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<figure><img src="image_29.png" /></figure>
Chapter 11
# There Are No Intermediate Stages: An Organizational View on Development

<figure><img src="image_30.png" /></figure>

Check for
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Leonardo Bich ID and Derek Skillings ID

**Abstract** Theoretical accounts of development exhibit several internal tensions and face multiple challenges. They span from the problem of the identification of the temporal boundaries of development (beginning and end) to the characterization of the distinctive type of change involved compared to other biological processes. They include questions such as the role to ascribe to the environment or what types of biological systems can undergo development and whether they should include colonies or even ecosystems. In this chapter we discuss these conceptual issues, and we argue that adopting an organizational approach may help solve or clarify them.

While development is usually identified with the achievement of an adult form
with the capability to reproduce and therefore maintain a lineage, adopting the orga-
nizational approach may provide a different strategy, which focuses also on the
maintenance of the current organization of the organism. By doing so an organiza-
tional approach favors a switch in perspective which consists in analyzing how
organisms maintain their viability at each moment of development rather than con-
sidering them as going through intermediate stages of a process directed toward a
specific goal state. This developmental dimension of biological organization has yet
to be given a general and detailed analysis within the organizational theoretical
perspective, apart from some preliminary attempts. How a biological organization
is maintained through a series of radical organizational changes and what these
changes are issues that still require clarification. In this chapter we offer the begin-
nings of such an analysis of developmental transitions, understood as changes in
functionality brought forth by regulatory mechanisms in the context of the contin-
ued maintenance of organizational viability at every step.

L. Bich (✉)
Department of Philosophy, IAS-Research Centre for Life, Mind, and Society,
University of the Basque Country (UPV/EHU), San Sebastian, Spain

Center for Philosophy of Science, University of Pittsburgh, Pittsburgh, PA, USA
e-mail: leonardo.bich@ehu.es

D. Skillings
Department of Philosophy, University of North Carolina at Greensboro,
Greensboro, NC, USA
**Keywords** Organization · Regulation · Functions · Developmental change · Adultocentrism

**11.1 Introduction**

Accounts of development are characterized by a common focus on changes taking
place during the lifetime of a biological system, usually centered on multicellular
organisms. These accounts may address how complex forms are generated, the ori-
gin of differentiation and morphological variation, growth, regeneration, metamor-
phosis, and other related phenomena (see, e.g., Muller & Newman, 2003). In some
cases, development is identified with any changes taking place throughout the entire
life cycle of an organism, including phenomena such as the production of new blood
cells or senescence (Gilbert & Barresi, 2018).

Yet, while differing on the type of change involved, development is usually iden-
tified with a process that gives rise to a complex multicellular organism (Barinaga,
1994; Martinez-Arias & Stuart, 2002; Wolpert & Tickle, 2011), more specifically
with the achievement of an adult form with the capability to reproduce (Minelli,
2011; Griesemer, 2016). As explicitly stated by Griesemer (2016): “Development is
the recursive acquisition, refinement, or maintenance of a capacity to reproduce”;
and “development can be seen as relatively continuous growth and differentiation of
shapes and sizes of parts along with the maturation necessary to reproduce.” On
these views, development is considered part of a larger life cycle defined by repro-
ductive events. As a consequence, explanations of change across whole life cycles
are usually focused on evolutionary considerations at the scale of lineages. This
directionality of developmental processes from the zygote to an adult form capable
of reproduction underlies these characterizations of development. By doing so,
developmental biology has become a field in which scientists and theoreticians
(implicitly or explicitly) face the issue of biological teleology and employ a teleo-
logical terminology.

Accounts of development face several internal challenges or puzzles. We intro-
duce some of them in Sect. 11.2. These challenges include issues deriving from
adopting notions of directionality and potentiality, especially if cases of reversible
and multidirectional development are considered. Further tensions concern the
problems of identifying the boundaries of development, i.e., the start and end points
of development. An important issue in this respect is identifying the distinctive
character of developmental change compared to other changes that living systems
undergo during their lifetime, such as individual adaptivity, growth, regeneration,
plasticity, acclimation, etc. Development is commonly defined in terms of the
organism. It is the history of a particular organism from its earliest form, e.g., egg,
seed, or clone, to its end, usually either reproductive maturity or death. Another
important question is what are the types of systems that can develop and whether
those systems should include unicellular organisms, colonies, superorganisms,
symbiotic associations, or ecosystems.
In Sect. 11.3 we argue that the organizational framework may provide a shift in perspective that may be helpful in relieving these tensions and contribute to a better understanding of development by complementing existing accounts. A deep change in strategy concerns how to pick out the relevant system. We decenter the organism to focus on living systems characterized by organizational closure and regulatory mechanisms. Focusing on a wider phenomenon realized on a longer time scale – the reproductive cycle or the lineage – misses the importance of the explanation of development from the point of view of the organization of the system undergoing processes of change. The organizational approach accounts not only for the maintenance of the lineage through reproduction and selection but also of the organization of the system.

Adopting an organizational approach means switching focus to how organisms – and possibly other biological systems – maintain their viability at each moment of the developmental process instead of considering them as going through intermediate stages of a process directed toward a predetermined goal state. How an organization is maintained through a series of radical changes and what types of changes are involved are issues that still require clarification. We argue that from an organizational perspective, development is a regulatory process that changes the number or types of functions of a regime of closure of constraints. The reasons why we recommend this conceptual switch is because it resolves some of the outstanding tensions or problems of generalization emerging in comparative work that tries to circumscribe developmental phenomena across the entire tree of life. These are the challenges we take up in Sect. 11.4. In Sect. 11.5 we conclude by summarizing the main conceptual points of our proposal for an organizational view of development and some remaining open questions for future work.

## 11.2 Puzzles and Challenges Within Theories of Development

There are a cluster of phenomena related to development that make the boundaries of this phenomenon difficult to define. Here we introduce a set of puzzles regarding development and development-like phenomena. They constitute challenges for any unitary theory of development. Few, if any, of these challenges are new, but neither are they universally accepted. The purpose of addressing them is not to provide a definition of development through a definitive set of necessary and sufficient conditions, which may not be desirable given the breadth and variety of work on development. Our aim is to build a conceptual account able to provide a different, theoretically coherent perspective from which it may be possible to better understand the implications of these puzzles and address them. We take as a starting point the work of Alessandro Minelli (especially Minelli, 2003, 2011, 2014). Minelli presents a definition of development that he thinks is often taken for granted: “development is a sequence of changes through which a multicellular adult is produced,
through an increase in complexity more or less strictly programmed in its genes,
starting from a single cell which in most instances is a fertilized egg" (p. 5). He uses
this definition as a jumping off point for showing how inadequate it is and to further
argue for "what development is not" (Minelli, 2011, p. 6). Minelli argues that the
given notion of development is inadequate in five ways, because "development (1)
is not restricted to the multicellular organisms, (2) does not necessarily start from an
egg, (3) does not necessarily start from a single cell, (4) does not necessarily imply
an increase in structural complexity, and (5) does not necessarily end with the
achievement of sexual maturity" (p. 5).<fnref n="1" /> We agree that these five points present
contentious problems for a comprehensive theory of development and will use them
as a starting point, taking and expanding on them one-by-one. We also introduce
two more problems for the given definition of development: development (6) can
proceed across complex life cycles punctuated by multiple reproductive events, and
(7) does not necessarily exclude multispecies complexes (e.g., lichens) and host-
microbe systems (e.g., aphids, corals, cows, or humans).

11.2.1 **Challenge 1: What Is Developmental Change, and Is It Restricted to Multicellular Organisms?**

Development is some sequence of changes, but what kinds of changes can count as
development? Organisms, for example, are constantly going through metabolic
changes in order to maintain themselves from moment to moment. However, meta-
bolic change is not sufficient on its own to count as development if development is
to retain any specialized meaning. To differentiate developmental changes from
metabolic changes, development is usually restricted to changes that have to do with
growth or a change in morphology or function. Acquiring new functions or chang-
ing the function of existing structures is especially central. The first challenge is to
establish whether or not single-celled organisms go through the right kinds of
changes to count as development. The answer might not be univocal due to the
diversity of organisms under consideration. Asexually reproducing bacteria might
only go through metabolic changes, some growth, and then reproduction, whereas
many parasitic eukaryotes have complex life cycles transiting through very different
morphologies. In these latter cases, the border between reproduction and develop-
ment gets fuzzy. We will return to this in challenge 6.

<footnote n="1">¹An additional source of inadequacy may be constituted by the idea that development is pro-
grammed in the genes. For criticisms of this idea, see Sonnenschein and Soto (1999) and
Veloso (2017).</footnote>
### 11.2.2 Challenge 2: Does Development Necessarily Start at Fertilization?

Pregnancy is a challenge when trying to draw clear cut lines between biological individuals (Grose, 2020; Kingma, 2020; Nuño de la Rosa et al., 2021). A fertilized egg makes for a clear starting point in the life cycle of a sexually reproducing species and is perhaps the obvious choice for where to pin the start of development. But this is clearly a byproduct of focusing on development in sexually reproducing organisms, primarily animals. It doesn't work for a general account of development because it ignores vegetative reproduction (e.g., cloning, budding) in plants, fungi, and many animals (Minelli, 2011). It doesn't even work for paradigmatic cases like humans because of monozygotic twins that develop from the splitting of a single embryo. Even more challenging is the case of the armadillo, which almost always produces four identical quadruplets, splitting at an even later developmental stage (Enders, 2002). Cases like these complicate drawing the line between developmental processes. For example, in the case of monozygotic twins, it seems like there are two equivalent interpretations of the developmental process: (1) there is one developmental process, and it is split between two separate entities, and (2) new developmental processes split off from an ongoing developmental process, but that splitting is not reproduction. Either interpretation produces a problem. In the first option, there is an apparent contradiction, as one and the same (token) developmental process is carried out within two distinct organisms. The second option undermines the initial claim that development necessarily starts at fertilization. Such claim is also undermined by phenomena such as parthenogenesis (Sonnenschein & Soto, 1999). There is a third option: the development of each twin starts at a stage later than fertilization. We will explore this option in Sect. 11.4.

### 11.2.3 Challenge 3: Does Development Always Start at a Unicellular Bottleneck?

This question is related to the previous one or is perhaps an expansion of it. Identifying the initiation of development requires identifying a new individual that is about to undergo development. A single cell that multiplies and transforms into a multicellular organism is a good candidate. Such a cell, especially when it is at least partially independent, is easier to delineate. Citing a multicellular clump as the start of development raises a few questions: (1) what is the origin of the clump, and what changes did it undergo to get to the multicellular stage?, (2) what kinds of changes did it undergo, if they were not developmental changes?, and (3) are there bounds on the size and complexity of an entity that both counts as a new individual and is able to undergo development?

In principle, is there a restriction on the types of mereological structures that can serve as starting points for developmental processes? The case of the armadillo, for
example, seems to point to a later beginning of the development of distinct embryos. One possible restriction is that a system must be unified as an individual whole, as opposed to a colony or a collection of individuals. Furthermore, such a system must not have yet started to undergo changes in the functional/structural relations of its parts since its formation as a new and discrete individual whole.

If it were the case that the formation of a new cell through the fusion of sperm and egg marks the beginning of development, as is commonly assumed, then what does that leave out? One possibility is asexual reproduction through budding or parthenogenesis, which are both common in multicellular systems. A second is symbiotic associations such as biofilms, holobionts, lichens, or other multispecies systems that seemingly fuse to form new individuals (Skillings, 2016). The symbiotes don't fuse into a new single cell that then begins development. The creation of these entities happens when the cells of different species join together. Thus, the initial condition of the association is multicellular.

Challenges 2 and 3 can then be generalized: instead of looking for specific structural features, is there a common functional starting point for every possible developmental process?

### 11.2.4 Challenge 4: Does Development Imply an Increase in Complexity?

There are two different ways the answer to this question is no, or at least ambiguous. The first answer is that different kinds of complexity can appear during a life cycle, and it is unclear how to compare them. For example, in species that go through metamorphosis, organisms will often lose some functions while gaining others. Through metamorphosis an organism might lose the capacity to feed but gain the capacity to sexually reproduce, such as in mayflies (Skillings, 2019), or behavioral complexity found in the larvae might be lost while structural complexity increases in the sessile adult form, such as in tunicates (Holland, 2016). Tunicates lose complex and energetically expensive structures like a head/brain that become unnecessary once they transform into sessile adults. In cases like these, it is unclear if there has been an overall increase in complexity.

The second, more definitive, answer to the question of whether development implies increase in complexity appears to be a straightforward no. Parasitic rhizospherealan barnacles transform from a free-swimming larval stage to a larval "injection" stage, where the organism essentially acts as a giant hypodermic needle. This stage then injects a small group of poorly differentiated amoeboid cells into the hemolymph of a crab host. Those cells later metamorphose into the adult form, which does not inherit any organs from the larval stage and consists of two parts: an interna, which is a system of ramifying rootlets spanning the body of the host, and an externa, which is a structure containing the reproductive system (Høeg et al., 2012; Miroliubov et al., 2020). In a more extreme case, the immortal jellyfish *Turritopsis dohrnii* (see Matsumoto et al., 2019) is able to reverse its developmental
trajectory from medusa back to polyp in response to stress without going through the whole cycle (i.e., through reproduction and the unicellular stage). It does so by going through a different intermediate stage, the cyst, constituted by a cluster of poorly differentiated cells. Is rejuvenation, with or without simplification, a kind of development? If it were the case, it would put into question the very idea of development as a unidirectional or irreversible process (of which an increase in complexity is one example).

### 11.2.5 *Challenge 5: Does Development End at Reproductive Maturity?*

According to Griesemer, development is intrinsically related to reproduction "Development is the recursive acquisition, refinement, or maintenance of a capacity to reproduce. Reproductive capacity is realized in diverse ways and modes of development in extant lifeforms on Earth" (Griesemer, 2016). He writes elsewhere that "reproduction involves the conveyance or conferral of developmental capacities. Not every mereological change achieves that. Moreover, since development is the acquisition of a capacity to reproduce, only lineage-forming (or terminating) mereological changes in development count" (Griesemer, 2016). It appears that Griesemer is using reproduction to explain development.

This focus on reproductive maturity as the endpoint of development can lead to a kind of "adultocentrism" (Minelli, 2011). This adultocentrism is an improper fixation, or essentialization, of the adult form of an organism as the true or proper form. This can create the view that the adult form is the form the "organism works toward," injecting a kind of teleology or forward-lookingness into all developmental processes. This risks overlooking the importance and distinctive features of other non-terminal forms, especially when studying organisms that are not amniotes (reptiles, birds, mammals). Let us think of organisms that have different free-living forms and may undergo metamorphoses, or that go through complex life cycles, where it is not clear if there is even an adult or terminal form.

It is not hard to find examples of adultocentrism; it is rooted in our language and maybe even our psychology. Picture a sea star, butterfly, or frog. It is probably the adults, not the larvae or juvenile forms, that come to mind. This is also the case for how organisms like mayflies are characterized, where the adult form is present for only a fraction of the life cycle. This is all fine for everyday use. It is the adult forms that we are most likely to encounter, because they are either larger or more active and consequently easier to see or come across. But this becomes misleading when thinking about the development or evolution of an organism. The organism has evolved to maintain itself at every point of the life cycle, and the maturation process (developing into an adult) constitutes an important part (and often a major one) of the whole life cycle. The question (for development) isn't only how did these features evolve in order to increase future reproductive function or output but how/why did these features evolve in order to maintain the organism at that stage of the life cycle.
cycle. The proximal selection pressure is at the maintenance of the organism at that stage, not some future reproductive stage that isn't realized at that point. The tadpole is an adapted self-maintaining organization subject to selection and lives freely as an agent in its environment. In the case of the axolotl, a pedomorphic salamander, it can even undergo reproduction. So, the tadpole's tail is just as important as the frog's four-legged form.

