The Metabolic Theory of Ecology as a Mechanistic Approach

Abstract

Philosophy of science has recently given a great deal of attention to the concept of mechanism. However, unlike the biological mechanisms identified in other fields of the life sciences, ecological mechanisms have not been exhaustively examined. The aim of this chapter is to critically analyze the Metabolic Theory of Ecology. This theory is supposed to provide a unification of population, community and ecosystem approaches rooted in the ecophysiology of individual organisms. In this context, metabolism plays a fundamental role as the unifying concept between levels. According to its authors, this is a mechanistic approach to ecology involving decomposability into parts that structure the different levels of ecological organization and into mechanisms that can be characterized by identifying a phenomenon, parts, causing, and organization. I shall first argue that its mechanistic nature needs clarification. I shall then suggest that the theory can explain some phenomena at various levels of ecological organization and can describe some patterns or tendencies in nature, although it is not able to completely elucidate their mechanistic basis, i.e., to explain the mechanisms that produce these patterns.

3.1 Introduction

The concept of mechanism has recently received a great deal of attention in the philosophy of science. The life sciences offer philosophers of science a variety of examples to challenge the more traditional deductive-nomological model of explanation, in which explanation is provided by derivations from laws. Different areas of biology indicate that scientific enquiry is driven by a search for mechanisms and that explanation is a matter of characterizing them in specificity (Bechtel & Richardson, 2010; Illari & Williamson, 2012; Craver & Darden, 2013; Raerinne, 2013; Pâslaru, 2018). Many biologists and ecologists effectively use a mechanistic research perspective, looking for mechanisms conceptualized as entities generating a phenomenon to be explained. The most basic concept of mechanism – as a start-to-finish sequence of qualitatively characterized operations performed by component parts – was provided by Machamer et al. (2000). This linear characterization is sufficient to single out some important epistemic practices by means of which scientists decompose mechanisms structurally into their parts and functionally into their operations. Glennan (1996) has also developed a mechanistic account, which, initially, retained the centrality of laws in order to explain the interaction of parts. More recently, Glennan (2002) has replaced the language of laws with that of “invariant change-relating generalizations”, an approach that I will also develop further in Sect. 3.4, when the putative mechanistic nature of the Metabolic Theory of Ecology (henceforth, MTE) is analyzed. Bechtel characterizes a mechanism as “a structure performing an action in virtue of its component parts, component operations, and their organization”, adding that “the orchestration of the mechanism is responsible for one or more phenomena” (Bechtel, 2006: 26). Machamer et al. (2000) rejected Glennan’s emphasis on interactions, something that is also relevant for Bechtel and Richardson (2010), and emphasized the dualism of entities and activities. Bechtel and Richardson (2010: 24) had already made implicit this dualism in their discussion of decomposition and localization within the mechanistic account, but they rejected the underlying linearity in Machamer et al. (2000) perspective and, using Glennan’s language of properties, have developed a more dynamical account of mechanistic explanation, assuming patterns of change over time in the properties of the parts and operations. More recently, Glennan et al. (2021: 145) have argued for a Minimal Mechanism Thesis, according to which “a mechanism for a phenomenon consists of entities (or parts) whose activities and interactions are organized so as to be responsible for the phenomenon”. According to these authors, this thesis identifies some points of consensus about what mechanisms are because they are identified and individuated by the phenomena they explain, by the entities or parts they are made of, by what their activities or interactions do, and by the organization in which they are structured.

The change in focus from characterizing explanation in terms of derivation from laws to understanding the role of mechanisms in generating phenomena provides a very different perspective. Let me briefly explain in what sense mechanicist explanation differs from the outdated – at least for many mechanists - deductive-nomological model of explanation (for a more historical overview, see Nicholson, 2011; Illari & Williamson, 2012).

Firstly, the crucial component of a mechanistic account is not the formulation of the relevant law; it is, instead, the determination of the parts of the mechanism, the operations they perform, and how they are organized (Bechtel, 2011; Craver & Tabery, 2019; Glennan et al., 2021). Secondly, although these parts and operations can be described linguistically, it is often more productive to represent them in diagrams (Bechtel, 2011). Thirdly, the demonstration that the mechanism can produce the phenomenon does not rely on logical derivations but, rather, on mental simulations of the mechanism in operation, later ascertained by empirical research. Fourthly, mechanistic explanations are inherently reductionist insofar as they require specifying the parts of a mechanism and the operations they perform (Craver & Tabery, 2019; Pâslaru, 2018). However, they also require consideration of the organization of the whole mechanism and its relation to conditions in its environment, since it is only when appropriately situated that a mechanism will produce the phenomenon of interest (Bechtel & Abrahamsen, 2005).

Mechanisms are decomposable in the sense that the behavior of a system as a whole can be broken down into organized interactions among the parts. There are numerous characterizations of mechanisms in the literature, and a “consensus concept” might be adopted: “A mechanism for a phenomenon consists of entities (or parts) and activities (or operations) organized in such a way that they are responsible for the phenomenon”.¹ All characterizations contain four basic features: a phenomenon, parts, causing, and organization. The phenomenon is the behavior of the mechanism as a whole, being all mechanisms the mechanisms for some phenomenon. The boundaries of a mechanism are fixed by reference to the phenomenon that the mechanism explains. The parts in a mechanism are component parts in virtue of being relevant to explaining the phenomenon.² There has been a great struggle to find a concise way to express the idea of what a part is, a crucial concept required to define the components of a mechanism.³ Mechanists have disagreed with one another about how to understand the concept of mechanistic cause (Craver & Tabery, 2019). New mechanists have been at pains to liberate the relevant causal notion from any overly austere view that restricts causation to only a small class of phenomena, generally associated with physics, such as collisions, attractions or repulsions. Another difficulty has been to distance themselves from the regularist conception of causation, in the Humean sense, common among the logical empiricists.⁴ The characteristic organization of mechanisms is also the subject of considerable discussion (Wimsatt, 1997; Machamer et al., 2000; Bechtel, 2011; Craver & Tabery, 2019). It is relevant to contrast mechanistic organization with aggregation, a distinction that mechanists have used to articulate how the parts of a mechanism are organized together to form a whole. This distinction is crucial in the analysis of some reductionist mechanistic approaches to ecology. Aggregate properties are properties of wholes that are simple sums of the properties of their parts. In aggregates, the parts can be rearranged and intersubstituted without changing the property or behavior of the whole; the whole can be taken apart and put back together without disrupting its behavior, and the properties of the whole change linearly with the addition and removal of parts. Organization can be conceived as non-aggregativity, allowing a mechanistic form of emergence (Wimsatt, 1997). Mechanists have also detailed several kinds of organization characteristic of mechanisms (Craver & Tabery, 2019), in particular spatial organization (including location, shape and orientation) and temporal organization (including order, rate and duration of component operations). Other important features of organization are modularity, a property characterizing the relative functional independence of some parts, i.e., meaning that it should be physically possible to intervene on a putative cause variable of a mechanism without disrupting the functional relationships among the other variables; jointness, a property related to modularity that characterizes the interdependent relationship between parts of a mechanism in the sense that components in a mechanism often form a more complex unit by virtue of the individual properties uniting them; and, finally, mechanists emphasize the hierarchical organization of mechanisms and the multilevel structure approaches in the special sciences, such as ecology, demanding an analysis of mechanistic relations across levels of organization (Craver & Tabery, 2019).

Concerning the issue of explanation, while in the deductive-nomological model explanations are considered arguments showing that the event to be explained is to be expected on the basis of the relevant laws of nature and antecedent and boundary conditions, mechanists, in contrast, insist that explanation is a matter of elucidating the causal structures that produce, underlie, or maintain the phenomenon of interest (Illari & Williamson, 2012; Nicholson, 2011; Craver & Tabery, 2019). Thus, the philosophical problem is largely about characterizing or describing the worldly or ontic structures to which explanatory models must refer to if they are to count as genuinely explanatory. The phenomenon must be situated within the causal structure of the world, and the explanation is an account of how the phenomenon is produced by entities and their properties. However, it is important to emphasize that, even if mechanistic explanations were ubiquitous across empirical sciences, this fact does not entail necessarily that all scientific explanations must be mechanistic, even though some critics claimed that New Mechanists are committed to such a radical position (Glennan et al., 2021).

