While organisms have for a very long time been a paradigm of what an individual in general is—a tree, a sheep, etc.—biology has displayed more and more examples of entities about which it is not obvious to decide whether they are indeed individuals: ant colonies or Portuguese men-of-war, which are made of an aggregation of multicellular organisms, and so on. For the past decade or two, individuals have been under the focus of theoretical biology and philosophy of biology (Wilson 1999, 2004; Folse and Roughgarden 2010; Bouchard and Huneman 2013). New advances in our understanding of the ways individuals such as multicellular organisms, cells, or chromosomes can and did evolve (Buss 1987; Maynard Smith and Szathmáry 1995; Michod 1999; Calcott and Sterelny 2011) have triggered a novel conceptualization of what “biological individual” means. At the same time, elaborated theories of mutualism and symbioses uncovered the extent to which all individuals, including cells, metazoans, etc., are made of symbiotic communities (Margulis 1970; Dupré and O’Malley 2009; Bouchard 2009, 2010). Actually, it is recognized that even “simple” metazoans such as mammals include a fascinating amount of commensal bacteria, making themselves therefore into collectives comparable to ecosystems (Huss 2014, this issue).

To this extent, some research programs have been elaborated that tend to handle organismal features and processes from an ecological viewpoint: the microbiome, in the human gut can be understood in this way (Costello et al. 2012). There has also for a long time been an evolutionary approach of host-parasite interactions that have consequences for our understanding of health and infectious disease (e.g., van Baalen 1998; Adiba et al. 2010). At another level there have also been projects to understand the dynamics of cancer and ontogenesis as an ecological process (Merlo et al. 2006), and more generally the cell itself has been understood in an ecological way (Scadden 2006). Therefore, theoretical ecology seems to be able to deal both with organisms and traditional ecosystems. Yet, if organisms can appear as ecosystems, this also suggests that in turn ecosystems themselves might be seen as organisms, or at least exhibit a kind of individuality that reminds us of the individuality of organisms.

Whatever the nature of this affinity between organisms and ecosystems, it means that they share the same kind of individuality. Thus, given that each of the individuals I mentioned is made up of elements—organisms are made up of cells and then many symbionts; cells are made up of genes and many other elements in the nucleus and cytoplasm, etc.; and, at the other pole of a biological hierarchy, ecological communities are made of populations of various biological species—the very general question is: what makes some of these assemblies genuine individuals, but not others? It is actually a version of an ancient metaphysical question, the same one that Leibniz was asking when he investigated what makes an animal one and the same thing, whereas a pile of stone is a mere multiplicity (Leibniz 1686). But here it has to be asked in the context of the scientific ecological research.

The present article aims at answering this question, by arguing that individuality can be seen as a very general conceptual scheme, through which our knowledge of interactions within a theoretical domain allows us to partition the assemblies into “individuals” and “nonindividuals.” The heart of the issue, in this perspective, is about discriminating various ways of coupling or uncoupling sets of interactions in a larger set of entities—robust uncouplings corresponding to possible individuals as sets of interacting parts.

After having reviewed a classical solution that relies on evolutionary theory, and indicated its failures regarding the question of the individuality of ecosystems and communities, I will describe such a scheme for determining individuals. In a follow-up paper (Huneman 2014b, this issue) I will focus on some specificities of what makes an ecosystem “one” ecosystem, and finally draw some conclusions about the individuality of organisms and of ecosystems.

Individuals in Ecology and in Biology

Regarding individuality, biology and especially evolutionary biology hold a dual position.

  • On the one hand, when philosophers take examples of individuals, they often turn to biological individuals, such as large metazoans: horses, elephants, triceratops, etc. Those seem to display the internal coherence, self-containment, persistence in time, and cohesion that is characteristic of our intuitive notion of individuality: while pile of stones and horses are both made of parts, horses are individuals and pile of stones are not. Metazoan organisms seem to be paradigmatic individuals.

  • On the other hand, biology has been constantly displaying examples of “weird” individuals, namely, entities that are not easily classified as individuals or as set of individuals. Ant colonies are sets of ants but display division of labor and functional cohesion in the same way as metazoan organisms do; slime molds seem to behave exactly as organisms when they are constrained by stress but they are made up of individual entities that most of the time live by themselves (Bonner 2009).

Metaphysicians such as Wilson (1999) tried to account for biological individuality in a way that accommodates these strange, context-dependent features of individuality, so that metazoan organisms cease to be the equivalent of individuality. However, even simple, ancient biological examples such as the metamorphosis of butterflies—in which an uncontroversial biological individual displays a lack of temporal consistency—call for a complex conception of biological individuality. And even Leibniz stressed the fact that concepts of individuality encompass several criteria, so that between the pile of stones and the horse there are many intermediaries that are more individuals than the former (they display more features of individuality) but less individuals than the latter: a pond full of fish, a herd, an army, a watch, and so on (see Huneman (2014a) for an analysis).