### 11.2.6 *Challenge 6: Are the Transitions Between Multicellular and Unicellular Forms in a Complex Life Cycle Development or Reproduction?*

Complex life cycles are probably the most common type across the spectrum of life. This includes sequences of forms that are divided by metamorphosis (like between the caterpillar and the butterfly), by both asexual and sexual reproduction (e.g., corals, and parasitic flatworms, etc.) and transitions between multicellular and unicellular forms (e.g., algae, ferns). Let us think of a life cycle with multiple stages divided by reproduction, where the same type of form doesn't come back until it has gone through different stages separated by reproduction. It is hard to parse a life cycle like this on an account of development that focuses on development as a unitary process that moves solely toward reproduction. Moreover, it makes it extremely problematic to distinguish development from reproduction. Is a single life cycle – say from haploid form to sexual reproduction to diploid form to asexual reproduction with multiplication at each step – made up of multiple and vastly different, reproductive and developmental cycles attached end to end? Or is it a single developmental process measured by one turn through the entire cycle but punctuated by “minor” forms of reproduction along the way? There isn't a knockdown argument for either interpretation (Godfrey-Smith, 2016). But there needn't be. What is needed is a conception of development that can make sense of this problem and the rest of the other problems.

### 11.2.7 *Challenge 7: Can Multispecies Assemblages Develop as One System?*

The deeper question behind this challenge asks what kinds of systems can develop: Is it only organisms that develop? Do symbiotic associations like lichens develop at the level of the whole? Can ecosystems develop?

Accounts of development focused on achieving reproductive capabilities as the end point of the process fail to be satisfactory when dealing with integrated symbiotic assemblages. These are systems where developmental phenomena appear to be
present in the more comprehensive system (the assemblage) but that do not reproduce at the level of the comprehensive system. Examples include symbiotic assemblages like lichens, biofilms, and holobionts. Lichens don't reproduce to form new lichens; the algal and fungal partners reproduce separately and then disperse and rejoin to form new lichens. Yet they undergo developmental changes at the level of the system as a whole. These systems are contradictory for developmental accounts focused on reproduction. Moreover, the boundaries might be drawn in the wrong places, because the overall developmental process of the assemblage would be overlooked. To address the question whether these associations undergo development, one needs to focus on how they change as integrated entities and abandon the idea of development as a tendency toward reproduction.

## 11.3 Gestalt Switch: Adopting the Organizational Perspective

The challenges discussed in the previous section put into question accounts of development as a progressive irreversible process directed toward the production of an adult organism capable of reproduction. They bring to the surface the need for a gestalt switch: development needs to be addressed also from a different point of view, one that is not directed toward some defined state in the future. A possible way of answering these challenges is through a change in perspective that centers on the maintenance of the living system from the very beginning of development. Such an account should be able to provide a general characterization of what development is, what type of changes it implies, and when development starts and ends. At the same time, it should be precise enough to address the challenges posed by phenomena such as rejuvenation, complex life cycles, and multispecies assemblages. Moreover, it needs to distinguish development from other types of change taking place during the life of an organism. By this, we do not claim that a different approach should replace those currently available but provide a complementary coherent theoretical perspective.

In the second part of this paper, we argue that this gestalt switch can be accomplished by adopting an approach focused on organization. We sketch a proposal of an organizational account of development, and we discuss how it can address the challenges presented in Sect. 11.2. The central idea is to focus on how the organization of living systems is maintained during the transitions that characterize development. This is a radical shift from a view of development as a process aiming toward a final state, or as an actualization of an intrinsic potentiality. Our focus is on what is maintained and on the developmental changes occurring at each moment, rather than interpreting them as early stages work toward constructing the adult form and achieving reproductive capabilities. According to the organizational approach, there are no intermediate stages, ones defined by their relation to some future goal state.
Every stage is equally important, because the system must build and maintain itself at every point of its existence.<fnref n="2" />

The organizational framework was built upon pioneering work on biological autonomy carried out by Jean Piaget (1967), Robert Rosen (1972), Humberto Maturana and Francisco Varela (Varela et al., 1974), and Howard Pattee (1972), among others. More recently it was further developed by Stuart Kauffman (2000) and by Alvaro Moreno and collaborators (Ruiz-Mirazo & Moreno, 2004; Moreno & Mossio, 2015), among others. The organizational account characterizes a biological organism as an autonomous system capable of producing its own components and maintaining itself in far from equilibrium conditions while interacting with its environment. To explain this capacity, this tradition appeals to the internal organization of the organism, which is maintained despite the continuous transformations that the organism undergoes at the level of its components. The core feature of this approach is the focus on the organization of the system: the identification of topological relations between the operations of components and between processes of transformation within a system. Organization refers to the way production and transformation processes are connected so that they are able to synthesize the very components that make them up, by using energy and matter from the environment. In this view, the fundamental feature of the organization of biological self-maintaining systems is its circular topology as a network of processes of production of components that in turn realize and maintain the network itself. This distinctive type of generative circularity that characterizes biological systems is known as “organizational closure.” The basic capability of a biological organization to self-produce and self-maintain has been explained in terms of closure of constraints (Moreno & Mossio, 2015; Montevil & Mossio, 2015). Constraints are characterized as material structures that harness processes and that by doing so specify part of the conditions of existence of those processes. According to this framework, living systems are capable to generate a subset of the constraints acting on their internal processes and realize a distinctive causal regime by which these constraints are organized in such a way that they are mutually dependent for their production and maintenance and collectively contribute to the maintenance of the conditions in which the whole network can persist.

The notion of closure of constraints focuses on the distinctive capability of living systems to contribute to their own conditions of existence and to the existence of their parts. This basic idea grounds two important biological notions: function and teleology. Within the organizational framework, a biological function is understood as a contribution of a part to the maintenance of a self-maintaining organization (e.g., a living cell) that, in turn, contributes to producing and maintaining the part itself (Mossio et al., 2009). Functional parts coincide with the constraints subject to closure. The telos of the system is understood in terms of

<footnote n="2">²It is important to make clear that considering different stages as equally important does not mean that they are all the same. On the contrary, it means that their distinctive features and how they are maintained should not be overlooked or interpreted in terms of a future state. However, some stages might be more relevant in relation to specific research agendas.</footnote>
self-maintenance (Mossio & Bich, 2017). The focus of the organizational account of teleology is on how the activity of a biological system contributes to determining its own conditions of existence. The organization of a living system is characterized as an intrinsically teleological causal regime where the conditions of existence on which the organization exerts a causal influence are the goal (*telos*) of the system. Other accounts of biological functions and teleology centered on evolution differ from the organizational one in that (1) they take the lineage rather than the current system as the grounds of intrinsic teleology; (2) they characterize functions of traits etiologically, as contributions to the survival of the ancestors of those organisms that currently carry those traits; and (3) the goals of the system are characterized in terms of adaptation by natural selection (inasmuch as they contribute to maintain the lineage). An important implication of adopting the organizational account is that it entails this distinctive teleological framework that is focused on the maintenance of the system. Applying this framework to development means identifying the *telos* of the developing system in its current organization, rather than in a future state that contributes to the maintenance of the lineage (i.e., the adult form and reproduction). As such, it provides a different theoretical perspective which is not based on a future-oriented directionality and is not subject to the issues discussed in the previous section.

A further aspect of the organizational approach needs to be taken into consideration before building an organizational framework of development. The idea of closure alone is insufficient to ground a theoretical understanding of this biological phenomenon. There are two primary reasons. The first is an intrinsic limitation of the very notion of closure alone in providing an understanding of biological organization. The second is the limitation of the notion of closure in accounting for change in general and, therefore, even more so for developmental change. Both limits can be overcome by employing the notion of regulation. Regulation is carried out by mechanisms realized by sets of constraints that are sensitive to internal and external variation and are capable of changing their activity accordingly. Regulatory mechanisms operate as higher-order constraints in the sense that they act on other constraints in the system. What they do is to selectively shift between different available regimes of self-maintenance, in such a way as to contribute to the viability of the system (Bich et al., 2016).

Let us consider the first limitation. The capability to produce their own functional components (i.e., constraints) is not enough to understand how biological organizations maintain themselves and actually realize closure. The basic biological constraints involved in a regime of closure are not always functioning or functioning whenever their substrates and energy are available. Their activities are constantly controlled (inhibited, activated, modulated) by other constraints on the basis of the state of the system and the environment:

> Cells, for example, engage in division, but they are not constantly dividing (when they do, the result is a pathology such as cancer). Cells metabolize glucose to produce ATP, but they only do so when ATP levels drop and energy is needed. Otherwise, they convert glucose to glycogen. Protein synthesis is another process that is inhibited or activated on the basis of the needs of the cell. Neurons generate action potentials, but either do so only when they receive an appropriate stimulus or change the rate at which they generate action potentials in response to stimuli. (Bich & Bechtel, 2022a).
To maintain itself, an organism needs to continuously modulate and coordinate the activities of its basic functional constraints, which directly harness thermodynamic processes, in such a way that they can realize a viable regime of closure (Bich, 2018). Equally important, an organism must interact with a changing environment, which is the source of matter and energy for its internal processes. To do so, the internal organization of an organism must manage adaptively the dynamical variability available within it. As argued elsewhere, this is achieved by means of regulatory mechanisms (Bich et al., 2016, 2020; Bich, 2018; Bich & Bechtel, 2022a, b). They continuously exert a fine-tuned functional control over the exchanges of matter and energy of the system with its surroundings and over the activity of the internal constraints in such a way that the system is able to bring forth different viable responses to environmental perturbations and internal needs.

The second limitation of an account of closure without regulation concerns the capability to account for change in biological systems. This is particularly relevant because development is a specific type of change. As argued in the previous paragraph, living systems do not only and simply produce, repair, and maintain their components. Such activities are continuously undergoing regulation. Importantly, on this view the basic regime of closure does not operate in a regular manner: an organism needs to constantly change in order to maintain viability. However, as argued by Bich et al. (2016), closure alone would account only for a very limited type of change, one understood in terms of a dynamic stability that is realized as a passive network property. The basic regime of closure simply “absorbs”, as a network, the effects of a limited set of perturbations or internal variations. The system compensates for perturbations by means of reciprocal adjustments between tightly coupled internal subsystems. The dynamics of the whole system are maintained in the initial attractor state or are pushed by the perturbation into a new stable attractor state. In living organisms, instead, regularity and stability in the activity of components are exceptions. A living system coordinates the activities of its components, modulates internal processes, and responds adaptively to environmental variation. The activity of each basic constraint is controlled according to the needs of the organization, starting from those basic constraints involved in transcription, translation, and protein synthesis. The system changes what activities its constraints perform in ways appropriate to the circumstances it faces and its internal state. On this view, active change is controlled by regulatory mechanisms (see Bich et al., 2016, 2020). Regulation is therefore a crucial notion to understand the organizational approach and its application to development.

In sum, adopting an organizational account implies focusing on how a living organization is currently maintained and on the functional contributions of its different components. Change, in this perspective, is understood as the result of the action of regulatory mechanisms which, on the basis of the state of the system and the environment, modify what functions are realized and modulate how they are performed.
## 11.4 Toward an Organizational Account of Development

What can an organizational approach say about development and its teleological dimension? As a starting point, this approach has a distinctive focus on developmental processes: on the system's current organization rather than on the realization of potentialities or the achievement of reproductive capability. The organizational account provides a conceptual framework which can be applied to development by accounting for how organisms, or biological self-maintaining organizations in general, maintain their viability at each moment of the developmental process. On our view it allows characterizing development as a regulatory process that changes the number and type of functions available to the system at a given moment while the system itself maintains its viability. From this perspective, development is not addressed as an adult-oriented process. Instead, the telos of the system is grounded in the maintenance of the viability of the organism at each stage of development, rather than in a future state.

To date, few contributions belonging to the organizational framework have addressed aspects of developmental processes. Arnellos et al. (2014) and Veloso (2017) focus on the role of intercellular signals and constraints in cell differentiation at early stages of development as an important factor to achieve integration. They contrast it with accounts of cell differentiation processes focused on intracellular factors such as genetics. Bich et al. (2019) point out the limits of cell differentiation alone to address multicellularity and development.<fnref n="3" /> They focus on what is a minimal multicellular organization capable of maintaining itself as an integrated system and what are the types of mechanisms that control individual cells and ensembles of cells to realize tissues and organs. They emphasize the importance of the control of spatial organization and the role of the extracellular matrix (ECM) in development.

The only work entirely centered on development within an organizational perspective is by Nuño de la Rosa (2010). She focuses on vertebrate development. She characterizes development as the generation of a fully-fledged autonomous organization, which happens in the later stages of this process. According to this view, development is considered as the *explanans* for biological autonomy.

This pioneering and detailed work has the merit to be the first and only to fully focus on development. However, it exhibits some features that make it incompatible with current organizational accounts. Moreover, it shares some of the limits exhibited by the other accounts of development discussed in the previous sections. In the first place, it focuses on a small subset of vertebrates: mammals and more specifically humans. Therefore, it might not be representative of development as a general biological phenomenon. In the second place, it focuses on autonomy considered as a form of independence from the mother organism, rather than a general form of self-maintaining organization characterized by a regime of organizational closure.

<footnote n="3">³Moreover, cell differentiation itself, is determined by the surrounding ECM and by tissue in which cells reside (see Sonnenschein & Soto, 1999).</footnote>
The problem is that biological autonomy does not imply independence. In principle, closure is not incompatible with forms of dependence, and a system can be autonomous in the sense that it realizes closure even though it is not independent from other systems. Examples are symbiotic associations, multicellular organizations, and, possibly, ecosystems (see Montevil & Mossio, 2015; Nunes-Neto et al., 2014, Bich, 2019). This is an important aspect of the organizational framework and allows it to account for forms of nested closure. In the third place, this account is in tension or even in contradiction with organizational approaches. Nuño de la Rosa's view is explicitly Aristotelian: development is characterized as a process of progressive actualization of autonomy. This account is characterized by a future-oriented teleology incompatible with the teleology that is characteristic of the organizational framework, based on current contributions to the persistence of an organization.<fnref n="4" /> Like other accounts, here again the goal of development is producing the adult organism. Finally, an implication of this focus on the progress from potency to actuality is that this account assumes change as an *explanans* of autonomy instead of an *explanandum*: on this view developmental change is what brings forth and explains the origin of an autonomous system. It is not the object of analysis.

The developmental dimension of biological organization has yet to be given a detailed analysis within the organizational theoretical perspective. The idea that an organization is maintained through a series of radical changes or transitions, such as those that take place in developmental processes, is an issue that still requires clarification. The application of this idea faces several internal tensions, insofar as the organizational approach is mainly focused on what is currently maintained – the whole organization – rather than what changes over a long sequence of often radical transitions. The first conceptual problem is determining what kinds of organization can undergo development as opposed to mere change. The second problem is how to account for the specificity of developmental change. It consists in distinguishing developmental changes from the other types such as metabolic changes. The third problem concerns the boundaries of development. To address it requires establishing when development starts within an organizational framework by identifying what is the initial self-maintaining organization that undergoes developmental change. It also requires establishing whether and when development stops and why. Common options have it ending with the realization of the adult form versus continuing through ageing or senescence.