Most mechanists recognize two main aspects of mechanistic explanation (Craver & Tabery, 2019): the etiological, which reveal the causal history of the explanandum phenomenon; and the constitutive, which explain a phenomenon by describing the mechanism underlying it. With increased attention to the latter, mechanists realized the need for an account of constitutive relevance, a principal need for sorting relevant from irrelevant factors within a mechanism. One central research problem is therefore to identify which of these entities, activities and organizational features contribute to the phenomenon and which do not. In a sense, the challenge is to define the boundaries of a mechanism, i.e., of saying what lies within and outside the mechanism.

It is relevant that in much of the literature on mechanisms, these are contrasted explicitly with laws of nature (Machamer et al., 2000; Craver & Darden, 2013; Craver & Tabery, 2019). This contrast grew out of an emerging consensus in philosophy of science that there are few, or perhaps no, laws in the life sciences (Lawton, 1996; Colyvan, 2003). The empirical generalizations found in biology and ecology tend to be hedged by ceteribus paribus clauses; whether they hold or not depends on background conditions that might not hold and on conditions internal to the mechanism that might fail to occur. In short, these generalizations are mechanistically explicable, and whatever necessity they might possess derives from a mechanism. Thus, mechanisms seem to play the role of laws in the life sciences, because one seeks mechanisms to explain, predict and control phenomena in nature even if mechanisms lack many of the characteristics that define laws in the logical empiricist framework, such as universality, inviolable necessity or unrestricted scope.

Research on mechanisms has also helped to clarify the idea of levels of organization and its relation to other forms of organization and non-mechanistic forms of emergence. Many mechanists emphasize that biological and ecological systems are hierarchically organized into near-decomposable⁵ structures (see Craver & Tabery, 2019, for a description of this perspective): mechanisms within mechanisms. Bechtel and Richardson (2010) argue that two essential claims concerning hierarchical organization can be distinguished: one states that nature is organized in terms of wholes and parts, mereologically; the other asserts that organization sometimes is hierarchical without being decomposable, but when it is decomposable, or nearly so, there is a very natural ranking of types of systems. Thus, when we have a case of strict decomposition, one can project the component part behavior to the systemic behavior; if we have a case of near decomposability, the component part behavior can be approximately projected to the systemic behavior; finally, even in the case of non-decomposition – in which the behavior of one part depends on the behavior of the other parts, as in ecology – assuming the decomposability of a system “can be highly informative” (Bechtel & Richardson, 2010: xxix). These authors defend that decomposition and localization are powerful heuristics for discovering mechanisms and for articulating their structure; however, in the case of the life sciences, they emphasized functional decomposition and localization, assuming that the system responsible for some phenomenon is hierarchical and decomposable – that is, it results from different parts within the mechanism performing their activities. Accordingly, researchers should aim to decompose the phenomenon into the component operations that produce it and localize them within the parts of the mechanism. This is the perspective adopted by the advocates of the MTE, when they decompose the ecosystem’s metabolism in the metabolic processes of populations and individual organisms, as I shall illustrate in Sect. 3.2. However, Bechtel and Richardson (2010) recognize that decomposition can be challenging for those researching natural systems because mechanisms usually do not reveal their parts, while the component operations can be even harder to differentiate. These authors also admit that the notion of localization can be criticized, with the assumption that specific activities can be localized in discrete parts of a mechanism. Nevertheless, Bechtel and Richardson (2010) defend a different construal of localization, which is neither direct nor simple, and whose goal is not to find where an activity takes place but to acquire information about the part involved. The conception of localization of Bechtel and Richardson (2010) is rather different from that assumed by their critics. First, the authors recognize that, although sometimes researchers begin by assuming that the activity of a mechanism is due to one component within it (direct or simple localization), this is only a preliminary step in research: once the component is identified and its behavior explored, it turns out not to generate the phenomenon on its own but to perform an operation that, together with the other operations performed by other components, generates the phenomenon. As research proceeds, it is not the whole phenomenon that is localized in a part of the system but, rather, individual operations, each of which contributes in some way to the phenomenon of interest. Second, although the authors think that the word localization suggests a single discrete spatial location, that is not necessary and is often not correct, because the functional component may be distributed in space, with the intervening space containing parts performing other operations or even entities that are not part of the mechanism responsible for the given phenomenon. A further criticism of localization is that identifying the part performing an operation is of no intrinsic interest. This points to the third, and probably most important, difference in the construal of localization by Bechtel and Richardson (2010): they treat localization not as an end of inquiry but as a heuristic. The goal of localizing is not only to find out where something occurs but to acquire information about the part that is engaged in that operation, which can inform further research. Thus, when direct or simple localization proves inadequate for understanding a given phenomenon, and the phenomenon is functionally decomposed into multiple operations localized in different parts, the issue of how these parts and operations are organized becomes important. In these authors’ perspective, researchers begin with simpler conceptions and hypothesize that a mechanism comprises component parts whose operations are performed sequentially. For the authors the simpler hypothesis may not be the best, but it is after all the simplest, making it easier to assess it. This is what they characterize as indirect or complex localization (a concept already envisaged in Machamer et al.’s (2000) linear characterization of a mechanism). Even when one knows that a simple model is not defensible, the attempt to understand mechanisms in terms of a linear execution can be very productive.

This view leads to the conclusion that evolved structures, such as biological and ecological ones, are more likely to be nearly decomposable into hierarchically organized, more or less stable structures and sub-structures. An important objection has been raised against this perspective (see Bechtel & Richardson, 2010; Craver & Tabery, 2019, for an overview of the discussion), − first by the vitalists and organic holists in the nineteenth and early twentieth century and, more recently, by certain dynamicists – stating that it is misleading because evolution does not construct natural systems from scratch, piece by piece. However, there have been some attempts to reconstruct this argument and tackle this kind of criticism, as a way of showing that evolved systems are more likely to be modular: systems made of independently manipulable parts that can quarantine the effects of changes to specific parts, giving them flexibility to make local changes without causing great side-effects. It is important to add that scientists can only describe and explain mechanisms through the construction of models, which are representations of mechanisms. Such representations are inevitably partial, abstract, idealized and plural (Glennan et al., 2021). Accordingly, the crucial point is that mechanist philosophers, whether they think that explanations are epistemic entities, such as models or representations, or that explanations possess a preponderant ontic component, they should grant that the models are required to provide good mechanistic explanations. This discussion will be relevant for the analysis of the virtues and limitations of MTE, in Sect. 3.3.

The near decomposability of mechanisms is directly related to the idea that mechanisms span multiple levels of organization. The behavior of the whole is explained in terms of the activities and interactions among the component parts. These activities and interactions are themselves sustained by underlying activities and interactions among component parts, and so on. Levels of mechanisms can be defined in terms of a relationship between the behavior exhibited by a system and the activity of some component part of that system (Craver & Bechtel, 2007). On this account, the activity of a component is at a lower level of mechanistic organization than the behavior of the system if and only if the component is a part of the system, and its activity is part of the system’s behavior. In short, to say that something is at a lower mechanistic level than the mechanism as a whole is to say that it is a working part of the mechanism.

For some mechanists, one implication of this view of levels, combined with certain familiar assumptions about causal relations, is that there can be no causal relationships between items at different levels of mechanisms (see Craver & Bechtel, 2007; Craver & Tabery, 2019, for a description of this posture). This is a position in contrast with some form of holism, which necessarily does not limit the analysis to the constitutive parts of – or their relations within – a specific level of organization. According to holism, both the higher levels (“downward causation”) and the lower ones (“upward causation”) might participate in determining the properties of specific levels. According to non-holist mechanists, claims about inter-level causation concerning mechanisms are expressed as hybrid claims combining, on the one hand, constitutive claims about the relationship between the behavior of the mechanism as a whole and the activities of its parts and, on the other hand, causal claims concerning relationships between things not related as parts and whole (see discussion in Craver & Bechtel, 2007). Bechtel and Richardson (2010: xxxiii) have taken “a step beyond decomposable and nearly decomposable modes of organization in characterizing integrated systems as those in which the operations of different component parts are interdependent; that is, they more or less continuously impact each other’s operations”.⁶ Bechtel and Abrahamsen (2010) have called this new perspective dynamic mechanistic explanation: when the component parts of a mechanism are highly integrated, so that the behavior of a given part can be affected by the activity of many others, mechanistic explanations increasingly rely on mathematical modeling. Thus, in this perspective, the mechanistic models become more quantitative as will become conspicuous in Sect. 3.2, when I illustrate the MTE.

