks. At an empirical level, there is considerable disagreement about whether and how to account for body size and temperature variation in metabolic comparisons (McNab 2002). And how we model and parameterize metabolism in theory is not particularly well aligned with how we measure metabolism in practice. As a result, many of the energetic or metabolic frameworks used to explain ecological patterns are rather loose in detail and mechanism, which makes them difficult to test and easy to confuse with alternative explanations and null model predictions (e.g. Currie et al. 2004; Price et al. 2012; Isaac, Storch & Carbone 2013).

From MTE to ecological dynamics and a second fundamental equation

Most of the recent MTE-related attention on ecological energetics has focused on whole-organism metabolic rates and the so-called pace of life, including a fundamental equation of the form

display math(eqn 1)

where E is metabolic rate or rate of energy expenditure (typically expressed per unit time), M is a measure of body size such as mass and T is temperature (Brown et al. 2004).

But given many questions in ecology are related to organism–organism interactions and allocations (May & McLean 2007), information about the movement, conversion, storage and allocation of energy within ecological systems can be as or more important than information about the metabolic rate of one or many components of the system. Many models cited in the metabolic ecology network we describe here (Table 1) are dynamical equations that consider the flow of biomass and energy between interacting populations (Yodzis & Innes 1992; Brose, Williams & Martinez 2006) or the allocation of accumulated resources to competing demands (Sheldon & Verhulst 1996; Strauss et al. 2002). Most, if not all, of these dynamic approaches to energy budgets are oriented around an equation of the form:

display math(eqn 2a)

where S is the energetic surplus per unit time, I is energy intake per unit time, c is conversion efficiency and E is energy expenditure per unit time. Equation (2a) is, fundamentally, an energy-balance equation based on the law of conservation of energy (energy can neither be created nor destroyed, only changed in from). Forms of this equation, or at least the principles on which it is based, are used to model the growth and nutrition of domestic animals (France & Kebreab 2008) and fish (Jobling 1994), body weight regulation and obesity in humans (Spiegelman & Flier 2001), environmental heat exchange (McNab 2002), and many other phenomena in physical, environmental and life sciences. Principles of energy conservation and allocation feature prominently in Kooijman's DEB (for example, fig. 1 in Nisbet et al. 2000) and form the basis of an extension of MTE to model ontogenetic growth (West et al. 2001). The ecological importance of this equation arises from its amenability to be expressed as a dynamical equation, where rates vary as a function of time, t

display math(eqn 2b)

These energy budget dynamics can then be incorporated into coupled-dynamical equations focused on the movement of energy within and among organisms, populations, species and ecosystems. For example, equations 3 and 4 in Yodzis & Innes (1992) can be re-expressed as:

display math(eqn 3a)
display math(eqn 3b)

where C is consumer biomass, t is time, dI/dt is per capita consumer intake (which varies as a function of resource biomass, R), c is conversion efficiency, dE/dt is per capita consumer expenditure, r is the intrinsic production–biomass ratio of the resource, K is the resource carrying capacity and fe = fraction of resource biomass removed that is eaten by the consumer. The correspondence between eqn 3a and eqn 2a is most obvious, but, in a broad sense, eqn 3b is also an energy- or mass-balance equation treating changes in resource biomass as a function of accumulation minus loss. Notice, however, that the loss term in eqn 3a is more narrowly defined as consumer energy expenditure or respiration, whereas the loss term in eqn 3b is more broadly interpreted as energy loss through consumption and mortality.

The more general point is that eqn (eqn 1) predicts metabolic rates, whereas eqn (2a) and its many variations (e.g. 2b, 3a, 3b, etc.) consider the movement of energy and materials between competing demands and through ecological systems, which brings a lot more ecology into play. Thus, we suggest that eqn (2a) and its many potential elaborations might be considered as the second fundamental equation of metabolic ecology.

Metabolism as something more than a subtraction term

Incorporating mechanistic rate predictions derived from eqn (eqn 1) into dynamic equations based on eqn (2a) offers considerable promise, and several of the special feature articles and papers summarized in Table 1 do exactly this. For example, Yodzis & Innes (1992) describe energetically explicit consumer–resource equations derived from scaling relationships and the DEB (Kooijman 2010) offers a comprehensive modelling framework incorporating, among other things, metabolic scaling, resource allocation and trophic interactions.