The organizational approach can provide a principled way to address these problems and helps refocus those tensions and puzzles discussed in the previous sections. We offer here the beginnings of a supplementary analysis of development that

<footnote n="4">⁴The criticism of future-oriented approaches and potentialities is shared also by early work on the organizational framework, such as the autopoietic theory, which is explicitly focused on the current system (Maturana & Varela, 1980). Change is understood in terms of “structural determinism,” that is, all changes a living organization undergoes at a given moment are determined by its structure at that specific moment. It is important to mention that autopoietic theory rejects teleology insofar as in the interpretation of Maturana and Varela teleology is future or past oriented (see Mossio & Bich, 2017).</footnote>
focuses on the continued maintenance of organizational viability at every step. The starting point is the idea that during the life of an organism, what is maintained through the deep and continuous changes of its components is the organization of the whole. The conservation of organization unifies the biological processes an organism undergoes, which includes development, growth, senescence, etc. This idea has been expressed by Di Frisco and Mossio (2020) through the notion of organizational continuity, that is, “the presence of a continuous causal process linking successive organizational regimes, irrespective of material and functional changes.” This is the foundational assumption that it is to be adopted in order to understand biological phenomena from an organizational perspective. However, it is a very general notion. Alone, it does not provide conceptual tools to distinguish between development and other phenomena such as reproduction and aggregation. To do so it requires additional assumptions such as on the necessary variation in the number of organizations.<fnref n="5" /> Even more importantly, it does not provide an account of change. It focuses on what is maintained. Understanding development exactly requires understanding change, a specific type of change, within a scenario of organizational continuity.

The first problem to face in order to address development is how to pick out the relevant system. Focusing on a system realized on a longer time scale than the organismic organization – the reproductive cycle or the lineage – would miss the importance of the explanation of development from the point of view of the organization of the system undergoing a process of change. The organizational approach focuses on the organization of current biological systems capable of maintaining themselves. In this context the relevant system is a functionally integrated self-maintaining organization. Functional integration on this view consists in the degree to which the different components that collectively realize a biological regime of self-maintenance depend on one another for their own production, maintenance, and activity. In principle, an integrated system can be a unicellular or a multicellular organization (see Challenge 1 in Sect. 11.2) or even a symbiotic association if it satisfies the requirements (Bich, 2019; see Challenge 7 in Sect. 11.2). Let us focus on the second type of organization, given that it is the one usually discussed in relation to development. To achieve functional integration, a multicellular system requires some internal differentiation, the basic requirement for division of labor. For example, internal differentiation depends on the presence of components that contribute in different ways to the realization of the system, such as cells and an extracellular matrix (ECM). Through functional differentiation multicellular systems become, in principle, capable of harboring components that have different functional roles. Hence, functional differentiation realizes division of labor under certain conditions. Integration between these different tasks is achieved when functions are coordinated at the system level such that the differentiated components actively contribute to the maintenance of the system while their activities are being

<footnote n="5">⁵Counting the variation in number of organizations might be problematic as well. For example, it does not respond to the question whether the first steps of cell division in the embryo count as reproduction or development and why.</footnote>
activated, inhibited, or modulated at different moments in time depending on the state of the system. This is achieved by means of mechanisms of control and spatial organization acting at different ranges or time scales. Examples include cell-to-cell interactions, an ECM dynamically constraining groups of cells, biomechanical forces, and long-range control exerted by the vascular, nervous, or immune systems (Bich et al., 2019; see also Sonnenschein & Soto, 1999; Montevil & Soto, this volume). To undergo development, this organization should also exhibit regulatory capabilities, that is, be able to determine its own processes of change. This means that it should be able to modify itself and modulate its internal dynamics in response to variation in internal and external conditions, rather than only passively undergoing change driven by perturbation (Bich et al., 2016).

The second problem faced by the organizational approach is that not all regulated change is developmental (see Challenge 1 in Sect. 11.2). Otherwise, development would include all possible biological dynamics. Let us sketch an account of developmental change. Regulation operates by sensing the internal and external conditions of the system. Most regulatory processes act upon available mechanisms and the processes responsible for energy production, synthesis of parts, and the like. Regulation in these cases consists in bringing forth change in the basic dynamics of the living system by selecting between available mechanisms, via activation or inhibition, or by modulating mechanisms already in operation. An example is the activation and inhibition of genes responsible for the synthesis of enzymes specific to the presence of variable food sources, as in the case of the *lac operon* in bacteria.<fnref n="6" /> In these cases, regulatory mechanisms select between available functions or functional regimes.

Development is qualitatively different from other regulatory processes because it does not operate only on available functions but also changes the set of functions available to the system. At each developmental step, some new functional traits are generated, such as in the appearance of new tissues, organs, or limbs. In unicellular systems development might include the production of new organelles or other functional supramolecular structures. Functional traits might also be shed. Think of the transition between tadpole and frog, with the appearance of legs and lungs and the disappearance of gills and tail. These changes are different from the activation or inhibition of mechanisms which are already present in the system, and they affect the way the multicellular organization maintains itself in its new regime of closure.<fnref n="7" />

<footnote n="6">⁶While the case of the *lac operon* is well-known and illustrative of regulatory mechanisms, self-maintenance and regulation do not only apply to metabolic processes. Many other types of processes that are not metabolic contribute to self-maintenance and are strictly regulated: for example, behavior, movement, perception, or the activity of an organ or an organelle.</footnote>

<footnote n="7">⁷This notion of developmental change has interesting implications. At a first approximation, it does not seem to necessarily apply to growth, unless a change of size of the system, or of part of it, implies the realization of a new function instead of a change in the realization of function that is already available.</footnote>
Developmental regulatory change on this picture is not necessarily irreversible.<fnref n="8" /> Nor does it imply that development necessarily tends toward some future adult state. There are cases that contradict the idea of development as either an irreversible adult oriented process or the actualization of a potentiality (see Challenge 4 in Sect. 11.2). The “immortal jellyfish” *Turritopsis dohrnii* can return to the juvenile polyp stage from the adult medusa stage through the action of regulatory mechanisms that kick in as a response to adverse conditions or damage (Matsumoto et al., 2019). It does so while maintaining its multicellular organization, that is, without going through the whole life cycle and passing through a unicellular form. On our account of development, there is no conceptual problem in including cases in which changes are reversed, if these changes contribute to maintaining organizational closure. Therefore, an organizational approach to development can go beyond the biology of vertebrates and account for controversial cases such as rejuvenation or reverse development.

Adopting a regulatory framework to understand development also addresses issues such as the role of environmental factors. On some accounts, these factors are viewed as directly regulating development (Gilbert & Epel, 2015). On our view, what triggers developmental transitions is the sensing of environmental conditions by regulatory mechanisms and the consequent changes they trigger, not the direct action of the environment. We do not deny that environmental factors modify regulatory mechanisms. But even in these cases, environmental factors engage regulatory mechanisms which then bring forth developmental change.<fnref n="9" /> Direct change from environmental causes, such as the loss of a limb to a predator or an accident, would not count as developmental.

Let us focus now on the third problem: identifying the boundaries of development. Regarding the starting point of development, some approaches, such as Minelli (2011), have questioned the idea that development begins with the egg (see Challenges 2 and 3 in Sect. 11.2). Reproduction can be also vegetative or occur via budding, that is, through a system that is already multicellular. However, Minelli's focus is centered on reproduction and so implicitly adopts the directional teleological framework underlying the adultocentrism that he criticizes. Accordingly, when he criticizes the identification of the adult as the end point of development, he does so on the grounds that some species of animals undergo reproduction before reaching the adult form (Minelli, 2011). This doesn't alleviate the problem. The adultocentrism is just a symptom; the real issue is the directional teleology that underlies it – reproduction as the goal of development.

<footnote n="8">⁸Many, if not most physiological and behavioral regulatory processes, are reversible, starting from the simple case of the *lac operon*. However, it is important not to confuse thermodynamic reversibility with regulatory reversibility (physiological, behavioral, developmental, etc.). In a nutshell, the reversibility of regulatory processes requires energy, so it is a thermodynamically irreversible process.</footnote>

<footnote n="9">⁹The only partial exception would be molecular compounds, such as, for example, hormones, released by other organisms and capable to operate in the receiving organism as if they were some of its own regulatory mechanisms.</footnote>
Our organizational account questions the idea that the egg is the starting point of development but does so on a different basis. The egg cell divides into several cells when it undergoes cleavage. But this is not the growth of a single developmental system because these cells do not realize an integrated multicellular organization but several distinct unicellular organizations. These cells do not communicate among themselves, do not realize division of labor, and therefore do not collectively realize closure. On our organizational view, development starts when cells come together to form one integrated multicellular system – one organism – that then undergoes changes regulated at the level of the whole. So one system, the egg cell, reproduces to form multiple connected unicellular systems that only later come together as a single system with organizational closure. To illustrate an alternative developing systems, such as in the case of monozygotic (identical) twins. Development does not start with the egg but with integrated organization capable of regulation.

What are the requirements for realizing an integrated multicellular organiza-
tion? One might say when cells start signaling to one another (Arnellos et al.,
2014), but this is neither necessary nor sufficient. What is needed is functional and
spatial differentiation and integration, that is, a differential contribution to the
maintenance of the organization. For example, when the ECM (a noncellular con-
straint) is deposited, it contributes to the maintenance of the system by controlling
cell differentiation and behavior, cell migration, and spatial differentiation and
subsequently allows different *groups* of cells to emerge that perform different
activities (see Bich et al., 2019). When these functional changes taking place
within an integrated multicellular organization are directed by regulatory mecha-
nisms, development starts. These organizations need not have parts that all have
the same origin (see Challenge 7 in Sect. 11.2). In principle, they can be realized
also by symbiotic associations such as lichens or biofilms insofar as they satisfy
requirements for integration and regulation.

When does development end? Not necessarily with the achievement of the adult
form (see Challenge 5 in Sect. 11.2). Adult organisms can still exhibit functional
changes, and in some cases they can undergo phenomena such as rejuvenation
(reverting to a previous stage) or regeneration (reestablishing a lost function).
According to the organizational view that we propose in this paper, development
ends when regulated changes to the number or types of functions no longer
take place.<fnref n="10" />

In this respect, it is important to distinguish development from senescence.
Senescence is a process of loss or decrease of functionality due to a change in the
properties of components (such as the ECM; see Moreau et al., 2017) or of the over-
all organization of the system. While development might also produce a loss of
functions, the difference is that in the case of senescence the loss of functions is not

<footnote n="10">¹⁰On this view, whether and when development actually ends is an empirical question and might have different answers for different species.</footnote>
determined by the action of regulatory mechanisms. It is rather a question of whether and how functions are realized, and therefore it could be fruitfully addressed in relation to the organizational view of malfunctions (Saborido & Moreno, 2015).

## 11.5 Conclusions

In this chapter we showed that from an organizational perspective, development is a process of regulated change in number or types of functions of a regime of closure of constraints. It starts when a functionally integrated multicellular organization endowed with regulatory mechanisms is realized, and it ends when there are no further regulated changes in functions. It is a goal-oriented process, but a special one that is focused on the present, in which at each stage the goal is to maintain a viable organization of the system.<fnref n="11" /> Development does not aim at a future goal state, and therefore there are no intermediate stages. Each stage of a life cycle is equally important from a point of view that is focused on the persistence of that life over the life cycle. The *telos* can be found in the actual developing system at any point during the entire process. This approach does not characterize living systems as the result of development, but the system undergoing development is already considered a self-maintaining organized biological system. With respect to environmental factors, the organizational approach can explain their role in relation to the internal logic of the system that undergoes a regulatory transition in the presence of these environmental conditions. There are still several challenges that an organizational approach needs to face. Some, not included among those discussed in Sect. 11.2, concern the range of developmental systems and phenomena. They include questions such as whether biofilms or ecological systems – to which some argue it may be possible to ascribe a closure of constraints (see Militello et al., 2021; Nunes-Neto et al., 2014, respectively) – can undergo development or not. A fundamental challenge among those mentioned in Sect. 11.2, which is still open, is related to the type of organisms taken into account to explain development. Most work has been focused on metazoa and specifically on vertebrates. Vertebrates along with many other animals have the advantage of being easily individuated, often exhibiting a straightforward developmental pathway. However, they constitute only a small portion of the multicellular systems which undergo development. Some steps have been taken in this direction in this chapter. However, a sufficiently general organizational account of development needs to be able to handle a wide range of multicellular systems and provide the tools needed to address problematic cases such as facultative multicellular systems with life cycles composed of alternating and

<footnote n="11">¹¹ Focusing on the present does not mean ignoring phenomena happening in the past. A system undergoing development is the result of a reproductive event and of a history of evolution. However, here we have been focusing on the developmental process itself. A direction for future work to expand this approach within the organizational framework is to integrate development with heredity (Mossio & Pontarotti, 2019).</footnote>
distinct life stages (e.g., multicellular and unicellular; see Challenge 6 in Sect. 11.2). These more basic, yet no less complex, cases constitute an important sample of all multicellular systems and might play an important role for our understanding the origin of multicellularity and development. However, they have been primarily explored only from a historical and evolutionary perspective (van Gestel & Tarnita, 2017). We have addressed this challenge by expanding the range of examples analyzed to include some of these organisms, but there is much more to do. This is surely a necessary and interesting avenue to be pursued in future work on development.

**Acknowledgments** This study was funded by the Basque Government (Project: IT1228-19 for LB), Ministerio de Ciencia, Innovación, Spain (research project PID2019-104576GB-I00 for LB and DS and "Ramon y Cajal" Programme RYC-2016-19798 for LB), and the John Templeton Foundation (Project 62220 – Subproject “Directedness in the physiology, ecology, and evolution of holobiont systems” – for DS and LB). The revisions were done during LB’s Visiting Fellowship at the Center for Philosophy of Science of the University of Pittsburgh (Spring Term 2022).

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Chapter 12
# Modeling Organogenesis from Biological First Principles

Maël Montévil and Ana M. Soto

**Abstract** Unlike inert objects, organisms and their cells have the ability to initiate activity by themselves and thus change their properties or states even in the absence of an external cause. This crucial difference led us to search for principles suitable for the study organisms. We propose that cells follow the default state of proliferation with variation and motility, a principle of biological inertia. This means that in the presence of sufficient nutrients, cells will express their default state. We also propose a principle of variation that addresses two central features of organisms, variation and historicity. To address interdependence between parts, we use a third principle, the principle of organization, more specifically, the notion of the closure of constraints. Within this theoretical framework, constraints are specific theoretical entities defined by their relative stability with respect to the processes they constrain. Constraints are mutually dependent in an organized system and act on the default state.

Here we discuss the application and articulation of these principles for mathematical modeling of morphogenesis in a specific case, that of mammary ductal morphogenesis, with an emphasis on the default state. Our model has both a biological component, the cells, and a physical component, the matrix that contains collagen fibers. Cells are agents that move and proliferate unless constrained; they exert mechanical forces that act (i) on collagen fibers and (ii) on other cells. As fibers are organized, they constrain the cells' ability to move and to proliferate. This model exhibits a circularity that can be interpreted in terms of the closure of constraints. Implementing our mathematical model shows that constraints to the default state are sufficient to explain the formation of mammary epithelial structures. Finally, the success of this modeling effort suggests a stepwise approach whereby additional

M. Montévil (✉)

Centre Cavaillès, République des Savoirs UAR3608, CNRS, Collège de France et École Normale Supérieure, Paris, France

A. M. Soto (✉)

Centre Cavaillès, République des Savoirs UAR3608, CNRS, Collège de France et École Normale Supérieure, Paris, France

Tufts University School of Medicine, Boston, MA, USA

e-mail: ana.soto@tufts.edu
constraints imposed by the tissue and the organism can be examined in silico and rigorously tested by *in vitro* and *in vivo* experiments, in accordance with the organicist perspective we embrace.