It is important to highlight the fact that Bechtel and Richardson (2010) reject a stricter and ruthless reductionism, in which lower levels are more important as a source of explanation.⁷ In this more nuanced position, the focus on the parts and operations must be relaxed and must shift toward the system through functional recomposition, in which one must show that the postulated component operations, with an appropriate organization, are sufficient to yield the systemic behavior. Therefore, Bechtel and Richardson (2010) assert the need to emphasize three points against ruthless reductionism within a mechanistic account: the fact that it is the whole organized mechanism that exhibits the phenomenon, not its component parts and operations; that mechanistic models are not typically governed by a single level;⁸ and that there are significant top-down constraints on the development of mechanistic models, in contrast with what is proposed by some mechanists that reject causal relations between different levels, as above referred. Thus, after localizing the parts and identifying the operations, a characterization of how the parts and operations are organized to make a functioning mechanism, and how the environment affects it, is needed. After decomposition and localization, the tasks of recomposing and situating the mechanism call for system thinking (Bechtel & Abrahamsen, 2005).

One of the major successes of the life sciences has been not just to identify numerous biological mechanisms but also to decompose them into their component parts and operations, with successful examples in different domains. Even though there are limitations in the basic account of mechanisms, I believe that one has to acknowledge that it describes the conceptual framework in which the vast majority of productive research in the life sciences has been conducted. However, and interestingly, philosophers of science have not exhaustively examined ecological mechanisms, even though ecologists describe mechanisms for purposes of explanation and prediction, whereby these latter might be different from the biological mechanisms that have so far received more philosophical scrutiny, such as the mechanisms uncovered in genetics, cell and molecular biology.

Ecologists have been intrigued since the beginning of the twentieth century by allometric and scaling relationships⁹ between organismal features and ecological phenomena (Brown et al., 2004; O’Connor et al., 2007; Raerinne, 2013, 2017). However, there was no widely accepted mechanism for the explanation of these patterns until recently. Very different explanations have been developed in the last two decades of the twentieth century, including those making reference to: structural and functional factors (e.g. surface area/volume effects on exchanges of heat and metabolites); biomechanical requirements for support and fracture resistance; natural selection on body size and life history (O’Connor et al., 2007). Thus, for some ecologists, the focus became on what different roles allometries and scaling relationships have in scientific mechanistic explanations and predictions in ecology, and how well allometries and scaling relationships are capable of functioning in these roles. Recently, several authors (West et al., 1997; Enquist et al., 2003; Brown et al., 2004; Allen & Gillooly, 2007; O’Connor et al., 2007) have developed a Metabolic Theory of Ecology (MTE) that, emphasizing allometric and scaling effects in ecology, has produced some interesting hypotheses.

After this brief introduction concerning the mechanistic account (Sect. 3.1), I shall therefore begin by characterizing MTE (Sect. 3.2). I then evaluate the virtues and limitations of this theory (Sect. 3.3). Following this evaluation, I explore and discuss the mechanistic nature of the theory (Sect. 3.4). Finally, I conclude by considering the general epistemological prospects of MTE for ecology (Sect. 3.5).

3.2 The Metabolic Theory of Ecology

MTE claims to provide a mechanistic explanation for known allometric relationships between biomasses and metabolic rates, postulating that these patterns of allometry and scaling relationships are driven by constraints of transport of energy and materials (West et al., 1997; Enquist et al., 2003; Brown et al., 2004; Allen & Gillooly, 2007; O’Connor et al., 2007).

This theory was advanced on the philosophical premises that allometric phenomena required a mechanistic explanation and that MTE could elucidate their mechanistic basis based on physical, chemical and physiological principles. More specifically, the formulation is based on the theoretical hypothesis that “the structure and dynamics of ecological communities are inextricably linked to individual metabolism” (Allen & Gillooly, 2007: 1073). This is a reductionist hypothesis in the sense that interactions between individual organisms and their environment are constrained by metabolic rates, which in their turn depend on factors like body size, body temperature and resource availability; as a consequence, the interactions between individual organisms and their environment will explain the most significant characteristics of higher ecological levels.

Therefore, the reason for considering MTE a mechanistic approach is that metabolism is assumed to be mechanistically explained in terms of biochemical reactions. According to the basic mechanistic account that I have described in Sect. 3.1, decomposability is clearly possible in the case of MTE: the metabolism of a community (or ecosystem) is the behavior exhibited by the entire system (i.e., the whole mechanism), and the metabolisms of the populations that compose it are the components’ activities of that entire system (i.e., the sub-mechanisms). In the same way, the metabolism of a population is the result of the metabolisms of the individual organisms, its components’ activities. Thus, the levels of the mechanism are defined in terms of a relationship between the behavior of a system and the activities of component parts. That is, to say that a population is at a lower mechanistic level than the mechanism as a whole (ecosystem) is to say that it is a working part of the mechanism. The same is true for individual organisms being the working parts of a population.

Metabolism therefore provides a basis for using basic principles of physics, chemistry and biology to link the biology of individual organisms to the ecology of populations, communities and ecosystems. A calculation is said to be from basic principles if it starts directly at the level of established laws of physics. Thus, the ecology of populations, communities and ecosystems can be studied starting from the physical laws concerning the movement of gases, chemical elements, compounds and fluids, including the laws of diffusion and evaporation. Then, ecologists can use the laws involving the kinetics of chemical reactions. Finally, ecologists can analyze the variation in the rates and specificity of the biochemical pathways of metabolism among different kinds of organisms and environmental settings.

Metabolic rate i.e., the rate at which organisms take up, transform and expend energy and materials, is, according to this approach, the most fundamental biological rate. Advocates of this approach have developed a quantitative theory for how metabolic rate varies with body size and temperature (West et al., 1997; Enquist et al., 2003; Brown et al., 2004; Allen & Gillooly, 2007; O’Connor et al., 2007). This theory predicts how metabolic rate – by setting rates of resource uptake from the environment and resource allocation for survival, growth and reproduction – controls ecological processes at all levels of organization from individuals to ecosystems (Brown et al., 2004).

Within this perspective, the complex, spatially and temporally varying structures and dynamics of ecological systems are all consequences of individual metabolism because individual organisms transform energy to power their own activities, convert materials into uniquely organic forms, and thereby create a distinctive biological, chemical and physical environment. Metabolism might be generally characterized as the biological processing of energy and materials whereby 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 to the environment. Metabolism therefore determines the demands that individual organisms place on their environment for all resources, and simultaneously sets powerful constraints on the allocation of resources to all components of fitness. In brief, the overall rate of these processes “sets the pace of life”, borrowing the expression of Brown et al. (2004: 1772). In particular, body size, temperature and chemical composition affect biological structure and function at various levels of organization (West et al., 1997; Enquist et al., 2003; Brown et al., 2004). This is because metabolism obeys physical and chemical basic principles that govern the transformation of energy and materials. Therefore, much of the variation among ecosystems – including their biological structures, chemical compositions, energy and material flows, population processes and species diversity – depends on the metabolic characteristics of the organisms living within them. The variation that is observed in individual organisms, including their life history, phenotypic features and ecological roles, is constrained by their own body sizes, operating temperatures and chemical composition (Brown et al., 2004). According to MTE advocates, these constraints of allometry, biochemical kinetics (i.e., rates of biochemical reactions) and chemical composition lead to “metabolic scaling relations that, on the one hand, can be explained in terms of well-established principles of biology, chemistry and physics and, on the other hand, can explain many emergent features of biological structure and dynamics at all levels of organization” (Brown et al., 2004: 1772).

MTE explicitly shows how many ecological structures and dynamics can be explained in terms of how body size, chemical kinetics and resource supply affect metabolism. MTE builds on them by providing a quantitative framework to better understand how these three variables combine to affect metabolic rate, and how metabolic rate, in turn, influences the ecology and evolution of populations, communities and ecosystems. The quantitative framework is illustrated by Brown et al. (2004: 1773–1786) as follows.