Most approach this integration using eqn (eqn 1) to predict E as a function of size and temperature, which is then included in eqn (2a) as something that is subtracted from assimilated energy to estimate the energy surplus. Both this model formulation and the comparative empirical tradition from which it is derived reflect a rather static view of metabolism and energy expenditure as a parameter that can be reasonably predicted from size and temperature, that is independent of energy intake, and does not vary substantially with resource abundance. In fact, energy expenditure and energy intake are functionally linked. For all animals, acquiring resources requires activity and activity requires increased energy expenditure (Kam & Degen 1997; Humphries & Umbanhowar 2007). Animals achieve energy surpluses when resources are abundant not because their intake increases above a fixed level of expenditure, but because, under these conditions, increases in expenditure return a more than compensatory increase in intake. In addition, many taxa possess physiological adaptations that permit reversible reductions in maintenance energy requirements during periods of resource shortage (e.g. diapause, torpor, body or organ size adjustment; Piersma & Lindström 1997; Guppy & Withers 1999).

A better representation of the process by which animals achieve an energy surplus can be achieved by re-expressing eqn (2a) in a manner that explicitly links energy expenditure to energy intake (c.f. Brown 1989; Kam & Degen 1997). Total energy expenditure (E from eqns (eqn 1) and 2a now expressed as Etot) can be divided into two components, one that directly enhances energy intake and another that does not. Given the functional association between activity and intake, we can designate one component as activity expenditure (Ea) and the other as maintenance expenditure (Em), such that Etot = Ea + Em. Considering only a single activity mode that is a prerequisite to intake, and that animals are active during time p and inactive the rest of the time (1−p), we have

display math(eqn 4)

This equation provides a much better functional representation of how individual animals acquire a surplus – energy accumulation is benefited by high activity (p), high net energy gains when active (IcEa) and low maintenance requirements (Em). If, as generally should be the case, IcEa is positive and Ea ≫ Em, then there will be a positive relationship between Etot and S rather than the negative relationship suggested by eqn (2a). Given associations between intake and activity and between activity and expenditure, it follows that energy expenditure will vary according to resource abundance, population density (see DeLong et al. 2014) and many other ecological variables beyond size and temperature.

The importance of activity in metabolic ecology

Equation (eqn 4) suggests a fundamental importance of activity in predicting and assessing the energetic status of animals and their resources. In fact, for most animals, activity is both a prerequisite for energy acquisition and a determinant of increased predation risk (Lima & Dill 1990; Adolph & Porter 1993). The association between activity and predation risk occurs because animals not actively seeking resources are able to occupy refuges (e.g. burrows, nests, cavities, crevices) where energy losses and predation risk can be simultaneously minimized. Even organisms unable to occupy discrete, structural refuges (e.g. freshwater and marine organisms, large terrestrial animals) may exploit thermal, solar, flow and wave refuges when inactive (Kramer, Rangeley & Chapman 1997) and are likely to experience increased predation risk during activity if they alternate between inactivity in low food, low-predation habitats and activity in high food, high-predation habitats (e.g. Creel et al. 2005; Ahrens, Walters & Christensen 2012). Therefore, we should expect most animals to alter activity, and thus energy expenditure, according to the abundance of both resources and predators.

Activity also affects the thermal conditions to which animals are exposed. Differential activity and occupation of microenvironments are the major reason why body temperature of terrestrial ectotherms and the thermoregulatory demands of terrestrial endotherms cannot be easily predicted from conditions measured at a nearby weather station. Similar but buffered activity–thermal exposure relationships can occur in aquatic environments, due to the differential activity responses of aquatic organisms to spatial and temporal heterogeneity of water temperature. Understanding how environmental conditions translate into metabolic status requires quite specific and comprehensive information about where animals are located and what animals are doing.

Activity and behaviour are therefore important, and we feel under-recognized, aspects of metabolic ecology – all animals alternate between inactive and active states, and this switch has simultaneous impacts on energy expenditure, energy intake and predation risk. In many ways, behavioural activity determines the extent to which animals are energetically engaged or disengaged from abiotic and biotic interactions. Thinking about animal metabolism in this way offers great promise in the application of bioenergetic and behavioural decision frameworks to the expanding ecological focus on trait-mediated indirect interactions (Werner & Peacor 2003).