**12.1 Introduction**

Throughout the twentieth century, biology underwent changes that little by little removed concepts which up until that time were considered to be the main characteristics of organisms, such as agency, normativity, and goal-directedness. Later on, even the concept “organism” was deemed superfluous and almost disappeared from biological theory as the idea of a genetic program gained acceptance (Nicholson, 2014). At the turn of the new millennium, critical appraisals of the reductionist stance of the molecular biology revolution became more numerous, both regarding the espousing of nineteenth-century physicalism and the questionable adoption of mathematical theories of information and the notions of program and signal (Longo et al., 2012). In addition to their critical analysis of the status quo, some biologists proposed alternative stances regarding organismal and evolutionary biology (Sonnenschein & Soto, 1999; Oyama, 2000; Kupiec & Sonigo, 2003; Moss, 2003, Jablonka & Lamb, 2005; Noble, 2006). It was clear to many that the promised reduction of biology to chemistry and physics was just a misplaced aspiration that did not translate into advances in experimental biology; various authors suggested alternatives. An alternative, both philosophical and theoretical, was to abandon reductionism by returning to organicism (Gilbert & Sarkar, 2000; Greenspan, 2001; Soto & Sonnenschein, 2005). Theoretical biologists inspired by an organicist stance started to reintroduce the very notions into biology that distinguished living matter from the inert, namely, agency (Kauffman, 2001). Another proposed alternative was technological, namely, the collection of data but at a larger scale (-omics). The idea was to transfer the task of making sense of phenomena to computers and data scientists by generating hypotheses from the data patterns revealed by such analysis (Bassett et al., 1999; Brown & Botstein, 1999). Another approach used the application of mathematical modeling, particularly various forms of “pragmatic systems biology” to search for molecular interactions (O’Malley & Dupre, 2005). Neither one of these technological fixes produced the expected advances in experimental biology; the theoretical work of the organicists, instead, has started to impact experimental work via mathematical modeling based on biological principles (Montévil et al., 2016b) and conceptual analysis (Bich et al., 2020).

In spite of these critical criticisms, the current practice of developmental biology is still guided by the metaphoric use of the mathematical concepts of information, program, and signal, particularly the idea of a teleonomic genetic program, shaped by natural selection. Determination of the organism follows from this program and thus is extrinsic to the developing organism as such. The developmental program is supposed to drive the developing organism toward a final state, thus defining development as an apparently goal-oriented process. This genocentric view, which
endows genes with a privileged causal role, suffers from many weaknesses (Longo et al., 2012; Longo & Mossio, 2020; Soto & Sonnenschein, 2020). It falls short of providing an understanding of how a complex, fully organized biological entity will systematically be formed from this putative “program,” where such a program is located, and how it is executed. One main reason behind these shortcomings is that while there is a close relationship between a DNA sequence and the corresponding protein, there is no such correspondence between genes and phenotypes because the possible properties of phenotypes are not prestatable (Moss, 2008). Consequently, the relationship between genes and forms is not straightforward (Soto & Sonnenschein, 2005). Moreover, the genetic program fails to account for the variability observed throughout embryogenesis and morphogenesis, which contradicts the invariance expected from a “program,” as exemplified by developmental plasticity (West-Eberhard, 2003). Additionally, because of this reliance on the genetic program, contemporary developmental biology tends to address causality in mechanistic terms, which conflicts with the interdependence between the whole, namely, the developing organism, and its parts (Soto & Sonnenschein, 2020). All these difficulties call for a reappraisal of the philosophical and theoretical frames that guide contemporary research in development in general and morphogenesis in particular. This essay will briefly discuss the concepts and theoretical frames that we use to construct a principle-based modeling of developmental and physiological processes. This will be illustrated by recent work on mathematical modeling of mammary gland morphogenesis.

## 12.2 Background Concepts

While reductionism became the dominant philosophical stance in twentieth-century biology, a movement named “Organicism” developed during the period between the two world wars. Organicism is a philosophical stance committed to the following general ideas: (1) the centrality of the organism concept in biological explanation, (2) the importance of organization as a theoretical principle, and (3) the vindication of the autonomy of biology as a science (Nicholson & Gawne, 2015).

Organicism is a materialistic philosophical stance whereby new properties that could not have been predicted from the analysis of the lower levels appear at each level of biological organization. Also, implicit in this view is the idea that organisms are not just “things” but objects under relentless change. While reductionist stances are usually derived from an ontology of unchanging substances, i.e., “being,” organicist stances are usually focused on an ontology of “becoming” (Dupré & Nicholson, 2018).

In the 1970s while molecular biologists aspired to reduce biology to chemistry, advances in the understanding of dissipative non-equilibrium physical systems that self-organize influenced theoretical biologists interested in biological organization. Many of these thinkers, such as S. Kauffman, H. Maturana, and F. Varela, went beyond the notion of far from equilibrium systems and were inspired by the Kantian
concept of biological organization that stressed the interrelatedness of the organism and its parts and the circular causality implied by this relationship (an organism is the cause and effect of itself). Recognizing that Kantian organization does not correspond to the spontaneous self-organization of physical systems, they worked out a new regime of circular causation. In this circular organizational regime, the parts depend on the whole and vice versa; this regime not only produces and maintains the parts that contribute to the functioning of the whole integrated system, but the integrated system also interacts with its environment to promote the conditions of its own existence. This view of organization neatly leads to conceiving intrinsic teleology as a concept compatible with scientific causality (Mossio & Bich, 2017). We can understand organisms as normative agents with the main aim of keeping themselves alive; their proper understanding requiring teleological principles of explanation. In the remainder of this section, we briefly delineate the main concepts in addition to organization and teleology that guide our efforts.

**Historicity** While physical self-organizing systems like flames and micelles appear spontaneously, organisms are generated by the reproduction of a preexisting organism. Historicity is fundamental to phylogenesis and ontogenesis. Historicity particularity establishes a difference from the theoretical frameworks of physics and creates methodological and theoretical challenges for mathematization in biology. Moreover, the historicity of organisms encompasses two time scales, the long scale of phylogeny and the short of ontogeny. Consequently, historical analysis is central to the understanding of biological organization (Longo & Soto, 2016; Montévil, 2020).

**Distinctive Materiality** Organisms are made up of chemicals such as DNAs, RNAs, proteins, and membranes. Unlike computer programs (software) that are independent of the materials of the “hardware,” the functions an organism accomplishes cannot be dissociated from the particular materials the organism is comprised of (Longo & Soto, 2016). This view precludes the software-hardware dualism from biological entities. The materiality of biological objects also has an epistemological dimension. This is evidenced by comparing physical objects with biological ones. In physics, objects are primarily defined by abstract mathematical constructs, as illustrated by the definition of the speed of light in a vacuum being the speed of any light ray. In contrast, biological objects are defined by referencing a particular specimen of an organism, the type, to which the scientific name of a species is formally attached. This specific materiality trickles down to all biological practices, so that biological objects are always defined in reference to concrete objects rather than to theoretical abstractions (Montévil, 2019).

**Agency and Normativity** Teleology is associated with the notions of autonomy and normative agency. The purposiveness of living entities is considered a consequence of the architecture of adaptive systems (Walsh, 2015). Organisms are normative agents, namely, they have the capacity to generate actions and their own rules. As extensively discussed by G. Canguilhem, normative agency is a major characteristic that differentiates living from inert objects. Organisms undergo individuation which is manifested in
their ability to change their own organization, that is, change their own rules. Another remarkable characteristic of organisms is their propensity to become sick and to overcome disease; pathology is an exclusively biological discipline (Canguilhem, 1991).

**Specificity** Physical theories describe generic objects fitting a mathematical construct; for example, as mentioned above, when one refers to the speed of light in a vacuum, there is no need to refer to a specific ray of light, as all travel at the same speed – an invariant of Einstein's relativities. Of course, the methodological approach of physics can accommodate a variety of situations, like phase transition and crystallization, however, always under the umbrella of a generic description that goes with mathematization. In contrast, biological objects are specific, for example, organisms are individuals in the process of undergoing further individuation. In other words, they are the result of history and continue to generate historical novelties. While variation in physical objects is merely a result of quantitative changes, in biology, in addition to the latter, variation is an intrinsic characteristic of organisms which plays a major role in evolutionary biology as the substrate of natural selection and in ontogenesis as the source of functional novelty (Longo & Montévil, 2011; Longo & Soto, 2016, Montévil et al., 2016a). Reductionist attribute a form of specificity to molecules (which are assumed to be defined by their structure; thus, they are ultimately generic), consequently eluding the epistemological challenge of working with specific objects. In contrast, the organicist perspective locates specificity in biological objects endowed with autonomy, that is, organisms and their cells. Cellular specificity is the result of the particular trajectory of each cell during embryogenesis, namely, its interactions with other cells as it proliferates and migrates during histogenesis and organogenesis.

**Constraints** Biological specificity does not negate the idea that aspects and parts of organisms are endowed with a kind of restricted genericity, namely, limited invariance. We call these elements constraints. An example of a constraint is the structure of articulations between bones which preclude certain movements and allow others. Typically, constraints may change over a longer time scale than the process they constrain. For example, the concentration of an enzyme does not change during the time it takes to catalyze the conversion of a substrate into products. Unlike physical invariants that are postulated and stem from fundamental principles, the existence of biological constraints requires explanations (by evolution and organization).

## 12.3 From Organicist Ideas to Principles for a Theory of Organisms

Scientific theories provide organizing principles and construct objectivity by framing observations and experiments (Longo & Soto, 2016). Theories construct the proper observables and provide the framework for studying them. The usefulness of
theories is not determined by their being “right.” Even a “wrong” theory can be use-
ful if, when proven incorrect it is modified or dismissed. The limiting factor for
being useful is that a theory should not be vague, as vague theories cannot be proven
to be incorrect (Feynman, 2017).

A theoretical principle of biological “inertia,” the default state of cells. A method used to develop a theoretical framework consists of positing what takes place when nothing is done to a system, that is, when discussing default states. For example, the inertial state of classical mechanics corresponds to the trajectory of an isolated object. In biology, we posit that the default state of cells is proliferation with variation and motility. It is based on the cell theory, and it relates to the specific materiality of the alive. The default state is a manifestation of the agency of living objects and, thus, a cause (Longo et al., 2015). In contrast to physical objects, the presence of sufficient nutrients is required to maintain the metabolic needs, keeping the biological object alive. In these inertial conditions, cells move and proliferate generating variation (Soto et al., 2016a, b; Sonnenschein & Soto, 2021). Moreover, in the same way that the departure of inertia enables physicists to define classical forces as cause, the departure from the default state defines what causes are. It follows that there are two causal levels in the default state: the level of proliferation and motility that comes from objects understood as specific objects (i.e., causality at the level of cells as such), and the level of constraints acting on the default state (i.e., constraints acting on cells).

*The principle of organization by closure of constraints.* In an organism, con-
straints depend collectively on each other thus generating a circle of dependencies
called closure (Montévil & Mossio, 2015; Mossio et al., 2016). In turn, closure
provides an understanding of the relative stability of constraints and more generally
of biological organizations. Moreover, the principle of organization leads to the
identification of specific constraints in an organism and to assess whether a given
constraint is functional, that is, it participates in closure.

*The principle of variation.* An implicit but overarching principle in physics is that we can understand the changes of an object by means of invariants and invariant preserving transformations (symmetries). For example, an inertial trajectory preserves momentum, energy, etc. This perspective is the basis for understanding physical objects as generic objects. By contrast, the principle of variation posits that biological objects are specific, and therefore relevant invariants and symmetries typically change over time. Modelers sometimes propose to accommodate biological objects with mathematical constructs that would change over time; these changes are somewhat similar to the phase transitions of physics. However, such a construct would again define a generic object, and assume that we can prestate the possible changes taking place. Instead, it is not possible to identify the objects of an experiment, let’s say a group of mice, with a mathematical construct that would accommodate the way they are organized on theoretical grounds. In other words, alternatives are always possible. As a result, biology must reason with a different kind of object when compared to physics, namely, specific objects.

Variation relates to the historicity of biological objects and their contextuality.
Historicity stems from the historical accumulation of variations that, by creating
novelty, co-define present biological organization. Contextuality is related to histo-
ricity because understanding the historical changes that formed current organisms
requires knowledge of the context that facilitated these changes. Contextuality is
obviously also relevant at the time of observation because the definition of experi-
mental objects depends on the context in which they are found. Different contexts
may entail different organizations. For example, during embryogenesis the relation-
ship of a cell with its environment, namely, the surrounding extracellular matrix and
the neighboring cells, is a major determinant of the morphology and function of this
cell within the organ in which it resides. Indeed, understanding a biological organi-
zation requires taking into account its interaction with the surrounding environment,
both at a given time-point and through the successive environments that the biologi-
cal object traverses (Soto & Sonnenschein, 2005; Miquel & Hwang, 2016; Montévil
et al., 2016a; Sonnenschein & Soto, 2016; Montévil, 2019).

Overall, these three principles provide a framework for understanding both gen-
eral aspects of biology and particular biological situations. Building on the organi-
cist and evolutionist traditions, they represent the beginning of novel thinking about
principles and their applications (Soto et al., 2016a, b).

A recent addition to this theory-building process is a symbol, $\chi$, to accommodate specific objects as such. The crucial point is that this symbol does not play the same role as the variable of mathematics; instead it refers to a material object and the objects that are related to it, in a manner that is compatible with the phylogenetic method of classifying living beings (Montévil & Mossio, 2020). It follows that this symbol is also a way of writing about specific objects such as cells on which constraints may act. Additionally, $\chi$ is a point of entry for modifications of an organization. As such, it represents the entry of diachronicity into the synchronic closure of constraints.

12.4 The Mammary Gland as an Organ Model for the Study of Morphogenesis

Let us now show how the theoretical framework summarized above can be applied
to the study of morphogenesis in general, as well as that of different organs, for
example, the mammary gland. Mammary glands are an evolutionary novelty of such
importance that they define the class Mammalia. The gland is made up of two main
components, namely, (1) the epithelial parenchyma, represented by the epithelial
cells, whose function it is to produce and secrete milk to nourish the growing new-
born, and (2) the stroma which surrounds the epithelium. The epithelium is com-
posed of two layers of cells: a continuous luminal cuboidal cell layer and a basally
located discontinuous myoepithelial cell layer. The stroma surrounding the epithe-
lium is composed of various cell types (fibroblasts, adipocytes, and immune cells),
blood vessels, nerves, lymph vessels, and an extracellular fibrous matrix of which
the main component is collagen (Howard & Gusterson, 2000; Masso-Welch et al.,
2000; Richert et al., 2000) (Fig. 12.1). In the resting gland, the epithelial compartment consists of a ductal system. During pregnancy alveoli grow from the ducts and these structures produce and secrete milk. Reciprocal interactions between the epithelium and the stroma mediate the development, function, and remodeling of the mammary glands. The development of the organ can be divided into the following stages: fetal, pre-pubertal, pubertal, pregnancy, lactation, and involution. Ovarian and pituitary hormones regulate the morphology and function of the gland during puberty and adult life, but the fetal and prepubertal isometric development is not hormone-dependent (Soto et al., 2013). Disruption of epithelial-stromal interactions results in various pathologies including neoplasms (Soto & Sonnenschein, 2011; Sonnenschein & Soto, 2020).

### 12.4.1 A 3D Culture Model for the Study of Mammary Gland Morphogenesis

3D models aim to mimic *in vivo* conditions while reducing the number of organis-
mal constraints to those which are hypothesized to be the most relevant ones for the
purpose of the study. This approach allows the researcher to obtain results from
which to estimate the contribution of these components to morphogenesis and/or
physiology of the gland inside the organism. Simpler models may then be compared
to more complex ones by adding other components. Ultimately, these models must
be compared to the behavior of the gland in situ.