Allometries and scaling relationships can be represented as regression equations or power equations, in which one variable changes as a power of another.¹⁰ According to MTE, all characteristics of organisms vary predictably with body size, a correlation captured by the so-called allometric equations:

$$ Y=a{M}^b $$

(3.1)

Y is the dependent variable, M the body mass, a is the normalization constant and b the allometric constant. In allometries and scaling relationships, body size or weight is treated as an independent variable of different anatomical, physiological, morphological, behavioral, social, ecological, and paleoecological dependent variables.

Depending on the value of their scaling exponents, allometries and scaling relationships are called either allometric (b ≠ 1) or isometric (b = 1). Scaling exponents can take both negative and positive values. In general, the larger the value of b, the faster Y increases (if b is positive in value) or decreases (if b is negative in value) with increasing M. If the scaling exponent, b, is less than unity, Y increases (or decreases if negative in value) more slowly than M does. On double log axes, the values of Y and M yield straight lines, and a gives the intercept or elevation of the regression line and b gives its slope. There is a plenitude of biological traits that correlate with body mass, M, and can be represented as dependent variables, Y. As Raerinne (2011: 194) illustrates, many scaling relations of putative ecological relevance can be derived on the basis of Eq. (3.1): fasting endurance scales as aM^0.44 for mammals and between aM^0.40 and aM^0.60 in birds; the size of the home range of birds and mammals varies positively with body size, aM¹; the inverse scaling rule: the maximum density, D, of herbivorous mammals declines as their body size increases, D = aM^−0.75; Kleiber’s rule: basal metabolism, an estimate of the energy required by an organism for the basic processes of living, varies as aM^0.75; an individual’s total energy consumption varies as aM^0.75; in most mammal groups gut volume is isometric to M, aM¹; heart rate varies as aM^−0.25.

Kleiber, in 1932, showed that the individual metabolic rate, I, scale as (Brown et al., 2004):

$$ I={i}_o{M}^{3/4} $$

(3.2)

The element i_o is the normalizing constant independent of body size.

It has been known that biochemical reactions rates, metabolic rates and nearly all other rates of biological activity increase exponentially with temperature. This kinetics is described by the Boltzmann factor or Vant’ Hoff-Arrhenius relation (Brown et al., 2004):

$$ {e}^{-E/ kT} $$

(3.3)

E is the activation energy, k is the Boltzmann constant and T is the absolute temperature. This equation specifies how temperature affects the rate of reaction by changing the proportion of molecules with sufficient kinetic energy. This relationship holds over the temperature range of normal activity, which is 0–40 °C for most organisms.

Gillooly, in 2001, developed a model for the scaling of metabolic rate that combines the effects of body size and temperature, preliminarily conceptualized in Eqs. (3.1), (3.2) and (3.3), which leads to a single equation for individual metabolic rate, I (Brown et al., 2004; Allen & Gillooly, 2007):

$$ I={i}_o{M}^{3/4}{e}^{-E/ kT} $$

(3.4)

This simple analytical expression yields quantitative predictions on metabolic rate that are supported by empirical data for a broad assortment of taxonomical groups. As a result, its explanatory power has been claimed to be substantial (Brown et al., 2004; Allen & Gillooly, 2007).

Characteristics of organisms vary with their body size, temperature and chemical composition or stoichiometry. In ecology, stoichiometry refers to the quantities, proportions or ratios of chemical elements in different entities, such as organisms or their environments. All organisms have internal chemical compositions that differ from those in their environments; therefore, they must expend energy to maintain concentration gradients across their boundaries, to acquire necessary elements and to excrete waste products. Fundamental stoichiometric relations dictate the quantities of elements that are transformed in the reactions of metabolism. Biochemistry and physiology specify the quantitative relation between the metabolic rate and the flows of elements through an organism. The metabolic rate dictates the rates at which material resources are taken up from the environment, are used to enact biological structure and function, and are finally excreted as waste back to the environment. The chemical equations of metabolism specify not only the molecular ratios of elements, but also the energy yield or the demand of each reaction. Ecological stoichiometry is concerned with the causes and consequences of variation in elements’ composition among organisms and between the organisms and their environment; indeed, there is great variation within and among organisms, and especially between different taxonomic or functional groups. The concentrations of elements in ecosystems are therefore directly linked to the flows and turnover rates of elements in the constituent organisms (West et al., 1997; Enquist et al., 2003; Brown et al., 2004; Allen & Gillooly, 2007). On the one hand, environmental concentrations can limit metabolic rates, and thereby growth rates, reproductive rates and quantities of organisms; on the other hand, the size of stock of elements and rates of turnover in organisms can regulate environmental concentrations of elements and compounds. The Eq. (3.4) gives, as referred above, the combined effect of body size and temperature on individual metabolic rate, I. Because the mass specific rate of metabolism, B, is simply I/M, it follows that B scales as:

$$ B\propto {M}^{-1/4}{e}^{-E/ kT} $$

(3.5)

The advantage of this concise mathematical expression is that it combines the effect of body size and temperature in a single quantitative expression. This allows making precise comparisons between organisms and different functional and taxonomical groups differing substantially in these variables (Brown et al., 2004). When such comparisons are made, the commonalities of life and their ecological manifestations are revealed. Brown et al. (2004: 1775) present empirical data plotting rates of T- corrected individual production against body mass for a wide variety of organisms, showing that MTE predicts that Eq. (3.5) should account for much of the variation in some characteristics of individual performance and life history, such as individual biomass production, ontogenetic growth, survival and mortality, as well as stoichiometry.

MTE extends this framework to population and community levels of ecological organization, claiming that many features of population dynamics and community organization are due to effects of body size, temperature and stoichiometry on the performance of individual organisms. The maximal rate of exponential increase in a population, r_max, is predicted to scale according to Eq. (3.5) (Brown et al., 2004); this inference follows from the fact that reproduction is fueled by metabolism, and that mass-specific production rates and mortality rates follow the same equation. Advocates of this metabolic ecological approach contend that it is possible to explain the equilibrium number of individuals or carrying capacity, K, predicted to vary as:

$$ K\propto \left[R\right]{M}^{-3/4}{e}^{-E/ kT} $$

(3.6)

Therefore, K varies linearly with the supply rate or concentration of the limiting resource [R], as a power function of body mass and exponentially with temperature. Thus, if [R] increases, there will be more organisms of decreased size. However, if temperature increases, the carrying capacity is reduced because the same supply of energy supports a smaller number of organisms, each fluxing energy and materials at a higher rate. Notably, Brown et al. (2004: 1775) present empirical evidence for an inverse Boltzmann relationship between equilibrium abundance and environmental temperature.

The mathematical structure of the theory, according to its authors, thus provides two concise mathematical expressions of particular interest, derived from Eq. (3.4): Eqs. (3.5) and (3.6). The first correlates the variation of B, the mass specific rate of metabolism,¹¹ with the combined effect of size and temperature in a single quantitative expression. What is observed is that B is negatively associated with body size and positively (exponentially) with temperature. The second correlates the variation of K, the carrying capacity of individual organisms,¹² with the combined effect of size, temperature and the available quantity of a limiting resource. What is observed is that the carrying capacity is negatively associated with body size, and positively with the resource concentration (linearly) and temperature (exponentially).

Ecologists have tried to understand how pairs of competing species or of predators and preys stably coexist in the same environment. Empirical evidence suggests that a number of interaction rates and times, including rates of parasitism and predator attacks, are inversely related with temperature. It has been argued that MTE predicts the pace of these interspecific interactions, because the rates of consumption and population growth are determined by the rates of individual metabolism and have the same body size and temperature dependence (Brown et al., 2004; Allen & Gillooly, 2007). Moreover, the scaling of rates of ecological interactions has important implications for coexistence and species diversity, because the qualitative empirical patterns of biodiversity would suggest that the processes that generate and maintain species richness scale similarly to other biological rates, as illustrated by Eq. (3.5). Other things being equal, there are more species of small organisms than larger ones as well as more species in warm environments than colder ones.