Ecologically relevant measures of metabolism

Metabolism and energetic status can thus be seen to be multivariate phenomena that vary overtime. Per unit time measures of whole-animal metabolism quantified via gas exchange have been and will continue to be pillars in the study of animal metabolism. The development of the double labelled water technique was revolutionary because it allowed the study of animal energetics to escape the confines of the small respirometry chambers and tethered masks (Speakman 1997). But we need another revolution that will allow the study of animal energetics to escape the confines of hourly and daily measurement windows to the seasonal and multiannual timeframes known to be critical in determining the outcome of ecological interactions. Determining how the metabolic status of different organisms change overtime as their resources and predators fluctuate is likely to yield more insight into the ecological importance of metabolism than carefully measuring a ‘snapshot’ or average value for the trait, which may be expressed only momentarily as an animal's physiology tracks constantly changing ecological conditions. Further, the rate of energy expenditure is only one of many components of energetic status of relevance to ecological dynamics – energy intake, storage and allocation, as well as activity and spatial location (see above), are of similar importance.

The rapidly advancing field of biologging, involving the use of miniaturized animal-attached tags for logging and/or relaying of data about an animal's movements, behaviour, physiology and/or environment (Rutz & Hays 2009), offers considerable promise in obtaining multiday, multiseasonal and multiannual measures of energetic status. When these continuous time measures are combined with spatial location, as recorded on GPS collars, an animal's energetic status becomes explicitly defined in both time and space. With the additional innovation of simultaneous deployment of these biologging units on, for example, predators and prey or multiple prey species experiencing indirect competition via shared predation, metabolic ecology enters a whole new realm of possibility.

But capitalizing on all this potential will not be easy and will require (i) solving the formidable logistical challenges related to device deployment, attachment, operation and data retrieval, which continue to constrain biologging research (Rutz & Hays 2009), (ii) an openness to alternative measures of energetic status (e.g. heart rate, body temperature, movement measures, behavioural status) because at present and in the foreseeable future, most biologging studies will not directly quantify O2 consumption, CO2 production, heat production or total caloric intake – the four standards of metabolic research, and (iii) creative biologging research design and theory-data integration to achieve broad conceptual advances in metabolic ecology.

Finding a balance between unification and diversification in metabolic ecology

Although allometric models provide useful generalities about metabolic variation across a wide range of body size, deviations from predictions are often as interesting and meaningful as the predictions themselves. Recent attention on curvature in metabolic allometry is one way in which variation from predicted patterns is being used to extend or refute general theory (Reich et al. 2006; Kolokotrones et al. 2010; Mori et al. 2010). But here, we focus primarily on the scatter – the substantial variation in basal rates of expenditure occurring at any given body size, regardless of the predictive model applied to the data. Residuals from predicted rates are correlated with a suite of environmental, trophic and life-history parameters possibly resulting from physiological and morphological constraints associated with adaptation to different ecological niches (Lovegrove 2000; McNab 2002). This variation offers insights into fundamental trade-offs that differentiate closely-related and similar-sized organisms, which could prove enormously powerful in understanding different types of population dynamics, interspecific competitive outcomes and trophic interactions. As such, a truly unified theory of metabolic ecology may have two parts: one part focused on broad, sweeping patterns and a few general processes that generate these patterns, the other part focused on the variance around these patterns and what they reveal about fundamental trade-offs and adaptive variation.