<figure><img src="image_33.png" /><figcaption>**Fig. 12.1** Schematic representation of a mammary gland. In the resting mammary gland of adult females, the epithelium is organized into a branching ductal system. Epithelial cells proliferate spontaneously unless constrained; here they are constrained by the stroma containing extracellular matrix and connective tissue cells</figcaption></figure>
Let's now discuss how our theoretical frame guides our strategy. Our theoretical proposition profoundly modifies both modeling and experimental practices. A main objective of this section is to discuss the theoretical determination of the object of study. It requires locating the part (i.e., the mammary gland) into a model of the whole (i.e., the organism). Prior to working on the isolated part (in vitro or in silico), choices must be made regarding what to extract from the whole (Bich et al., 2020). Then, we identify the process that we aim to elucidate: in this case, ductal morphogenesis, where given classes of constraints emerge, such as epithelial structures similar to ducts (which have a geometric feature and undergo cell polarization while developing a lumen). We next hypothesize that some elements are critical, and to an extent, sufficient for this process: some constraints, such as collagen type I fibers, and some specific objects, here epithelial cells from suitable cell lines. This simplification is only possible in a given context that roughly mimics the outcome of critical physiological processes: an incubator for temperature, CO2, sterility, and humidity; media for the chemical milieu, including nutrients; and an extracellular matrix that allows the growth in 3D of the cells into structures. Now, even if such conditions are sufficient for the intended constraints to emerge in vitro, it does not follow that these elements provide a full understanding of the actual phenomenon, and the integration in the organism (with more complex in vitro experiments) is critical to genuinely understand it.

Herein we use a human breast epithelial cell line, MCF10 cells embedded in 3D matrices containing only collagen I or constant concentrations of collagen I and variable concentrations of a mixture of basement membrane proteins (Matrigel); these components of the mammary stroma allow for breast epithelial cells to organize into structures that closely resemble those observed *in vivo* (Fig. 12.2) (Krause et al., 2008; Dhimolea et al., 2010; Krause et al., 2012; Barnes et al., 2014; Speroni et al., 2014).

## 12.5 From the 3D Culture Model to a Mathematical Model

To understand the morphogenesis taking place in 3D culture, we methodically used the principle of the default state to build a first mathematical model and then a computational one (Montévil et al., 2016b).

### 12.5.1 Proliferation

Breast estrogen-target epithelial cells express their default state proliferating maximally in serumless medium. Addition of hormone-free serum (or serum albumin, the inhibitor of cell proliferation present in serum) to the culture medium results in a dose-dependent inhibition of cell proliferation. This inhibitory constraint could be removed by lowering the albumin concentration or by adding estrogens
<figure><img src="image_34.png" /><figcaption>**Fig. 12.2** Mammary epithelial morphogenesis in 3D culture. Mammary epithelial MCF10 cells were seeded in matrices containing a constant concentration of collagen type I (1 mg/ml) and varying concentrations (0–50%) of a basement membrane preparation (Matrigel™). High concentrations of Matrigel resulted in the formation of acini (spherical structures), while ductal elongated branching structures became increasingly prevalent as the Matrigel concentration decreased. Scale bar: 200 µm</figcaption></figure>

(Sonnenschein et al., 1996). Additional constraints are those imposed by cell-cell contact and more generally the mechanical properties of the cells and the matrix in which they are embedded (Barnes et al. 2014).

### 12.5.2 Motility and Constraints to Motility

In biology, cells are agents, they generate forces and initiate motion. They proliferate and move unless there are constraints which prevent them from doing so. In general, classical mechanics imposes that cells exert forces on something to move, and the way they can exert forces depends on their history, both history at the evolutionary level and the history of their lineage inside the organism (and in laboratories in the case of established cell lines). Specifically, breast epithelial cells need a support to crawl on since they do not have a flagellum or a functionally analogous set of constraints. Notably, they use fibers to which they can attach and that they can pull in order to move. Moreover, cells are not simple mechanical structures that remain invariant over time; they react in a diverse manner to a mechanical force,
<figure><img src="image_35.png" /><figcaption>**Fig. 12.3** A cell emits projections, here in a fibrillar matrix of collagen type I. [Reprinted with permission from Elsevier (Montévil et al., 2016b)]</figcaption></figure>

depending on their history and normativity. For example, mechanical compression
induces the expression of a set of genes (Soto et al., 2008; Longo & Montévil, 2014).

The constraints to motility that cells experience in situ can be modeled in a 3D
culture system. The matrix in which the cells are seeded mimics the tissue environ-
ment. Once embedded in a matrix, breast epithelial cells emit projections, like filo-
podia and pseudopodia, which are used for motility; matrix composition may
facilitate or hinder the ability of these projections to generate locomotion (Fig. 12.3).

In a fibrillar matrix, these projections can attach to fibers and exert forces on them. This activity leads to cell elongation and later to the appearance of structures geometrically akin to ducts (Barnes et al., 2014). Similarly, cells use these projections for locomotion. The latter is constrained notably by adhesion to other cells but also by the space occupied by the matrix. Specifically, pore size and matrix rigidity are constraints on cell migration. Pores are larger in the fibrillar matrix than in the globular matrix, while the latter is stiffer than the fibrillar matrix (Barnes et al., 2014). It follows that these properties contribute to morphological differences among epithelial structures.

Breast epithelial cells growing in a globular matrix emit short projections into the matrix that retract soon afterward and display limited motility (Montévil et al., 2016b). Cells rotate and divide resulting in the formation of an acinus, a sphere with a central lumen (Tanner et al., 2012).

Cells that touch each other, whether as a result of migration or after cell division,
can attach to each other. Adhesion, and more specifically the physicochemical struc-
tures involved, constrain cell movements. Moreover, during morphogenesis, cells
may detach from a structure and later reintegrate with it (Barnes et al., 2014).

**12.5.3 Determination of the System**

Cells are specific objects and should therefore be modeled by including the χ sym-
bol (Montévil & Mossio, 2020). Unlike properties in physics, which are described
by their causal relations and their underlying invariants, χ is defined by its past,
including past contexts, for example, the common ancestor of a population of labo-
ratory animals. This symbol enables us to transcribe with theoretical accuracy what
we know about the objects involved, for instance, the cells are from a given cell line that may be found at a specific place and that have been grown in a given context for several generations. At the time of the publication of our first model, these methodological problems were raised by the principle of variation; we are now ready to use the $\chi$ symbol to address this problem in theoretical writing; our model is undergoing a formal rework.

In the biological model, causality takes place in different ways. The default state of cells frames how objects designated by $\chi$ proliferate. The departure from the default state describes how constraints act on cells, that is, objects designated by $\chi$. Finally, constraints acting together, here mainly in the matrix, are analyzed in a more standard biophysical manner – except that they are in relation to cells. An example of such a constraint is collagen orientation with respect to force transmission.

Specifically, following the default state, cells proliferate, leading to an increase in cell number. Cell accumulation has several consequences: the redistribution of fluids, compression of matrix, and/or matrix degradation. Cells exert the other component of the default state, motility, by exerting forces on the matrix if they can do so. In Matrigel rich matrices, cells cannot attach to the matrix, and this component of the default state is constrained. That is, cells emit filopodia and exert their motility but cannot migrate. By contrast, in collagen matrices, cells grab fibers and exert forces on them, leading to changes in fiber organization [orientation notably, but also density (Dhimolea et al., 2010)]. The forces propagate in the matrix depending on its specific state (i.e., fiber orientations) and can reach over long ranges (Guo et al., 2012). As fiber organizations change, so do the constraints that they exert on cells. At the beginning of the formation of a structure, there is a symmetry breaking that leads to the emergence of a main direction in which forces are exerted (the direction of the elongated structure). In particular, forces exerted by cells on each other and on the structure's tips also constrain the default state due to the strain that follows from this force (Fig. 12.4). Collagen bundles facilitate the merging of epithelial structures initially positioned at a long distance range (Guo et al., 2012).

## 12.6 Mathematical Model

Mathematical modeling of biological phenomena is usually practiced using principles from one discipline (i.e., physics) and applying them to biology without evaluating the theoretical meaning these principles have when transported into the theoretical context of biology. It follows that, when models include cells as elementary components, the latter are described by ad hoc hypotheses that we reviewed elsewhere (Montévil et al., 2016b). This modus operandi is properly interpreted as imitation (Turing, 1950); stricto sensu mathematical modeling must be based on the theoretical principles of the discipline being studied. Below we describe the mathematical model both from the theoretical framework provided by the principles and the analysis briefly described above.
<figure><img src="image_36.png" /><figcaption>**Fig. 12.4** Schema of the determination of the system. The biological component is determined by the default state, while the physics component is determined by the physics of material. The two are related since the matrix constraints the default state, and cellular activity, notably motility, affects the fibers. [Reprinted with permission from Elsevier (Montévil et al., 2016b)]</figcaption></figure>

The theoretical framework restricts what is acceptable in order to model cellular behaviors. For example, the absence of proliferation requires constraints and quiescence cannot follow from ad hoc rules describing cells in agent-based modeling. More generally, it means that mathematical modeling, in this iteration, is about the interplay between the *default state* and the constraints acting on it (principle of organization); thus, it is not admissible for models of cells to follow arbitrary computational rules.

### 12.6.1 Description of the Model

In this initial model, we opted for a macroscopic and mesoscopic description of the 3D cultures, meaning that we described cells as elementary units and the fibers by their local orientation in a small spatial volume. We used agent-based modeling for cells and lattice modeling for fibers (limited to fiber orientation), mechanical forces, and a hypothetical chemical inhibitor of cell proliferation. The later seemed to be required to understand some aspect of the biological model, and this fact is also an illustration that theoretical principles constrain mathematical modeling and lead to the formulation of hypotheses.

The core and the originality of the model reside in our the method of understanding cell behavior. First comes the modeling of the default state, a modeling that evolves and expands in future works with the introduction of $\chi$. Cells proliferate after a fixed time, unless constrained. One of the two cells produced by cell division occupies a random adjacent position to the mother cell, while the other occupies the
position of the mother cell. Motility, instead, is more complex to model. Cells move unless constrained, according to the default state. When the cell environment is symmetric, this motion is random. Moreover, motility also encompasses the forces exerted on adjacent cells and extracellular matrix. The latter depends on the force exerted by cells, the orientation of the cytoskeleton, and that of the neighboring fibers.

Second comes the modeling of the constraints on cell proliferation and motility. As mentioned, proliferation requires that space is available for the new cell. Proliferation tends to occur along the direction of forces, so that a cell under a significant mechanical strain may not be able to proliferate even when an adjacent free position exists. Third comes the modeling of the hypothetical chemical inhibitor which slows down proliferation and lessens movements.

Overall, even in this simple iteration, the default state leads to a practice of modeling where spontaneous cellular activity, endowed with randomness, is central. Constraints limit this randomness and orient cellular behavior toward structures that are functional in the organism's life cycle. Moreover, the relationship between the default state and constraints is not just a molding of cell behavior by constraints because the constraints are transformed by cells exerting their default state in a manner that depends on their historical path (both evolutionarily and inside the organism) – the outcome of this historical path is made explicit to an extent by intracellular constraints such as the cytoskeleton.

## 12.6.2 Outcomes of the Mathematical Model

Here, we are discussing the outcome of the initial model as described in Montévil et al. where the details of the model and the analysis can be found (Montévil et al., 2016b).

### 12.6.2.1 In a Globular Matrix

In globular matrix, cells cannot attach to the matrix, and, therefore, cannot use it to move nor rearrange it. It follows that cells only exert forces on each other and crawl on each other when not attached. As a result, cells proliferate and remain tightly together, leading to a spherical structure (Fig. 12.5). Proliferation takes place at the periphery of the structure because cells inside stop proliferating due to the lack of available space. The structure stops growing after some time (due to the chemical inhibitor).
12.6.2.2 In a Fibrillar Matrix

In fibrillar matrices, things are a bit more complex because cells interact actively
with the matrix and the latter constrains them. In the beginning, a single cell is sur-
rounded by collagen, and it starts to pull on fibers, possibly moving, and the colla-
gen tends to align with the direction of the force exerted. The structure gains
additional cells by cell proliferation, and the new cells tend to remain together by
cell adhesion (though some may escape the structure). By pulling on each other and
on fibers, a dominant direction emerges. This direction is both influenced by the
direction in which the first cells pull but also by the random initial orientation of
every part of the collagen. Mathematically, it comes from an instability leading to a
symmetry breaking, so that any small asymmetry in the initial condition is amplified
leading to a large system-wide dominant direction (Longo & Montévil, 2018).
Motility and proliferation are mostly constrained in this direction (due to the
mechanical constraint imposed by this force). It follows that the structure becomes
elongated. The chemical inhibitor, in combination with the mechanical forces, leads

<figure><img src="image_37.png" /><figcaption>**Fig. 12.5** Epithelial cells and collagen orientation in a plane of the simulation. (a) A case of a globular matrix: the cells cannot attach to the matrix nor reorganize it, leading to a spherical structure, an acinus. (b) A case of a fibrillar matrix: the cells reorganize collagen along a dominant direction, leading to the progressive formation of a duct. [Reprinted with permission from Elsevier (Montévil et al., 2016b)]</figcaption></figure>
<figure><img src="image_38.png" /><figcaption>**Fig. 12.6** Example of a branching duct resulting from a simulation run</figcaption></figure>

to a stop of the proliferation in the middle of the structure, while the tips can continue to expand (Fig. 12.5).

Due to the randomness used to model cellular behavior under constraints and the initial matrix, the elongated structure is not perfectly straight but can form a curve-shaped structure. Moreover, the instability at the tip also sometimes allows the structure to branch (Fig. 12.6). This outcome was not expected when establishing the model and is a very interesting result of the method, as in the *in vivo* condition, the mammary gland ductal tree exhibits branching.

## 12.7 The *In Vitro* System and the Organism

By accepting the reciprocal relationship between the whole (organism) and its parts, our theoretical proposition profoundly modifies both modeling and experimental practices. A main objective of our work is the theoretical determination of the object of study. This requires locating the part (i.e., the mammary gland) into a model of the whole (i.e., the organism), an operation that requires further modeling work. Prior to working on the isolated part (*in vitro* or *in silico*), choices are made regarding what to extract from the whole. In this case, our model only dealt with epithelial cells and extracellular matrix. Next, results are compared with information gathered from observing the part within the organism. To bridge the gap between what is observed in the whole organism and in the *in vitro* model, we add other components of the mammary gland stepwise such as relevant cell types (i.e., mammary gland stromal fibroblasts). To grasp the organismal constraints that affect mammary gland development and function, we add hormones to the model consisting of epithelial cells, fibroblasts, and different matrices. We aim to identify primary constraints (Bich et al., 2016) which in our model are the matrix with or without stromal
fibroblasts and regulatory constraints, which in our model are the mammotropic hormones (estradiol, progesterone, prolactin) (Bich et al., 2020).

Regarding the role of mammotropic hormones, at the onset of puberty, estrogen influences the formation of terminal end buds, the structure at the end of the ducts that invade the stroma and guide ductal growth. Progesterone promotes side-branching, and prolactin facilitates alveolar development in preparation for lactation. The dominant reductionist approach focuses on the hormone-receptor interactions and consequent induction of gene expression inside the cell rather than searching to explain the shape changes of the epithelial structures resulting from these hormonal influences in the epithelial cells. Instead, by applying an organicist perspective using a hormone responsive cell line, we found that exposure to hormones leads cells to modify the collagen fiber organization of the matrix in which they are embedded. This, in turn enables the cells to generate the distinct epithelial organization patterns observed in situ, namely, estrogen-mediated ductal elongation, progesterone-mediated lateral branching, and prolactin-mediated budding (Speroni et al., 2014). *In vitro* 3D models can also be used to manipulate constraints beyond the range operating *in vivo*. For example, to learn how rigidity affects shape beyond the limits imposed by the organism, Paszek et al. showed that by increasing the rigidity of the mammary gland model to mimic that of bone, lumen formation was inhibited and epithelial structures disorganized in a way reminiscent of neoplasms (Paszek et al., 2005).