The corroborated hypothesis that species diversity varies inversely with body size suggests, according to MTE, that metabolism plays a central causal role in determining ecosystems’ species composition. It has long been known that the diversity of most taxonomic and functional groups is highest in the tropics, but this has usually been attributed to higher productivity or reduced seasonality, rather than to the kinetic effect of higher temperature (Pianka, 1966).¹³ However, empirical evidence suggests that species richness in many groups of animals and plants has the same relationship to environmental temperature that metabolic rate has (Brown et al., 2004). This result holds true not only along latitudinal gradients, but also along elevation gradients, where variables such as light intensity, seasonal changes in day length and biogeographic history are held relatively constant. The implication is that much of the variation in species diversity is directly attributable to the kinetics of biochemical reactions and ecological interactions (Brown et al., 2004; Allen & Gillooly, 2007). Clearly, much additional work on the relationship between metabolism and biodiversity is needed, but a metabolic perspective, as proposed by MTE, demonstrates the centrality of many of these questions and suggests ways to look for in pursuit of appropriate answers.

Some of these questions can be addressed by assessing the effects of biological metabolism on the paths of energy and materials in ecosystems (Brown et al., 2004: 1782). It may be suggested that the biologically regulated whole ecosystems’ stores and fluxes of elements and compounds are simply the sums of the stores and fluxes of the constituent organisms. Thus, MTE is putatively able to predict the contribution of the biota to biogeochemical cycles. Specifically, in this framework, Eq. (3.6) provides the ground for predicting how body size, temperature and stoichiometry determine specific magnitudes of stores and rates of flux within and between “trophic compartments” such as primary producers, herbivores, predators and detritivores.¹⁴ It is possible to derive from Eq. (3.6) expressions for the stored biomass, the energy flux and biomass production, the biomass turnover, and for trophic dynamics (Brown et al., 2004: 1784). MTE also provides a framework for more explicitly incorporating stoichiometry and understanding the effects of limited water and nutrients supply on variation in productivity and other processes across biomes (i.e., collections of organisms that have common characteristics with respect to the environment they inhabit) and physical gradients. According to the MTE advocates, regressions incorporating these variables are able to account for much of the observed variation.¹⁵

In summary, MTE:

• 1. conjectures that a complex structure of distributional networks of essential nutrients and chemical elements, such as the circulatory systems in metazoans (i.e. multicellular animals), requires an allometry in order to explain the need to minimize transport costs of energy and materials as body size increases;

• 2. hypothesizes that minimizing these transport costs requires a scaling exponent of -¾, as defined in Eq. (3.5);

• 3. links metabolism and temperature, via the Boltzmann factor, used to predict the rate of simple biochemical reactions, essential to living processes, as defined in Eqs. (3.5) and (3.6).

The theory was advanced on two philosophical premises (O’Connor et al., 2007: 1059). First, that allometric phenomena require a mechanistic explanation and that MTE is able to identify that mechanism, based on physico-chemical, biochemical and physiological basic principles. That is, MTE characterizes a mechanism, according to the account described in Sect. 3.1: the metabolism of an ecosystem (or community) is the behavior of the mechanism as a whole, the phenomenon to be explained, the relevant component parts are the individual organisms composing the populations, which in their turn compose communities, which in their turn compose ecosystems; the metabolisms of populations (and the metabolisms of individual organisms) are the relevant operations of the component parts, organized in accordance to the levels of ecological organization and causally related to produce the phenomenon. The second premise is that the postulated mechanism motivates and justifies renewed and expanded work on the ecological implications of allometry. I think these premises are valid, with the caveat that allometries and scaling relations are not universal or exceptionless laws; on the contrary, they capture observable tendencies, generalizations underpinning ecological systems (Lawton, 1996, 1999; Colyvan, 2003). If it is true that allometries and scaling relationships do not represent biological laws, the covering-law account (Hempel, 1965) cannot be used to explicate how and under what conditions they function in articulating explanations and inferring predictions. Thus, in order to salvage the putative explanatory and predictive roles of allometries and scaling relationships, one feasible alternative is that provided by a mechanistic approach because, as I have related in Sect. 3.1, in such account mechanisms are contrasted explicitly with laws of nature (Machamer et al., 2000; Craver & Tabery, 2019).

The putatively mechanistic explanation articulated by MTE has energized the consideration of allometric effects in ecology, producing a number of substantial hypotheses. Consequently, the expectation was that MTE would be able to provide a quantitative framework to better understand how the variables of resource availability, body size and temperature combine to affect metabolic rate and, in turn, how metabolic rate influences the ecology of populations, communities and ecosystems. However, there is a considerable debate regarding the support for the predictions articulated by MTE as well as the validity of the theory’s underlying assumptions. This is the issue that I shall explore in the next section.

3.3 Virtues and Limitations of MTE

O’Connor et al. (2007) recognized two putative advantages of MTE: the first is that it is based on basic principles of physics, chemistry and biology; the second is that it depends on fewer assumptions and parameters than other explanatory frameworks. However, these authors are also of the opinion that the notion of first principles should be defined in a better way. Additionally, they argue that relative freedom from assumptions is hardly an advantage in itself. In fact, while well-elaborated ecological models based on physical laws and relationships have the virtue of, first, depending on models of processes whose dominant dynamics are putatively better understood and, additionally, of clearly outlining the models’ underlying assumptions, they are not free of such assumptions. In fact, the application of simple physical principles to ecological systems requires many assumptions because of the complex series of organizational levels, ranging from macromolecules to ecosystems, through which physical effects are filtered to produce ecological dynamics. O’Connor et al. (2007: 1060) contend that the potentially limiting assumptions of MTE regarding metabolic allometry include: that metabolic rate is primarily limited by distributional networks of nutrients (such as circulatory systems); that circulatory transport costs will indeed be minimized; that the capillary diameters of such networks are size invariant; that the simplified description of the circulatory system is inadequate, even for organisms with open circulatory systems or no cardiovascular systems; that branching in real bodies sufficiently approximates the simplifying assumptions to justify MTE arguments; and that the normalization constants in the allometric power equations are unimportant in comparing scaling exponents.

Thus, following O’Connor et al.’s (2007) argument, MTE shall be hardly free from or independent on fewer assumptions. I shall now argue that some of these are hardly tenable. Characterizing MTE as based on first principles does not mean that the assumptions are easily identifiable and the consequences of violating them are easily understood. Moreover, all this should not confer special status on MTE as an explanatory mechanism.

In spite of these possible limitations, some authors disagree with O’Connor et al. (2007), arguing that the proposed mechanisms underlying the body size and temperature dependencies of individual metabolic rate represented in Eq. (3.5) can be accurately described (Allen & Gillooly, 2007: 1074). O’Connor et al. take issue with the Brown et al.’s network model as a mechanistic explanation for the ¾ power scaling of metabolic rate (2004); however, Allen and Gillooly (2007: 1075) argue that this model is indeed mechanistic because: it invokes a few simplifying assumptions that allow causes to be postulated; it yields quantitative predictions by explicitly linking organism structure to function based on these assumptions; it can be extended to predict how deviations from assumptions affect model predictions. This network model represents a manifestation of general principles that entail the maximization of the number of metabolic units where metabolism occurs – as respiratory complexes, for instance – and, at the same time, minimizing the transport distances to those metabolic units (Allen & Gillooly, 2007: 1074). These general principles are geometric. They are applied by assuming that natural selection will lead to evolutionary optimization of network geometry, subject to physical and physiological constraints. Given this evolutionary optimization assumption, quarter-power scaling of metabolic rate is predicted to apply at multiple levels of biological organization, in agreement with what is showed by the empirical data (Allen & Gillooly, 2007). O’Connor et al. (2007: 1061–1062) criticize the general hypothesis that natural selection results in the network optimization in organisms. According to these authors, the minimization of transport costs is a tenable criterion for evolutionary optimization, although it is clearly not the only factor upon which selection operates; consequently, this simple optimization criterion is necessary but not sufficient to describe the variety of selective forces that likely operate in determining metabolic rates. Thus, for O’Connor et al. (2007: 1062), the degree to which minimizing a subset of costs of metabolite transport determines metabolic rates needs to be substantiated by further research. In the perspective of these authors, to whatever extent selection might optimize bulk transport via distributional networks, the specific mechanism proposed by the MTE (i.e., isolated minimization of fluid transport costs, without taking into account other criteria) is an insufficient explanation for minimization because it is unlikely that transport costs map in a uniform and simple manner onto fitness. In my view, O’Connor et al. (2007)’s stance is correct, because natural selection optimizes organismal fitness (and not the fitness of isolated organismal parts), implying that the optimal design hypotheses must consider costs and benefits of parts optimization (O’Connor et al., 2007). As these authors say, “what is actually required in order to maximize fitness is that simultaneous optimization, of both the costs and benefits, is expressed in a common currency, organismal fitness being the logical candidate” (O’Connor et al., 2007: 1062).