As an example, several authors have interpreted residuals around metabolic rate – body size relationships as representative of a fast–slow metabolic continuum that may be correlated with life-history and behavioural variation (Lovegrove 2000; Ricklefs & Wikelski 2002; Réale et al. 2010). Thus, metabolically fast organisms may not only expend more energy than metabolically slow organisms, they may also have more capacity for higher energy intake under the right conditions and be more prolific at transforming excess resources into powerful numerical responses. On the other hand, metabolically slow organisms may have enhanced capacity to reduce already low rates of energy expenditure (via dormancy, cryptobiosis or other forms of metabolic depression) when resources are low or conditions are harsh (Guppy & Withers 1999). Such a metabolically constrained continuum may, then, nicely delineate suites of traits that can be expected to generate strong (i.e. metabolically fast) to weak (i.e. metabolically slow) interaction strengths. This fast–slow continuum provides a general approach to fundamental ecological problems that transcend scales. For example, patterns in the variance allow us simple predictions about organismal population dynamics (e.g. fast/strong tend to be more variable, McCann 2012), community composition (e.g. coexistence in temporally or spatially variable environments, Chesson 2000) and whole food webs (e.g. strong/fast vs. slow/weak pathways in food webs, Rooney et al. 2006).

This promise of moving from organismal metabolic constraints to whole ecosystems has begun to play out in recent food web theory. One of the central goals of ecology is to understand how energy and material flows govern ecosystem function and stability. Arguments abound that human impacts are depleting diversity (Loreau et al. 2006), but the question remains as to whether and how this will reroute ecosystem energy pathways in a way that leads to the collapse of critical ecosystem function. Towards this, ecologists have begun to look at the patterning of interaction strengths (or energy fluxes) in the complex food web networks that make up ecosystems. Theory to this point has taken a body-size allometry perspective such that standard organismal scaling patterns (Peters 1983) act to constrain model interaction strengths (Yodzis & Innes 1992). Rather intriguingly, those that expanded on Yodzis & Innes (1992) energetic framework have found that, on average, these metabolically and energetically bound systems tend to persist far better than randomly assembled food web networks (e.g. Brose, Williams & Martinez 2006). Remarkably, this simple result suggests that physiological, or metabolically derived, organismal properties, in and of themselves, likely contribute significantly to the maintenance of complex networks.

While it is known that metabolism is strongly linked to activity, which in turn mediates species interactions (e.g. consumption rate, predator avoidance, etc.), this mechanistic bridge between physiology, behaviour and ecology is not yet part of the energetic framework that has been employed in food web theory. As discussed above, organisms can be expected to respond to changes in resource and predator density by mediating their activity levels and, as a result, their metabolism. This relationship between metabolism and activity, therefore, ought to strongly affect the expression of interaction strengths of predator and prey and competitors. The likelihood that behaviour expresses itself as variance in the rate parameters governing interaction strengths (e.g. attack rate per prey) may be fundamental to the maintenance of complex webs, yet remains largely unexplored. Further, and perhaps more alarming, the diversity and ecosystem impacts of environmental change (e.g. as a result of climate and land use change), will be dictated by a physiological–behavioural–ecological nexus that we know very little about. Dell et al. (2014) and Houston & McNamara (2014) illustrate some of the biology and theory that needs to be incorporated into food web models.

The MTE of Brown et al. (2004) represents an impressively general framework for understanding size and temperature-dependent metabolism, which has been very successful because of its focus on standardized metabolic rates, which are frequently measured, and consideration of organisms of vastly different body size and temperature, which enhances explanatory power. Metabolic ecology is, by definition, a more diversified set of metabolic theory. And when applied to more subtle forms of ecological differentiation than microbes vs. mammals, most metabolic ecology models will achieve less explanatory power with more parameters than the fundamental equation of MTE. But ecology is, for better or worse, a discipline focused on diversity in its many forms. In this context, the best unifying principles that can be reasonably hoped for are ‘a few general propositions that characterize a wide domain of phenomena and from which can be derived an array of models’ (Scheiner & Willig 2005; see also Murdoch, Briggs & Nisbet 1997; Paine 2002). The metabolic ecology network described here and the special feature articles that follow outline an array of metabolic models derived from the proposition of animals as energy processors. We hope these articles contribute to the advancement of metabolic ecology and its application to a wide diversity of animal ecology research.

Acknowledgements

Manuelle Landry-Cuerrier completed the literature search and network analysis, with the helpful assistance of Dr Manuel Jesus Cobo who kindly converted the Web of Science search results into bibliographical networks based on shared cited references. We thank all the authors of special feature articles, and three anonymous reviewers, for their insights regarding metabolic ecology. MMH and KSM are supported by funding from NSERC, the Natural Sciences and Engineering Research Council of Canada.

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