## 12.8 Conclusions

Experimental research guided by our global theoretical approach addresses different questions from those guided by the metaphors of information, signal, and program borrowed from mathematical information theories (Longo & Montévil, 2011). The use of information metaphors drives experimenters to search for causality in discrete structures such as molecules. Additionally, ignoring the circular interdependency of the organism and its parts while embracing the idea that explanations need to uncover “molecular” mechanisms precludes the identification of physical “constraints” which causally contribute to the generation and maintenance of the organism.

Some of these shortcomings have been addressed by a view that, to account for the acquisition of form, combines the genetic program with physical determinants. This view facilitates the introduction of mathematical modeling of morphogenesis whereby matter plays an active role in the stability of local processes and the appearance of shapes. Nevertheless, it has shortcomings: (i) it addresses development, a phenomenon that results from a historical process, evolution, with tools designed to study spontaneous phenomena resulting from ahistorical laws, (ii) it conflates theories of physics with existing models in physics and with the method of modeling of physics (Arias Del Angel et al., 2020), and, finally, (iii) purposiveness is still understood as genetic teleonomy (Montévil, 2020).
Rather than applying the usual procedure of transferring mathematical structures developed for the understanding of physical phenomena into biological ones, we model biological processes from a biological theoretical framework. Here we base our approach on two principles (default state and principle of organization) of the three principles proposed as foundations for a theory of organisms. We have thus provided the proof of principle that *mathematical modeling* based on the theoretical framework of the discipline to which the modeled phenomenon pertains, namely, biology, is feasible and provides biological insight.

In fact, the two principles (default state and constraints leading to closure) were sufficient to show the formation of ducts and acini. Cells generated forces that were transmitted to neighboring cells and collagen fibers, which in turn created constraints to movement and proliferation. Additionally, the model pointed to a target of future research, namely, the inhibitors of cell proliferation and motility which in this mathematical model are generated by the epithelial cells. For a better integration with the principle of variation and the historicity of cells, we are introducing the use of the new symbol $\chi$. Finally, the success of this modeling effort performed as a “proof of principle” opens the possibility for a stepwise approach whereby additional constraints imposed by the tissue (additional cell types) and the organism (hormones) could be assessed in silico and rigorously tested by *in vitro* and *in vivo* experiments.

**Acknowledgments** This work was conducted as part of the research project entitled “Building bridges between natural and social sciences through the prism of a theory of organisms” during AMS tenure as a Fellow of the Institute for Advanced Studies of Nantes, France. Additional support to AMS was provided by Grant ES030045 from the US National Institute of Environmental Health Sciences and the research project entitled “Toward a science of intrinsic purposiveness: shaping development,” supported by the Templeton Foundation (PI, AMS). The funders had no role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript. The authors are grateful to Cheryl Schaeberle and Victoria Bouffard for their critical input and to the reviewers for their helpful suggestions. The authors have no competing financial interests to declare.

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Chapter 13

From the Organizational Theory
of Ecological Functions to a New Notion
of Sustainability

Charbel N. El-Hani, Felipe Rebelo Gomes de Lima,
and Nei de Freitas Nunes-Neto

**13.1 Introduction**

In this chapter, we will address criticisms to the theory of ecological functions intro-
duced by Nunes-Neto et al. (2014). In doing so, we intend to further develop the
theory, as a possible basis for naturalizing the teleological and normative dimen-
sions of ecological functions. We will also take the first steps in the construction of
an integrated scientific and ethical approach to sustainability that is intended to
avoid an anthropocentric perspective.

The problems of teleology and normativity are two classical problems related to the
ascription of functions to biological items (Cooper et al., 2016). In a causal

C. N. El-Hani (✉)

Institute of Biology, Federal University of Bahia, Salvador, Bahia, Brazil

National Institute of Science and Technology in Interdisciplinary and Transdisciplinary Studies in Ecology and Evolution/INCT IN-TREE, Salvador, Bahia, Brazil

Graduate Studies Program in History, Philosophy, and Science Teaching, Federal University of Bahia/State University of Feira de Santana, Salvador and Feira de Santana, Brazil

F. R. G. de Lima

National Institute of Science and Technology in Interdisciplinary and Transdisciplinary
Studies in Ecology and Evolution/INCT IN-TREE, Salvador, Bahia, Brazil

Graduate Studies Program in History, Philosophy, and Science Teaching, Federal University of Bahia/State University of Feira de Santana, Salvador and Feira de Santana, Brazil

N. d. F. Nunes-Neto

National Institute of Science and Technology in Interdisciplinary and Transdisciplinary
Studies in Ecology and Evolution/INCT IN-TREE, Salvador, Bahia, Brazil

Graduate Studies Program in History, Philosophy, and Science Teaching, Federal University of Bahia/State University of Feira de Santana, Salvador and Feira de Santana, Brazil

School of Biological and Environmental Sciences, Federal University of Grande Dourados,
Dourados, Brazil
explanation, causes are presented in order to explain effects that are assumed to follow
from them. Functional explanations are suspected to invert the temporal order of causes
and effects. When one speaks of functions in biology, one often assumes that the expla-
nation for the presence or existence of a given trait lies in its future utility. This is sug-
gested, for instance, when one says that the function of sea turtles' paddle-shaped limbs
is to increase swimming efficiency, which implicitly amounts to saying that they are
born with such limbs for swimming efficiently in the future. This is the problem of
teleology. After all, teleological explanations point to the fulfilment of a given goal. In
a teleological explanation, it is claimed that an event takes place for a given purpose,
i.e., that it occurs because it is the kind of event that brings about that goal. The fact that
this is the necessary event for a given goal to be obtained in a certain state of affairs is
regarded, in this mode of explanation, as a sufficient condition for the occurrence of the
event (Taylor, 1964). Bearing in mind this temporal reversion problem, one of the phil-
osophical challenges of ascribing functions to a trait or other biological item is to do so
from a scientifically acceptable, naturalized perspective that implies a legitimate and
admissible conception of causality from the standpoint of the natural sciences, not
appealing to ontological conceptions inconsistent with scientific knowledge and prac-
tices (Mossio et al., 2009; Moreno & Mossio, 2015).

The second problem is that of *normativity*. When one ascribes a function to a trait, one refers not merely to what the trait does but to what it arguably *should do* (Cooper et al., 2016). Increasing swimming efficiency, for instance, is not simply something that the sea turtles' paddle-shaped limbs do but what they should do, as their function. That is, "attributing functions to traits implies a reference to some specific effect, which constitutes a criterion against which the activity of the trait can be normatively evaluated" (Mossio et al., 2009, p. 814). This normative evaluation, in turn, seems to depend on the teleological relationship expected to be fulfilled. If the expected specific effect does not take place, this entails malfunctioning (Davies, 2000; Cooper et al., 2016; Saborido et al., 2016), which is not an all-or-nothing feature but rather a matter of degree (Krohs, 2010, p. 342). A particular sea turtle limb, say, can be said to be malfunctioning (to some specific degree) when its activity fails in fulfilling the expected norms for efficient swimming. When one accounts for the normative dimension of functional ascriptions, it will be necessary, thus, to theoretically justify why a specific means-end relationship is the norm in that ascription. It is important to bear in mind, however, that it is not a moral sense of normativity that is at stake, but just an expectation about a given acceptable relationship of causality.

A scientifically compatible theory of functions that intends to preserve their teleol-
ogy and normativity should do so in the context of a naturalized approach to purpose-
fulness. This can be done, for instance, by appealing to the notion of “intrinsic
purpose.” This notion entails the idea that the organization of living beings is inher-
ently teleological, i.e., that their own activity is, in a fundamental sense, first and
foremost oriented toward an end, which is to determine and maintain themselves. The
concept of self-determination connects biological organization to intrinsic teleology:
biological organization determines itself in the sense that the effects of its activity
contribute to establish and maintain its own conditions of existence (Moreno &
Mossio, 2015; Mossio & Bich, 2017). This framework establishes a biologically
distinctive notion of purposiveness: teleology is intrinsic in the case of biological systems, while it is extrinsic in the case of artifacts (Jonas, 1966; Aristotle, 1984).<fnref n="1" />

The question is how to build a theory of biological functions that can take in due account the intrinsic teleology of living systems and properly justify the teleological and normative dimensions of functional ascriptions and explanations. To address this question, we will begin by considering three approaches to function, namely, dispositional, etiological, and organizational theories, and how they deal with the teleology and normativity of functions. Then, we will introduce the organizational theory of ecological functions proposed by Nunes-Neto et al. (2014). We will then tackle the main criticisms raised against this theory, related to difficulties in individuating ecosystems such that they can be treated as organizationally closed, the importance of integrating evolutionary considerations into an organizational understanding of ecological functions in order to support the conceptual role of functional explanations in contemporary ecological research, and the ascription of functions to abiotic items. Finally, we will explore the implications of the organizational theory to environmental ethics, taking the first steps toward an integrated scientific and ethical approach to sustainability. This is intended to lead to a new notion of sustainability that offers an alternative to its common interpretation in anthropocentric and economically based terms.

## 13.2 Philosophical Theories of Function and Their Approach to Teleology and Normativity

Two philosophical approaches have been typically used for understanding functional explanation in biology (Cooper et al., 2016). On the one hand, dispositional theories explain functions in terms of the contribution(s) or causal role(s) of a system's part to an emergent capacity at the level of the whole (e.g., Cummins, 1975; Adams, 1979; Bigelow & Pargetter, 1987; Craver, 2001). To use a classical example, from this perspective, the function of the human heart is to pump blood because pumping blood is what the heart does that contributes to a specific human systemic capacity, namely, the circulation of gases and nutrients. This is an approach that relies on current means-ends relationships to conceive of functional explanation, intending to ground normativity without appealing to teleology – an approach that has been argued to be able to support only an epistemic normativity, dependent on the researchers' choices about which systems and which systemic capacities to

<footnote n="1">¹ Babcock and McShea (2021) argue that this distinction between externalist and internalist teleological explanations, which comes back to Aristotle's *Physics*, has been a misstep in the debates on teleology. They argue, in contrast, for a single type of legitimate teleological explanation, an artifact model of teleology in which goal-directed entities are guided by a nested series of upper-level fields (McShea, 2012, 2016). In this chapter, we will keep reference to the usual distinction between intrinsic and extrinsic teleology, leaving Babcock and McShea's proposal to be discussed elsewhere.</footnote>
study (see below). It intends to dissolve the problem of the teleology of functions by reducing them to any causal contribution to a higher-level capacity that a trait/part may give, such that the normative dimension of functions is reduced to the claim that the causal effect must contribute to a higher-level capacity, with no reference to a “benefit” for the system. For those committed to this approach, teleological reasoning is merely an element of a superseded worldview, which should have no application in the way modern science explains natural phenomena. However, a common criticism of this way of understanding biological functions follows from the fact that it does not include a teleological element, namely, that it underdetermines the normative dimension of functional ascriptions, being unable to distinguish proper functions from accidental effects and to account for malfunctionality, because in the end functional ascription depends on the observer’s choice of the phenomenon to be accounted for in functional terms (Millikan, 1989; Kitcher, 1993; Mitchell, 1993; Godfrey-Smith, 1994; Mossio et al., 2009). Novel versions of the dispositional theories of function have been proposed in order to include additional requirements in an effort to avoid the drawbacks pointed out by critics (e.g., Weber, 2005).

On the other hand, etiological theories seek to naturalistically ground both the teleological and normative dimensions of functions by appealing to an evolutionary perspective, i.e., turning to the selective causal history (or etiology) of organisms' traits/parts (Wright, 1973, 1976; Millikan, 1984, 1989; Neander, 1991; Godfrey-Smith, 1994). From this perspective, organisms have functional traits because those traits have increased the fitness of past organisms in their respective lineages. Accordingly, function is not a mere effect of a trait but a selected effect that explains its current presence or prevalence. From this perspective, the function of the human heart is to pump blood because pumping blood is the selected effect that explains the current presence of hearts in humans. A causal loop between the functional effect of a given trait and its persistence through time grounds the teleology and normativity of functions: Fitness-enhancing effects of past tokens explain the presence of the contemporary trait type and provide a normative standard for evaluating present tokens. This approach has been criticized, however, for being too narrow to accommodate all functional talk in biology, particularly because it makes the current contribution of a trait irrelevant to determine its function and, thus, does not account for functional ascriptions that are often made in several areas of biology in relation to current rather than past effects. This is at odds, in short, with the fact that functional attributions to biological items do seem to bear some relation to what they currently do that increases an organism's survival and reproduction chances, and not only to what explains their current existence. It is in the sense that it has been argued that etiological theories seem to offer a problematically epiphenomenal account (Christensen & Bickhard, 2002). Another criticism concerns the fact that this sort of explanation appeals only to natural selection, while this is neither the single evolutionary process important to explain how organisms came to be how they are nor the single explanation for the presence of all traits to which we ascribe functions (Cooper et al., 2016). These criticisms have been discussed and addressed by
advocates of the etiological theories, which have developed them in different versions in an attempt to overcome the pinpointed problems (see, e.g., Garson, 2015, 2016).

Organizational theories offer a third way for building an understanding of functional ascriptions and explanations (e.g., Schlosser, 1998; Bickhard, 2000, 2004; Collier, 2000; McLaughlin, 2001; Christensen & Bickhard, 2002; Delancey, 2006; Edin, 2008). In particular, we rely here on the theory developed by Mossio et al. (2009), which aims at explaining at the same time the persistence of a trait through time and its current contribution to the maintenance of a system.

As formulated by Saborido et al. (2011), a trait *T* has a function if, and only if, it exerts a constraint subject to closure in an organization *O* of a system *S*, which entails the fulfilment of three conditions:

C₁: *T* exerts a constraint that contributes to the maintenance of the organization *O*.

C₂: *T* is maintained under some constraints of *O*.

C₃: *O* realizes closure.

These conditions naturalize teleology as they state how the system realizes a circular causal regime that can be grasped through the concept of “closure” (Varela, 1979; Moreno & Mossio, 2015).<fnref n="2" /> If the heart pumping blood makes it possible that the organization of a living system and, consequently, the heart itself be maintained, then that activity of the heart is a cause of its very existence and can be identified as its function. Normativity is also naturalized by these conditions, since the expected behavior of an organism’s trait is related to the production of the specific effect that contributes to the systemic organization in which the trait is included and that is responsible for its very maintenance. The specificity of this effect allows for a distinction between function and nonfunctions, as well as between proper and accidental functions.