In my opinion, this is the correct perspective: true optimization of isolated physiological systems (like metabolism) is difficult, if not impossible, to achieve in nature. Pleiotropy,¹⁶ multiple use for structures (in the sense of a metabolic component part being causally involved in non-metabolic processes), and variable selective environments all constrain optimization of physiological systems. Selection more likely might optimize the reproductive success of entire organisms rather than the efficiency of a particular component of metabolism, although the two may well be correlated. Many aspects of metabolism, active and resting, could conceivably heavily affect the fitness of an organism. Therefore, the idea that natural selection would optimize circulation transport costs (in isolation from other systems), which would then come to dominate metabolic allometry, seems unlikely. When conflicting demands are placed on a system, biologically optimal solutions are context dependent and the results of optimality analysis depend on the optimization criteria. Rarely can any of a set of criteria be confidently identified with the fitness of an organism. This is the issue raised, as I have anticipated in the introduction, by the supposed near-decomposability of structures into sub-structures, piece by piece. O’Connor et al. (2007: 1063) present evidence that shows that predictions made by MTE regarding single cells are poorly supported by data and that empirical evidence disputing the main predictions of MTE with regards to the mechanism of metabolic standing and transport systems in vascular plants is growing. According to these authors, it is difficult to understand how a cell of a multicellular organism, being part of the whole organism, can be optimized in an isolated way, i.e., expecting that component parts’ optimization ensues and furthermore causes organism optimization in terms of transport distances. However, Allen and Gillooly (2007: 1074), opposing this criticism, argue that there is considerable empirical evidence to support the network model assumptions and predictions in unicellular organisms, plants and a variety of animal taxa.

Nevertheless, even if I concur with O’Connor et al.’s (2007) criticisms based, first, on the difficulties related to decomposability and, secondly, on picking out the relevant structural/functional units of the mechanism underlying MTE concerning the optimization of nutrient circulation, I suggest that Bechtel’s (2015) approach – in which living systems are considered to exhibit the properties of scale-free small-word networks can be valuable on this issue. The idea is to draw boundaries for explanatory purposes at particular locations. In such networks, some nodes can have a number of connections much larger than others, in which case there is no scale for characterizing the distribution of number of connections. This is why these networks are termed scale-free (Bechtel, 2015: 89). The issue here is that there is no point on the scale at which one can capture all the relevant connectivity. This can be problematic since the nodes with more connections are typically very important to the functioning of the network, due to the fact they have more widespread effects, and for this reason O’Connor et al. (2007) criticize predictions for transport systems based on single cells. Maybe the modularity that I have referred to in Sect. 3.1 can be helpful, because in Bechtel’s (2015) perspective a module in a scale-free small-world network can be considered as a mechanism if its nodes collaborate in the production of a phenomenon. Considering the case of a circulatory system, to take fully into account how the module behaves, a mechanist would need to take into account both the connections between the nodes in the module and the connections between the same nodes and the nodes elsewhere in the larger network (e.g., respiratory system, digestive system). Therefore, the mechanistic account would only focus on the connections within the module, except for connections that are treated as providing inputs and outputs (Bechtel, 2015). This would be a misrepresentation of how the module behaves, since it does not consider all the interactions with nodes outside the module, a critique in line with O’Connor et al.’s (2007). However, I believe that Allen and Gillooly (2007) think that the proposed mechanism of MTE provides an account that approximates the behavior of the mechanism, and that can be “accurate to a first approximation” (Bechtel, 2015: 89). Despite these promising developments within New Mechanistic Philosophy, it seems to me that, even recognizing that the alternative would be a holism making it impossible to identify the distinctive contribution of the parts of the system, mechanist researchers will often discover that the mechanisms they investigate are much more integrated than they initially had assumed.

Another criticism advanced against the MTE by O’Connor et al. (2007: 1063), and with which I partly concur, is that, even accepting that most components of metabolism are affected by temperature, proposing Boltzmann relationships as the only explanatory mechanism for the temperature dependence of metabolism is untenable because no macroscopic equivalent of activation energy exists.¹⁷ At the level of the cell, with its complex, feedback controlled network of reactions with numerous metabolic checkpoints, each of which responds to several controllers and external conditions, no equivalent of activation shall exist. Furthermore, at this level the simplicity of control implied by the Boltzmann relationship does not exist (O’Connor et al., 2007). Accordingly, as one moves to consider organ systems, entire individual organisms, populations and ecosystem levels of organization, the complexity and diversity of the organization networks and their responses to temperature all increase progressively. Any putative relationship based on activation energies for the processes of the different levels of organization can be, at best, an observed correlation with temperature, but not necessarily a mechanism. Mechanisms demand productive causation adequate to describe phenomena, both qualitatively and quantitatively, that is, a connection between the dependent effect and the causative process. In this respect, O’Connor et al. (2007) have a substantive criticism: it would be very difficult to identify a causative process that could explain the effect of temperature moving across all the levels of ecological organization. Moreover, as I have related in the introduction, the near decomposability of mechanisms is directly related to the idea that mechanisms span multiple levels of organization. However, this view, according to some mechanists, has the implication that there can be no causal relationships between items at different levels of mechanisms (Craver & Bechtel, 2007; Craver & Tabery, 2019), making it difficult to postulate the role of a causative process moving across all the ecological levels. However, if we adopt a less ruthless mechanistic account, such as that advocated by Bechtel and Richardson (2010), causal relations between different levels can be recognized, and the effect of temperature moving across all the levels of ecological organization could be possibly explained. In this sense, I would argue that Bechtel and Richardson’s stance needs further attention, and maybe MTE can elaborate on this issue along similar lines, coming up with a suitable answer. Probably most importantly, according to O’Connor et al. (2007: 1063) correlative relationships like those proposed by MTE cannot be regarded as mechanistic because they are merely couched in a mathematical form, lacking the reference to the causative linkage between the postulated mechanism and the temperature dependence of metabolism. O’Connor et al. (2007: 1063) argue that the reservation about Boltzmann’s relation arises from “a poor fit to thermal physiology, particularly the short- and long-term variation of metabolism in response to changes in body temperature”. O’Connor et al. (2007: 1064) present data from the literature on acclimation,¹⁸ particularly acclimation of metabolic rates to varying temperatures in ectotherms,¹⁹ showing that the dependence of metabolism on temperature is both subject to selection among animal taxa and physiologically adjustable within a single organism. Thus, this range of variation is inconsistent with Boltzmann’s relation. O’Connor et al. (2007) do not argue that temperature does not affect metabolism, but that the proposed Boltzmann relationship cannot wholly encompass the patterns of variation commonly seen in nature. On the contrary, Allen and Gillooly (2007: 1075) argue that the Boltzmann relationship can capture the complexities of metabolism, claiming that a large and growing body of empirical evidence supports the commonality of temperature responses rather than the ability of individual species to overcome the physical constraints of temperature. These authors argue that the Boltzmann’s relation is firmly based in statistical thermodynamics and present empirical data relative to heterotrophic organisms (diverse taxa of insects and marine larvae), showing that the temperature dependence of metabolic rate reflects the temperature dependence of respiration on individual mitochondria, according to Eq. (3.5). They also show that, for plants, this same temperature dependence is expected to hold over the short term.