The causal loop involved in the intrinsic teleology of living systems shows the distinctive property of being a closure of constraints, rather than merely a closure of processes, as we observe in a number of physicochemical systems showing mutual dependence of entities and processes. Constraints are local and contingent causes that reduce the degrees of freedom of the dynamics on which they act (Pattee, 1972) but remain conserved at the time scale relevant to describe their causal action with respect to those dynamics (Mossio & Bich, 2017). Thus, the kind of closure expressed in conditions C₁ and C₂ is a closure of constraints, i.e., an organization in which each constraint is involved in at least two different dependence relationships, playing the role of enabling and dependent constraint, respectively (Moreno & Mossio, 2015). Therefore, as developed in detail by Mossio and Bich (2017), it is not any form of causal circularity that will show intrinsic teleology. Rather, it should be a circular causal regime of constraints that are collectively able to self-determine

<footnote n="2">²In very general terms, by “closure” one means a feature of systems by virtue of which their constitutive components and operations depend on each other for their production and maintenance and, also, collectively contribute to determining the conditions under which the system itself can exist (Mossio, 2013).</footnote>
(or, more specifically, self-maintain) through self-constraint. Or, to put it differently, circularity is a necessary but not sufficient condition for intrinsic teleology, and biological organization shows this distinctive property because it realizes self-constraint. In these terms, the idea of biological function does not rely only on teleological and normative dimensions but also on the idea of organization. Or, to put it differently, the idea of organization as closure necessarily includes teleological and normative dimensions.

## 13.3 The Organizational Theory of Ecological Functions

Functional language is ubiquitous in ecology. Ecologists commonly talk about the function of a given tree species in a forest, or the function of decomposers in relation to soil properties, or the functional role of organisms' traits in a given ecological process, among many other possible examples (for detailed analyses of the uses of function by ecologists, see Jax, 2005; Nunes-Neto et al., 2016a). However, in spite of this extensive reliance on functional language in both descriptions and explanations in ecological research, it is not clear yet how to properly justify the use of functional language in ecology in scientifically compatible terms. However, several steps have been taken in this direction in a number of recent works (e.g., Jax, 2005; Nunes-Neto et al., 2014; Dussault & Bouchard, 2017; Odenbaugh, 2019; Millstein, 2020; Lean, 2021).

We have proposed a theoretical perspective to justify functional ascriptions and explanations in ecology from an organizational point of view (Nunes-Neto et al., 2014; El-Hani & Nunes-Neto, 2020). In order to explain it, let us begin by considering the ways in which the concept of function is used in ecology (see Jax, 2005; Cooper et al., 2016). Jax, for instance, differentiates between four different and complementary ways this concept is employed by ecologists: (1) as a purely descriptive meaning that refers to some change of state or to what happens in the relationship between biotic or abiotic objects; (2) to refer to the functioning of a whole ecosystem; (3) to refer to the role functions of biotic and abiotic components of an ecosystem in relation to its functioning as a whole; and (4) to refer to ecosystem services to some human need or purpose. Here we are specifically interested in use (3), related to the role functions of ecosystems' parts in relation to ecosystem processes (e.g., the role of plants as primary producers within an ecosystem).<fnref n="3" /> These

<footnote n="3">³When we refer to ecological role functions, this is not in opposition to thinking on individuals or groups/types from an organizational perspective. Rather, as we make explicit in the organizational account, functions are specific roles ascribed to items of biodiversity or abiotic items (under the influence of the biotic community) that constrain the thermodynamic flows in an ecological system. These parts are identified through decomposition/localization analyses (Bechtel & Richardson, 2010), but these are not arbitrary, or under the mere discretion of the researcher, since they should be guided by hypotheses or models on the contributions of the components to the norms of the ecological system's behavior, i.e., to the maintenance of its conditions of existence. Therefore, the components fulfil the causal roles defined in a given decomposition/localization model or hypothesis when they do what they are supposed to do in relation to those norms.</footnote>
role functions are connected, in turn, with the use of functional reasoning to classify
organisms or species according to their effects on ecosystem processes, as we see in
the common reference to functional traits and functional groups in ecological
research (see, e.g., Hooper et al., 2005; Petchey & Gaston, 2006).

Based on the organizational theory of functions developed by Mossio, Saborido,
Moreno, and colleagues, we have defined an ecological function as “a precise (dif-
ferentiated) effect of a given constraining action on the flow of matter and energy
(process) performed by a given item of biodiversity, in an ecosystem closure of
constraints” (Nunes-Neto et al., 2014, p. 131). At the same time, assuming this defi-
nition as a starting point for an organizational theory of ecological systems under
construction, we have recently proposed to broaden the range of organizational
functional items in the ecological domain in order to include abiotic items, if one
shows how they can play the role of constraints (El-Hani & Nunes-Neto, 2020).<fnref n="4" /> In
other words, an adequate set of functional items should include not only items of
biodiversity (i.e., organisms, populations, functional groups, guilds, etc.) but be
more encompassing, including abiotic items. Looking at individual organisms helps
making this clear: a honey bee nest is an abiotic, non-biological structure (in the
sense that it is not made of living cells) but at the same time is clearly functional (or
at least it is typically assumed to be so by biologists). The same seems to be true of
ecological systems: abiotic parts of ecosystems (for instance, fire) may play relevant
functions in the whole system of which they are parts. The key point when ascribing
functions to abiotic items in either organismic or ecological systems is to show how
they can act as constraints internal to the organization of the systems, involved in the
maintenance of their conditions of existence.

To consider an example of how the organizational approach works, let us look at
an ecological system from the point of view of its main activities, decomposing it in
three functional groups: producers, consumers, and decomposers. Consider, also, an
abiotic factor that producers subject to their closure, namely, carbon dioxide. The
functional groups form a hierarchical organization comprising two levels (i.e., a
hierarchy of control, cf. Ahl & Allen, 1996): the level of the functional items – in
this case composed by items of biodiversity – which act as constraints, and the level
of the material, thermodynamic flow of carbon atoms, which is the constrained pro-
cess. Considering the functional items, the producers of organic matter (plants) con-
strain, through photosynthesis, the flow of carbon atoms, reducing its degrees of
freedom, which is something that can be clearly noticed in the building of complex
biomolecules from carbon atoms as basic ingredients. The flow of carbon atoms

<footnote n="4">⁴The individuation of abiotic items, as components of ecological systems, poses in itself important challenges. Here we will not focus on these challenges, which will be faced, in fact, by any theory that intends to ascribe functions to abiotic items, such as Dussault and Bouchard's (2017) persistence enhancing propensity (PEP) or Odenbaugh's (2019) systemic capacity accounts. Rather, our main concern in the present work is the individuation of ecological systems. In passing, we can remark, however, that the fact that abiotic items can only be ascribed role functions according to the organizational theory if they act as constraints in relation to the organization and conditions of existence of ecological systems means that we may be able to individuate at least their role as constraints, even if it may be difficult to individuate them as entities.</footnote>
becomes more determinate, more harnessed, as these atoms, initially contained in atmospheric carbon dioxide molecules, become part of plant biomass. Parts of plant biomass (leaves, fruits, sprouts, etc.) are eaten by consumers (herbivorous animals), which realize a second channeling of the flow of carbon atoms, when these atoms in the plant biomolecules, after digestion and absorption of nutrients, become part of their bodies. And the same is true of a whole network of consumers. In turn, when the consumers and producers die, the animal carcasses and plant leaves, fruits, twigs, and roots become part of the organic matter that is further processed by decomposers, which transform it into available nutrients for plants, thus closing the cycle by reducing once again the degrees of freedom of the flow of carbon atoms. Moreover, due to respiration, along the whole chain of processes, carbon dioxide molecules are sent back to the atmosphere, from where they can be cycled back to the system through photosynthesis (Fig. 13.1).

There is a clear mutual dependence between these constraints. By constraining the flow of matter (carbon atoms), the consumers, for example, create conditions of possibility (or enabling conditions) to the existence of the decomposers and, in this manner, exert an effect on the ecological system as a whole. And while, on the one

<figure><img src="image_41.png" /><figcaption>**Fig. 13.1** Organizational functions in an ecosystem closure of constraints – a schematic view. (Figure elaborated by Felipe Rebelo Gomes de Lima)</figcaption></figure>
hand, the consumers are enabling conditions to the existence of decomposers, they
depend, on the other hand, on the producers from which they derive the matter and
energy needed for their self-maintenance. Therefore, we can say that they are depen-
dent on both the producers of organic matter and the very decomposers that mobi-
lize nutrients to the producers. In sum, producers, consumers, and decomposers – as
functional items – exert specific constraining actions that amount to the role func-
tions they play within the ecological system of which they are parts, contributing to
the self-maintenance of its organization.

13.4 Organizational Functions and the Individuation of Ecological Systems

Ecosystem individuation raises questions for the organizational theory of ecological
functions (Cooper et al., 2016). As functions are ascribed in this theory to con-
straints subject to closure, it is a requisite to functional ascription to establish where
the ecosystem closure of constraints lies. In more detail, the problem consists in
that, as ecological systems interpenetrate one another at their fringes, this fuzziness
of physical boundaries typically also entails a fuzziness of functional relationships,
making it harder to decide which constraints are part of one or another ecosystem
(or, perhaps, both) and, thus, which functions are to be ascribed to them as subject
to the closure of the distinct systems. In short, to ascribe functions to ecosystem
components and, accordingly, to naturalistically justify the teleology and normativ-
ity of ecosystem functions depend on the ecosystem closure of constraints and
mutual dependences between items of biodiversity and abiotic items.

This does not seem to be a particular problem challenging the application of the
organizational theory to ecological cases. As Bich (2019) argues, to account for
limit cases in which functional closure cannot be realized from within is a more
general challenge faced by this theoretical framework. This follows in fact from the
thermodynamic openness of living systems and, thus, goes all the way back to
Piaget's (1967) crucial conception of the complementarity in such systems between
organizational closure and thermodynamic openness. In order to self-maintain
themselves, biological systems often need to recruit external constraints or expand
their network of control interactions to include previously external constraints,
which belong to other systems, subjecting them to their own organizational closure.
As we will elaborate below, the control of flammability by fire-adapted plant spe-
cies in ecosystems is an example of how a boundary condition<fnref n="5" /> external to the

<footnote n="5">⁵Boundary conditions are typically conceived as conditions defined externally to a system that contribute to determine its behavior and dynamics, but typically do not depend on the dynamics on which they act. When the behavior of a system is sub-specified, as it happens when it depends on variable, contingent local circumstances, boundary conditions related to these circumstances are added to its description for providing the lacking specifications. Boundary conditions are imposed on the laws of physics and chemistry and provide additional specifications by decreasing the</footnote>
system has become part of its internal dynamics, once it has been subject to their closure, turning from a destructive force into a constraint that is both enabling (e.g., of regrowth processes) and dependent (on fire-adapted plant species) (e.g., Mutch, 1970; Schwilk & Ackerly, 2001; McLauchlan et al., 2020). This kind of process can blur, however, the functional boundaries of the system, jeopardizing the very idea of closure, which depends on the capability of living systems of specifying their functional boundaries from within. This threat to closure may be solved by recognizing the fact that, once an external constraint is *recruited* by a system A, it simply becomes a part of that system. Yet, as this was an external constraint, say, initially belonging to some system B, we need clear criteria to state whether the constraint is part of A, B, or both, which will affect which functions may be ascribed to it. That is, as functions are ascribed in the organizational theory to constraints subject to closure, the problem of specifying where the organizational closure of the living system lies will affect functional ascription, i.e., the identification of what can be considered a functional component of the system and what cannot. To trace the precise functional boundaries of a system can be regarded, thus, as a requisite to build functional explanations according to this theory, which is under challenge in other cases than just ecological systems. Yet, as we shall see, the theory has the resources to face this challenge.

Based on the assumption that one could rarely individuate ecosystems as organi-
zationally closed systems, a number of criticisms of the organizational theory of
ecological functions suggested that the range of ecological systems to which it
applies is rather limited. Dussault and Bouchard (2017), for instance, argue that the
organizational theory is too restrictive to accommodate key aspects of contempo-
rary ecology, for instance, related to the biodiversity and ecosystem function (BEF)
research program. They go on to discuss cases related to the ascription of functions
to biodiversity, abiotic factors, and source-sink populations. We will engage with
these cases below. Let us begin, however, by considering a critical appraisal of the
organizational theory claiming that the domain in which this theory can be applied
is very narrow.

Focusing on the bromeliad example chosen by Nunes-Neto et al. (2014) to illus-
trate the organizational theory of ecological functions, Lean (2021) argues that
organizational closure is an exceptional case in ecological systems, and organiza-
tional functions will be less likely as ecological systems scale up in size, complex-
ity, and openness. In this manner, the individuation of ecosystems as organizationally
closed systems and the scope of the organizational theory can be seen as

<footnote>degrees of freedom of the system’s dynamics. In this manner, they harness the physico-chemical
processes involved in such dynamics (Polanyi, 1968). A constraint is a particular kind of boundary
condition, characterized by both its causal role in relation to a particular process *P* under its influ-
ence, such that *P* takes place differently under and free from the influence of the constraint, and its
conservation or symmetry at the time scale characteristic of *P*, which follows from being locally
unaffected by *P* (Mossio et al., 2013). A central difference between living and non-living systems
is that in the former part of the constraints/boundary conditions acting over the system are pro-
duced by the system itself, and, moreover, the set of internal constraints show mutual dependence,
while in the latter constraints/boundary conditions are externally produced.</footnote>
interconnected issues. Lean argues that one can only take ecological systems to be closed self-maintaining units based on a strong commitment to equilibrium ecology, according to which population interactions would stabilize the composition of communities. Then, if such stabilizing interactions are coupled with stable populations, we would obtain bound self-maintaining ecological systems. However, the problem is – Lean argues – that equilibrium ecology has been extensively criticized in the history of this discipline and ultimately replaced by non-equilibrium ecology, which describes ecological communities as causally open collections of species, and local community composition as a result of path-dependent historical processes and random dispersal of populations from other local communities. The outcome of this picture would be that ecological communities are not closed systems but rather the product of many populations moving around larger biogeographic regions. With the large turnover of species within a local area, there would be changes not just in the populations playing a functional role but also in the overall causal structure of the system. Lean's conclusion is, thus, that the domain in which the organizational theory of ecological function may apply is very limited: organizational functions would only occur in some ecological systems, generally rather small ones, with just a couple of populations in close physical proximity.

Besides organizational functions, Lean (2021) also discusses selected effects, persistence, and causal role functions, concluding that all those that include a normative dimension (i.e., all of them except causal role functions) are sporadic and rare, such that ecological functions would be nearly always dispositional rather than normative. That is, they should be conceived, according to him, as descriptions of causal structure that can be used to identify features that we should preserve. As teleological arrangements of ecological systems would be extremely spotty, with just some “blips of teleological arrangement” (Lean, 2021, p. 9327), founding conservation on teleology would be a misstep. Teleological organization would not include much of what conservation biologists intend to protect and, accordingly, would not provide a strong enough scaffold to support conservation ethics. To deny intrinsic teleological grounding for conservation ethics may limit conservation decisions, however, to anthropocentric reasons, leaving instrumental values in relation to human activities as the major if not exclusive reason that would be relevant for such decisions.<fnref n="6" />

This is related to a key difficulty for causal role functions, which several critics have pointed out: they lack a normative component, just describing the presence or absence of a function, not whether a system's trait is malfunctional or accidental. Even though Lean's position can be described as pluralistic (see Dussault, 2022), we think his conception of ecological functions is more closely related to causal role functions. But, be that as it may, his position shares with the latter the lack of a

<footnote n="6">⁶This is recognized by Lean (2021, p. 9328) himself: “By deploying [Causal role] functional analysis, we can identify what supports the ecological features that we do, or should want to, protect. These could be features of the environment which have moral utility or preference. While this does not offer us a non-anthropocentric justification for intervening on ecological communities, it does offer a way of identifying which populations make a disproportionate impact on the community.”</footnote>
normative component. Now, this has been generally regarded as a shortcoming of
dispositional theories of function, as shown by the well-known argument that these
theories are too liberal for proper functional ascription (e.g., Millikan, 1989; Kitcher,
1993). However, Lean (2021) thinks differently, claiming that this is a positive char-
acteristic of the theory, a flexibility that allows explaining any ecological system’s
capacity, provided there are constitutive and causal relations in the community at
stake. He does not see as a weakness of dispositional theories that the system and
capacity of interest are defined by the researcher. This is a defensible view, but not
easily so, given the common criticisms of dispositional theories for being too broad
and under-specified, incapable of capturing the explanatory force of functional
ascription, or making sense of malfunction and differentiating between functioning
and mere usefulness, or, else, the criticism that they allow arbitrary, subjective attri-
bution of functions depending on which capacities of a system interest us, and on
criteria to identify relevant systems that are entirely dependent on the observer (e.g.,
Neander, 1991; Mitchell, 1993; Godfrey-Smith, 1994; Moosavi, 2019).<fnref n="7" />

To our understanding, Lean’s arguments about organizational functions show
two major problems: first, they do not take in due account that non-equilibrium
ecology does not exclude ecological interactions and ecological interactions can
generate community-level functional organization; second, they do not consider
that closure of constraints is not an all-or-nothing property that would necessarily
require a strongly cohesive unit to obtain.<fnref n="8" /> As we will argue later, it is sufficient that
just part of the constraints exerting influence or control over the system be included
in the closed organization, and, accordingly, an organizationally closed system can
show different degrees of cohesion or functional integration.<fnref n="9" /> But let us focus, first,
on the idea that one might appeal to closure of constraints to individuate ecosystems
only if committed to equilibrium ecology.