Bechtel and Bollhagen (2021) try another approach to activities in biological mechanisms. These authors start from the acknowledgement that, on the standard account of mechanistic explanation (outlined in Sect. 3.1), a phenomenon is explained by appealing to the entities and activities constituting it, even though “the active nature of activities remains unexplained” (Bechtel & Bollhagen, 2021: 12721). Following the same kind of reasoning, the standard account is not sufficient to understand how mechanisms are active. In the MTE case, we should be able to explain why there is a continuous metabolism in individuals, populations, communities and ecosystems, being the source of activity the metabolism of individual organisms. Accordingly, one should recognize that mechanisms are only active when free energy is employed by them,²⁰ something that has not been emphasized in the accounts of New Mechanists, but that is fundamental because a mechanism without free energy will not perform work. What happens to the free energy depends on how it is constrained because, if it is not constrained, it simply dissipates, with an increase in entropy and without the possibility of generating work; in contrast, if it is constrained, work can be performed, with the nature of the work depending on the constraints imposed (Bechtel & Bollhagen, 2021). What is then assumed is that there are entities engaging in activities, whose basic explanatory principles are energetics and constraints, showing that there is a need to clarify what the activities are in order to explain the mechanism, subjecting them to further analysis (Bechtel & Bollhagen, 2021: 12723). When Allen and Gillooly (2007) argue that the Boltzmann relationship can capture the complexities of metabolism in MTE, and that there is a common response to temperature, I would argue that these authors, for the purpose of explaining the activities of the entities involved (individual organisms, populations, communities and ecosystems), are construing them based on the activity underlying organismal metabolism being the reference, which is constrained in different manners (because different species have different metabolisms). That is the reason why the activities of different entities respond in distinct characteristic ways as free energy flows through them, and the Boltzmann relationship is able to generalize over this variation.²¹ Bechtel and Bollhagen (2021) also argue that energetics and constraints are also relevant to understanding mechanisms at higher levels of organization, and across all levels in the mechanistic hierarchy. Just as the bottom-level, higher-level activities depend upon the release of energy and, importantly, higher-level entities also constrain those at the bottom level, determining, for instance, how energy used and released by individual metabolism results in the activities of populations, or even communities and ecosystems. This fits well with Bechtel and Abrahamsen (2010) perspective of a dynamic mechanistic explanation, when the parts of a mechanism are highly integrated, as I have described in Sect. 3.1. These mechanistic developments can benefit MTE, in the sense that they can help to localize where the work is done, ultimately explaining the source of the activity of the relevant component parts of the mechanism, providing a reference point for understanding the operation of the whole mechanism, that, in the case of MTE, would be the ecosystem.

Another point of contention is that, according to O’Connor et al. (2007: 1061), these attempts to link individual metabolic rate to the structure and function of higher levels of biological organization are neither useful nor valid: MTE only describes “pre-existing” patterns, and these patterns are dissociated from underlying mechanisms. Allen and Gillooly (2007: 1075) argue that these claims are false and reflect a poor understanding of MTE; in fact, these authors argue, “the vast majority of MTE studies have been motivated by new questions that have resulted in the generation of new hypotheses, models, and empirical relationships”. In each of these studies, new patterns have been described and directly linked to individual metabolic rate.

In this section, I have showed that a significant debate about the capacity of MTE to explain and predict ecological phenomena has taken place since its inception. I shall now discuss the issue of the mechanistic nature of MTE because a central question needing clarification is whether the explanation in terms of allometric relationships provided by MTE is actually mechanistic.

3.4 The Mechanistic Nature of MTE

In the discussion concerning the mechanistic nature of MTE, it is crucial to distinguish between different types of explanatory models (O’Connor et al., 2007; Pâslaru, 2009; Raerinne, 2011; Raerinne, 2013): a phenomenological type, which requires an empirical, but not a mechanistic, relation between variables – e.g., regressions of metabolic rate on mass fall in this category –, where this implies that perhaps there are hidden variables creating the pattern, thus engendering a problem of extrapolation and prediction; a mechanistic type, in which the input variables are indeed linked to output variables by a series of causal relationships, whereby these variables can be considered mechanistic. The models proposed by MTE are, I argue, a compromise between these two types of models; in fact, proxy variables²² for factors of likely mechanistic importance are embedded within MTE’s statistical framework.

In spite of the long and useful history of the program of physiological explanation of ecological processes, the extent to which regressions provide broadly generalizing mechanisms for variable physiologies, distributional systems of chemical elements and their constraints, and selection forces, remains an open question. Likewise, in my opinion, the extent to which the linear equations,²³ fitted by regression, constrain the mathematical form of a generalized mechanism is unclear, particularly in systems whose dynamics result from multiple, interacting, nonlinear subsystems such as ecosystems.²⁴ Therefore, some critics of MTE argue that most putative MTE mechanisms must be regarded as mere statistical models based on plausibly mechanistic variables. According to O’Connor et al. (2007: 1060), “arbitrarily assigning some components of interspecific allometric variation to the scaling, while assigning others to the normalization constant, is a reification of assumptions of statistical fitting and not an expression of mechanistic understanding”. Such speculations may ultimately be justified by the discovery of genuine mechanisms, but so far they are merely statistical and, as such, they do not possess the robustness of mechanisms and cannot be justified by the very patterns to which the statistical models fit.

In this sense, I would argue that it is difficult to understand how allometries and scaling laws, such as those exemplified by West et al. (1997), Enquist et al. (2003), and Brown et al. (2004), represent generalizations with causal or explanatory relevance for ecology, in the sense of representing a causal or explanatory relation between variables, dependent and independent, with well-defined values. Even though it is well known that correlation does not necessarily amount to causation or provide causal explanation, in practice this point is often forgotten in the literature on allometries and scaling relationships, whereby body size or mass as an independent variable is claimed to explain a major part of the variation in the dependent variable. In this respect, it is instrumental to consider the analysis of causation suggested by Raerinne (2011), who defends an interventionist account of causal explanation to which I have already referred to in the introduction (see footnote 4). In such an account, invariance should be the correct relation of explanatory relevance in the case of causal explanations, which should be conceptualized as descriptions of objective dependency relations between entities or variables. Raerinne (2011: 253) claims that an invariant generalization “is one that continues to hold under a special change – an intervention – that alters the value of its variables”. According to this interventionist account of explanation, regressions or correlations,²⁵ by themselves, are not explanatory, regardless of how strong the correlation between the two factors is. For a correlation to count as genuinely explanatory, an intervention must be performed, whereby the relationship between factors actually remains invariant. In order for there to be an intervention and a possibility of manipulation, at least some of the predicate terms of a generalization are required to be representable as variables. If a generalization cannot be tested for how it might behave under interventions in or manipulations of its variables, the claims made about its explanatory status should be parsimonious.

Accordingly, many large-scale ecological generalizations are not explanatory for the reason that they do not describe invariant relations. Even though some of these relationships represent change-relating generalizations,²⁶ it is quite possible that they might be joint correlation effects, because of their common causes or the causal influence of certain background conditions. That is, they would amount to cases of “spurious causation”, in the words of Raerinne (2013: 195). Moreover, even if one finds that some of these generalizations are change-relating and invariant, allometries and scaling relationships seem to rather offer phenomenological explanations that require, in order to be genuinely explanatory, to be supplemented with information about the mechanisms underlying them. Allometries and scaling relationships with ill-defined variables are thus non-explanatory as generalizations. Indeed, in ecology, phenomenological explanations – in which one has an invariant relation between variables but no account as to why or how the relation holds between variables – are abundant (Raerinne, 2011).

In the interventionist account of explanation defended by Raerinne (2011), causes are difference-makers. Causes and effects should be understood as representable variables. Causes are difference-makers in the sense that they can be intervened upon to control or manipulate their effects. A change in the value of a cause makes a difference in the value of its effect. It is useful to distinguish between two kinds of causal explanation in the philosophical literature: simple causal claims and mechanistic explanations (Raerinne, 2011, 2013). A simple causal claim describes the causal connection between the phenomenon to be explained and the thing that does the explaining. It refers to a phenomenological or superficial causal explanation in which one has an invariant relation between variables, but no account – or mechanistic explanation – as to why or how the relation holds between variables. This account of explanation describes how simple causal claims function by identifying what is required of a causal dependency relation in order to be considered explanatory. That is, simple causal claims need to be invariant during interventions. Describing a mechanism of a phenomenon is not something that is contrary to the spirit of describing what the causal dependency relation of a simple causal claim actually is. Instead, a mechanistic explanation is a complement to a simple causal claim, since it describes how the dependency relations produce the phenomenon to be explained. In particular, a mechanistic explanation describes the internal causal structure of the phenomenon to be explained, as I have related in Sect. 3.1. It describes the underlying mechanism within the system by showing how the system is constituted and how the mechanism produces the phenomenon to be explained. According to Raerinne (2011), mechanistic explanations are causal and bottom-up reductionist explanations; they are causal explanations as a result of their invariance; they are true if they correctly describe the mechanisms in nature.

Describing an “underlying mechanism” becomes, henceforth, a paramount complement to an invariant causal relationship because it shows how the relationship produces the phenomenon (Raerinne, 2013). A causal explanation that is complemented with mechanistic details provides us with possibilities of more precise interventions and information about the extrapolability of a causal relationship, because with mechanistic details we obtain information about how the parts of a system are organized and under what conditions the parts of the system fail to operate. In brief, with mechanistic explanation one gains explanatory depth (Raerinne, 2013). Many ecological mechanisms are not well known (Raerinne, 2011). In fact, most mechanistic explanations in ecology are either underdetermined by the available data or by their absence (Raerinne, 2011, 2013). Thus, many causal explanations in ecology are simple causal claims in the sense that there are no known or confirmed mechanistic explanations. When one contrasts ecology with genetics, molecular biology or neuroscience, disciplines where mechanistic explanations seem to be more prominent and better founded mechanistically, ecological causal explanations appear to be merely phenomenologically invariant generalizations (Raerinne, 2011). I would argue that the same might be said about the explanations provided by MTE.

In this sense, MTE’s reference to allometries and scaling relationships should be understood as elucidating phenomena already known given available data in the sense of accommodating them. That is, allometries must be used to discover, describe, and classify the phenomena or patterns to be explained rather than being the things that do the explaining. Raerinne (2011: 261) illustrates this point with the following example.

Homeotherms (i.e., the organisms that exhibit the specific thermoregulation capacity of maintaining a stable internal body temperature regardless of external influence), poikilotherms (i.e., the organisms whose internal temperature varies considerably, being the opposite of a homeotherm) and unicellular organisms have different i₀ values (i.e., the normalizing constant independent of body size in the equations that relate metabolic rates to body mass in Eq. (3.2)). The values of i₀ are 4.1, 0.14 and 0.018 for, respectively, homeotherms, poikilotherms, and unicellular organisms. Some of the questions that need addressing concern the reason why the unicellular organisms have the lowest value of i₀ and how and why homeotherms metabolize at a higher rate (and therefore seem to use and exhaust relatively more resources) than poikilotherms and unicellular organisms of similar size. These are questions demanding an explanation. Knowledge of allometries spurs this kind of questions without, however, providing a direct answer; the only answer that is given is in terms of a phenomenological description, but surely not in terms of a mechanistic explanation. Nonetheless, allometries and scaling relationships may serve a heuristic role by suggesting new research questions, prompting the generation of new explanatory hypotheses and helping to discover regular connections between body size and other biological variables (Raerinne, 2013). Rather than providing explanations, many allometries and scaling relationships represent interesting objects of explanation, giving ecology interesting phenomena to be explained and the potential to progress and mature. This is a position close to that of some other authors, according to which ecologists seek regular patterns in nature even though they do not try to organize them within a body of theoretical explanations (Lawton, 1996). The reason is that they assume that ecology has no universal laws but just observable tendencies that cannot be derived from basic principles (Lawton, 1996; Colyvan, 2003). Accordingly, I would argue that most ecologists accept patterns of dependence as mere descriptions (as seems to me clearly the case with allometries and scalings), but not as causal explanatory relations. Instead, what they take to be explanatory is a description of the mechanism that produces these patterns. I would thus conclude that MTE cannot generally elucidate this mechanistic basis.

3.5 Conclusion

In summary, even though MTE has been praised for reinvigorating the study of metabolic and other allometries in ecology, thus aiming to capture interesting explanatory hypotheses, many criticisms have ensued. The theory aims to show how the metabolism of individual organisms affects the structure and dynamics of ecological systems, assuming that, at all levels, from individual organisms to ecosystems, the processing of energy and materials is linked through metabolic constraints and that the biogeochemical processes in ecosystems are largely consequences of the collective metabolic processes of the constituent organisms. Some ecologists (West et al., 1997; Enquist et al., 2003; Brown et al., 2004; Allen & Gillooly, 2007) think that metabolism is one of the great unifying processes in biology, making connections between all levels of organization possible, a theoretical hypothesis that I personally consider quite robust.

Notwithstanding this significant virtue, I would argue that the proposed (para) mechanistic hypotheses underlying MTE are problematic when tested, and that they are not fully consistent with fundamental aspects of ecology and physiology. My argument is underpinned by two critical considerations: that the cost of transport minimization is not a wholly tenable form of optimization by natural selection and that the Boltzmann normalization of thermal effects on metabolism requires a uniform response to temperature that sometimes is not observed. Due to these concerns, it is difficult to resist the conclusion that the assumed mechanisms underlying metabolic allometries postulated by MTE advocates are perhaps not the only ecologically relevant ones. From this point of view, the main problem of MTE is that the mechanisms postulated are treated as presumptively validated as well as mutually exclusive of other mechanisms proposed to explain allometries.

Thus, I find MTE lacking a complete explanatory mechanism for allometries and scaling relationships because: first, the proposed mechanisms are disconnected from the hypotheses they motivate; secondly, the putative mechanisms seem to be, biologically, not completely plausible; and, thirdly, the proposed universality of the mechanisms is hardly tenable. The theory, at best, highlights potential physical constraints imposed on the allometry of metabolic rates. It might therefore be considered as an oversimplified and insufficient description of the mechanisms underlying metabolic allometries. The upshot is that it cannot be considered a unifying model of mechanistic explanation in ecology for the simple reason that one must acknowledge that multiple mechanisms are likely to be involved in engendering the extant patterns of metabolic allometries. I would also argue that we cannot suppose that the so far illustrated criticisms are based, rather than on the analysis of available empirical data, on purely philosophical grounds. The “metaphysical” critics of MTE²⁷ seem to operate under the belief that unifying principles in biology and ecology, as metabolism surely is, do not exist and that all species are unique. Consequently, they argue that the optimization of physiological traits is almost impossible in nature and that all aspects of natural selection are idiosyncratic and therefore unpredictable. I would argue that this latter critical perspective leaves no room for general predictive theories in ecology, and, for this reason, it is not a reasonable criticism of MTE. The MTE approach, in contrast, is based on the theoretical assumption that ecology is well served by the development of general quantitative theories yielding testable predictions, including how organisms will respond to environmental change. This theory is formulated on the premise that organisms share many common attributes, particularly with respect to metabolism, also assuming that there are general principles governing the process of evolution, and that these are inextricably linked to individual energetics, therefore embracing the principle of evolutionary optimization. I am not a “metaphysical” critic and I think that ecologists should not abandon the quest for unifying principles. The crucial issue is, as I have argued in Sects. 3.3 and 3.4, the oversimplifications adopted in the description of the putative mechanisms of the MTE, which become conspicuous when we consider the contradictory empirical evidence in support of MTE.

I suggest that we must recognize that a general theory such as MTE will never be able to explain all the variation of biological phenomena due to the inherent complexity of ecological systems and that, necessarily, further work is required, potentially testing all assumptions and predictions of its models. Nevertheless, I believe that MTE has succeeded in partially explaining a good range of phenomena at various levels of ecological organization and that it eventually holds some promise for somehow linking individual organisms to populations and then to communities and ecosystems using metabolism. Thus, MTE can turn out to be a valuable contribution to study some ecological phenomena within a mechanistic approach since it provides a deep study of components and their activities at various levels of ecological organization. The simple account of mechanisms in terms of delineated organized systems that operate in a linear start-to-finish sequence that is so prominent in the new mechanist literature is arguably a simplistic one as it does not often correspond to actual biological dynamics. My suggestion is that more integrated scale-free networks can point to a more accurate description of mechanisms as they operate in the actual world, while the appeal to free energy and its constrained release can also help to explain the nature of the activity of living mechanisms, a critical issue when we are linking the metabolism of individual organisms, populations, communities and ecosystems in a mechanistic model such as the MTE. In brief, my proposal is that we should not view mechanisms as entities in the world but as posits in mechanistic explanations that provide idealized accounts of what is in the world. It is reasonable, from this perspective, to argue that when scientists demarcate the boundaries of a mechanism, decompose it and localize its parts, they are following heuristic principles. As such, scientists use simplifying assumptions that facilitate the investigation, but which may turn out to be false, especially when they are dealing with systems that are non-sequential in nature and that are characterized by non-linear operations, such as all ecological systems are.