<footnote n="7">⁷Lean's approach is to justify conservation decisions based on analyses of the causal structure of ecological systems, in order to identify populations that we are interested to preserve, given their role in supporting ecological features that interest us, and populations we may want to control, due to their role in reducing biodiversity. He does not appeal to any normative reason that could justify treating systems with particular populations (say, invasive species) as malfunctioning. It is clear that these conservation decisions would be mostly based on what we are interested into, and may suffer from the same sort of arbitrariness criticized in dispositional theories. At most, Lean can introduce a justification for conservation decisions based on what "... all prudent agents should want to preserve."</footnote>

<footnote n="8">⁸Here we should admit that in our original 2014 paper, we were not explicit about the idea that organizationally closed systems can show different degrees of cohesion or functional integration, such that Lean cannot really be blamed for overlooking it.</footnote>

<footnote n="9">⁹This can be related to the view that biological individuality and functional integration come in degrees even in the case of organisms (see, e.g., Queller & Strassmann, 2009; West & Kiers, 2009; Clarke, 2010; Strassmann & Queller, 2010; Godfrey-Smith, 2013; Huneman, 2014a, b; Sterner, 2015; Skillings, 2016; Bich, 2019; Wilson & Barker, 2019).</footnote>
### 13.4.1 Ascribing Organizational Functions in Non-equilibrium Ecology

Non-equilibrium models resulted from the work of neo-Gleasonian ecologists (e.g., Whittaker, 1951, 1975; Curtis & McIntosh, 1951) who proposed that typical ecological communities are composed of species which have evolved independently and were combined through chance immigration and individual suitability to ecological contexts. As Whittaker and Woodwell (1972, p. 141) argue, “communities are related by a blurred reticulateness of many intersecting strands (i.e., species) relating a present community to many past communities.” But, as Dussault and Bouchard (2017) emphasize, Gleasonian or neo-Gleasonian ecology does not deny community-level functional organization as depicted, say, by Elton’s (1927, 1930) trophic model of ecological communities or as studied by ecosystem ecologists (Hagen, 1989, 1992). Even though Gleason and his followers adopt a population-reductionist stance concerning the migration and establishment of species in a location, they do not deny that these species interact once they are established, and their interactions can give rise to community-level functional organization (Eliot, 2011; Nicolson & McIntosh, 2002).<fnref n="10" /> Symptomatically, we find that contemporary ecologists often do not shy away from conceiving communities and/or ecosystems as functionally organized systems, in which organisms, species, or abiotic items fulfil functional roles (e.g., Naeem, 2002a; Schulze & Mooney, 1993).

If we take into account these aspects of Gleasonian or neo-Gleasonian ecology, Lean’s (2021) interpretation that one can only consider ecological systems as organizationally-closed if strongly committed to equilibrium ecology is not well supported. And, if we consider the issue more generally, the current state of knowledge in ecology does not support this interpretation either. It is truly an empirical issue which ecological systems are subject to non-equilibrium dynamics and which are in equilibrium, but it is not the case that closure of constraints would only obtain if community composition was established as depicted in equilibrium models. As in non-equilibrium models community-level functional organization can emerge once the biotic community is formed in the intersection between the distribution of several to many species, closure of constraints can also obtain even if community

<footnote n="10">¹⁰Here it is important to notice that generic interactions among species are not sufficient for functional ascription. If interactions are generic, it will be difficult to maintain that ecological function bearers contribute to their own maintenance by contributing to the maintenance of the system. Strictly speaking, a species that generically contributes to the maintenance of the ecological system as a whole cannot be convincingly described as contributing to its maintenance *per se*. Rather, it can be said to contribute to the provision of conditions that fulfil the needs of any species with sufficiently similar niches – be it itself or another species. On this issue, see Dussault (2019). For an item of biodiversity or abiotic factor to be functional within a community-level functional organization, it should have specific rather than generic effects. That’s why the proviso that an ecological function amounts to a precise (differentiated) effect of a constraining action on the flow of matter and energy in an ecosystem is very important in the account proposed by Nunes-Neto et al. (2014, p. 131).</footnote>
composition results from path-dependent historical processes and random dispersal of populations, provided that their interactions once together in the same community give rise to a functional organization.

Vellend's (2010, 2016) proposal of a conceptual synthesis in community ecology offers a case in point about how the role of local species interactions, which can give rise to community-level functional organization, is recognized in ecological models not committed to equilibrium assumptions. He claims that, despite the large number of mechanisms underpinning patterns in ecological communities, four distinct kinds of processes are combined in them, namely, selection, drift, speciation, and dispersal. The focus on these processes resulted from conceptual developments along the history of ecology. In the 1950s and 1960s, equilibrium ecology was consolidated, based on the idea that patterns in the composition and diversity of species in communities were the deterministic outcome of local interactions between functionally distinct species and their environments (importantly including other species). Thus, those patterns could be explained mostly by fitness differences among species, or, in other words, by selection.

Non-equilibrium ecology emerged in the 1980s and 1990s, bringing a more inclusive approach to community ecology, which recognized the importance of processes at broader spatial and temporal scales for understanding local-scale patterns. This does not mean, however, that the latter patterns could be simply dismissed, and, accordingly, it does not entail that local species interactions and their fitness consequences, or community-level functional organization, would have to be simply dropped from the picture. Rather, what was at stake was the need to take into account that the composition and diversity of species at a local scale fundamentally depend on the composition and diversity of regional pools of species, such that speciation is also a process to consider when explaining community-level features.

The next step was the incorporation of drift, with the neutral theory of biodiversity. By “ecological drift” one means random fluctuations in population size resulting from ecological equivalence in the probabilistic sense, i.e., in the sense that individuals have equal chances of reproduction or death regardless of species identity (Rosindell et al., 2012). Pure ecological drift would happen if individuals of different species were demographically identical, a very unlikely situation, but drift will be equally important when it is not the only active process at stake. In any case, there will be ecological drift, and its importance will be greater the more modest is the functional differentiation between individuals or species in a given set, or, to put it differently, the more ecologically equivalent they are. Again, the recognition of drift does not entail a denial of a role for local-scale species interactions and patterns. Finally, dispersal was incorporated into community ecology models in the form of the metacommunity concept, which concerns the influence of dispersal among local communities over community patterns at multiple scales.

As Vellend (2010, p. 185) sums up, “selection, in the form of deterministic interactions among species and between species and their environments, was always recognized as important.” Accordingly, in non-equilibrium models, incorporating drift, speciation, and dispersal, local-scale species interaction is recognized, as well as the possibility that community-level functional organization emerges. The upshot
is that we do not need to be committed to equilibrium ecological models to explain
ecological functions from an organizational perspective. In non-equilibrium mod-
els, organized systems can be also identified, and, accordingly, the domain of the
organizational theory is much larger than Lean recognizes. Moreover, it has been
argued that the processes identified by Vellend (2010, 2016), which structure spe-
cies dynamics within a community, can be interpreted as constraints, even though a
convincing demonstration that this is really the case is yet to be done (Peck &
Heiss, 2021).

Interestingly, Lean (2021) situates his own position between two extremes he
identifies in ecological science: either ecological systems would be mere collections
of populations, largely independent of each other (Gleason, 1926), or analogous to
organisms, possessing functional organization that maintains mature organism-like
individuals (Clements, 1916).<fnref n="11" /> He associates, then, the idea that ecological systems
may have functions from which conclusive statements about what is normatively
functional or malfunctional can be made with the claim that they are organism-like.
However, ecology is not trapped between those two extremes but also formulates an
understanding of ecological systems that sits between them. Similarly, we do not
need to treat ecosystems as organisms to ascribe organizational functions to their
components. On the contrary, there are important differences between ecosystems
and organisms, as the former typically lacks the sort of agency and regulation<fnref n="12" /> that
characterize the latter. Moreover, ecological systems do not show the same degree
of stability and cohesion observed in organisms, or at least in many cases of organ-
ismality. Accordingly, there is no requirement that one is committed to an interpre-
tation of ecosystems as superorganisms to apply the organizational theory. What is
necessary to ascribe function to components of a system based on this theory is just
organizational closure, conceived as closure of constraints. Or, to put it differently,
what we assume is just that organisms and ecosystems can share the property of
organizational closure, despite their several differences. It is sufficient, also, that a
self-maintaining, organizationally closed system shows a tendency to closure,<fnref n="13" /> and

<footnote n="11">¹¹See Eliot (2007, 2011) for a critical appraisal of the sheer opposition between Clements' and Gleason's approaches to explaining vegetation.</footnote>

<footnote n="12">¹²As defined in the organizational theory we take as a starting point. See, e.g., Moreno and Mossio (2015) and Bich et al. (2016).</footnote>

<footnote n="13">¹³We use the expression “tendency to closure” following its usage by Montévil and Mossio (2015). However, this expression may be interpreted in a manner that raises unnecessary difficulties to the theory, since it may suggest that we would be referring to a process showing a tendency that closure emerges as its outcome. This interpretation may lead to a counter-argument that a tendency toward closure would be no guarantee (or support no prediction) of achieving it. Nevertheless, what is meant by “tendency to closure” is that interdependent subsystems (or modules) within a containing system (which is itself organizationally closed) showing a relatively large degree of internal cohesion (i.e., interdependent modules) can be said to tend to be closed, despite the fact that they functionally depend on one another. In this precise sense, organizationally closed systems may come with different degrees of cohesion and functional integration (either diachronically or synchronically), to the extent that it is sufficient for closure that part of the constraints affecting the system’s dynamics are mutually dependent such that each of them is involved in at least two different dependence relationships in which it plays the role of enabling and dependent constraint.</footnote>
even if regarded as closed, this does not mean all constraints or boundary conditions
affecting its dynamics should be included within the closed organization.

13.4.2 On the Domain of the Organizational Theory
of Ecological Functions

In this section, we intend to reinforce the claim that the organizational theory of
ecological functions does not apply only to small ecological systems, with just some
limited number of populations in close physical proximity. If the theory applied
only to such exceptional cases, its utility would be surely quite limited. We do not
think, however, that this is a correct assessment.

In our original paper (Nunes-Neto et al., 2014), we did not present key concepts of the original organizational theory that provide ways to respond to criticisms about the scope of the organizational account of ecological functions (Dussault and Bouchard, 2017; Odenbaugh, 2019; Lean, 2021). Valuable as these criticisms are for sharpening our ideas, there are central aspects of the theory that need to be made explicit to tackle them.

For instance, the concept of constraint has not been given by both Dussault and Bouchard (2017) and Lean (2021) the central role it has in the organizational theory. Organizational closure is explained as follows by the former authors:

... traits have functions relative to what its proponents call the *organizational closure* of a system, which is a causal loop that occurs when the parts of a far-from-equilibrium system contribute to its self-maintenance, and the system, in turn, maintains those parts. (Dussault & Bouchard, 2017, p. 1133)

Lean (2021) also describes organizational closure without considering the concept of constraint in any detail but rather just mentioning it once in the entire explanation of the organizational theory and that as part of a quote from Mossio et al. (2009). In this manner, closure of processes and closure of constraints are not properly differentiated. This differentiation is, however, a key aspect of the organizational theory of biological functions.

Since these authors do not properly consider the concept of constraint in their arguments, they neglect aspects showing how the organizational theory is less restrictive than it might seem at first sight. Lean (2021), for instance, argues for the rarity of organizational functions based on the difficulty of satisfying the requisite of causal closure in ecological systems since they are rarely, if ever, closed systems. But for properly understanding the organizational theory, it is important to consider that a closure of constraints does not correspond to any set of causal relationships but to a rather specific state of affairs. There is indeed a clear criterion postulated in the organizational theory for constraints to be regarded as part of a closed organization, which is enunciated by Moreno and Mossio (2015, p. 20) as follows:
In formal terms, a set of constraints **C** realizes closure if, for each constraint $C_i$ belonging to **C**:

1. $C_i$ depends directly on at least one other constraint of **C** ($C_i$ is dependent).

2. There is at least one other constraint $C_j$ belonging to **C** which depends on $C_i$ ($C_i$ is enabling).

If one takes into account the meaning of closure, not in isolation but within the overall framework of the theory, it will not be difficult to conclude that a closed organization of constraints requires that just some but not all constraints relevant to the system's self-maintenance be included within its organizational closure. Precisely, only constraints that are both enabling and dependent are considered part of the organizational closure. If this is lost from sight, the demand that the system be organizationally closed will seem more restrictive than it is in fact.

As Bich (2019) argues, biological systems should be capable of generating within themselves *some* of the internal constraints that control their dynamics, such that they remain in far from equilibrium conditions by harnessing the thermodynamic flow. Closure is a regime of mutually dependent constraints that determines a subset of its own conditions of existence, not all of them. In these terms, we can tackle the problem posed by the expansion of the functional boundaries of an organizationally closed system that recruits external boundary conditions or extends its network of control interactions. In short, we can do so by considering how this problem follows, in fact, from an incorrect interpretation of the notion of closure of constraints, which conflates the self-specification of the functional boundaries of a system with functional self-sufficiency. Based on how the functional components of a biological organization are wired together to collectively achieve self-maintenance, one can propose criteria to characterize the *degree of functional integration* and, accordingly, the *degree of internal cohesion* of a system, i.e., the different ways and extents in which constraints are mutually dependent and realize closure (Bich, 2016, 2019). When we take into account different degrees of functional integration in organizationally closed systems, we can realize that there is a variety of ecological systems that can be described as such.

A minimal theoretical example of functional integration by means of cross-control (Bich, 2019) is found in Kauffmann's (2000) autocatalytic sets, in which a catalyst **A** is produced thanks to the action of another catalyst **B** that controls kinetically its synthesis, while **A** itself contributes, in turn, to **B**'s existence by controlling directly its production or some intermediate steps in the production of **B**. An autocatalytic set realizes a basic form of closure, given that each constraint depends for its production and maintenance on the direct action of (at least) another constraint, and together the components of the autocatalytic set (in the example, **A** and **B**) collectively realize self-production and self-maintenance. Autocatalytic sets exhibit closure because each constraint plays a function in collective self-production and self-maintenance, and we can consider the same to be true of ecological systems. Indeed, we find in the literature theoretical treatments of ecological systems as autocatalytic sets (see, e.g., Cazzolla Gatti et al., 2017, 2018). The issues related to