It is in this context that the very concept of “superorganism” resurfaced, with a focus on collectives such as hymenopteran colonies, termite colonies, etc. (Wilson and Sober 1989; Sober and Wilson 1998; Turner 2000; Gardner and Grafen 2009; Strassmann and Queller 2010). Here, it even appeared that the term “organism” is not as simple as one would have thought on the basis of the consideration of metazoan organisms, and that it may be better to talk about a continuum of organismality, things beings more or less an organism rather than being an organism or not (Reeve and Hölldobler 2007; Queller and Strassmann 2009). Hence an ant colony is less an organism than a horse, but much more an organism than a pack of wolves. A consequence is that “superorganism” becomes a term of no use. Queller and Strassmann (2009) argued that the two criteria to situate collectives in a space of organismality are the degree of cooperation and the decrease of conflict. Going one step further Haber (2013) advocates avoiding the very term “organism” since what is at stake is only the various degrees of individuality. On the other hand, Gardner and Grafen (2009) argue that it is only via either suppression of conflict or clonality that a set of individuals can become an organism, therefore implying that there are many fewer organisms than it seems within the “organismality continuum” approach.

In any case, evolutionary biology seems capable of handling the concepts of organisms and of individuality. Yet the very question of individuality also affects ecology, and mainly as a question about the nature of ecological communities. Whereas many ecologists think that the set of different species that make up a community are indeed genuine individuals, likely to interact with other individuals in a metacommunity, others rather think that communities and, to a wider extent, ecosystems (i.e., communities considered within their abiotic environment), are mainly entities that the scientist somehow defines and carves according to her explanatory project. As Sterelny states it, “indexical communities” are opposed to “ontological communities” (Sterelny 2006): the indexical community corresponding to an ecologist who specializes in the polar bear would be the set of species with which the polar bear interacts—the species indexed to the polar bear, so to speak. It is indexical because, of course, this set has its existence only with regard to this ecologist’s research program, and not in nature. By contrast, an “ontological” community is a cohesive and functional whole of species that is naturally bounded, so that whether a species belongs to it or not does not depend upon an ecologist’s interests.

Actually, this is a controversy that traces back to the origins of community ecology. Forbes (1887) already envisaged a lake as a “microcosm.” In a more elaborated way Clements (1916) argued that communities were so much individualized that they behave like organisms, displaying the same kind of internal cohesion, division of labor, and persistence in time as organisms do—he coined the word “superorganism.” He was soon contradicted by Gleason (1926) who argued that the grouping of species is somehow arbitrary, and only individual organisms of different species are real; boundaries between communities are arbitrary and blurred, unlike boundaries between organisms. The only rules of assembly and succession that govern communities are about the individual organisms of given species that occur in it, but there is nothing special about the community itself that would entail some laws or rules for the assembly. Whittaker’s studies about the variations of species populations along some gradients (temperature, moisture, etc.) backed up this claim: it is hard to find overlapping constant clusters of individual species across those gradients. In the end, in ecology since the 1960s the call for superorganisms has been quite discredited. Most recently, Ricklefs (2008) argued against the concept of “local, interacting assemblage of species” as having prevented progress of the understanding of the dynamics of species at a regional scale, which implies that “community” is not a meaningful ontological level in nature. Yet the very notion of “superorganism” indeed had resurfaced, in evolutionary biology (Sober and Wilson 1998).

One of the main features of individuality, in biology as well as in ecology, is that it can be nested. As Leibniz remarked: “Each portion of matter may be conceived as like a garden full of plants and like a pond full of fishes. But each branch of every plant, each member of every animal, each drop of its liquid parts is also some such garden or pond.” (Monadology, §67). In ecology, a microbiome as ecosystem living in the gut of a primate is also part of the ecosystem that is made of this primate, his conspecifics, the trees under which he is living and a few other trees, which in turn is part of a large ecosystem, for example the Barro Colorado forest in Panama. In biology, this nestedness comes as biological hierarchies, that Eldredge (1985) defined in two ways: hierarchy of interactors (chromosomes, cells, organisms, colonies, demes) and of replicators (genes, organisms, species, clades). Therefore any account of biological individuals has to make sense of the possibility of nestedness, i.e., of making up individuals on the basis of other individuals. In evolutionary biology, this requirement means a call for an explanation of how individuals evolve from the grouping of extant individuals. The research program about “evolutionary transitions in individuality” addresses exactly such a question, but it is also an issue faced by the evolutionary explanations of ordinary symbioses, to the extent that symbiosis results sometimes in new individuals made of hosts and symbionts (Bouchard and Huneman 2013).

However, any understanding of the evolution of individuality seems to require a concept of what an individual prima facie is. A very powerful concept of individuality was indeed elaborated in the 1980s by David Hull and widely accepted then. Hull contrasts it with intuitive apprehensions of individuality, and pretheoretic or metaphysical concepts of individuality. For him, the concept of individuality in a given ontological domain has to be provided by our best theory of this domain. And in this sense, given that evolutionary biology is the overarching theory of biology—as is well known, “nothing in biology makes sense except in the light of evolution”—this concept should be given by evolutionary biology. According to Hull (1980) indeed, notwithstanding all the subtleties about what “organism” means, or the variety of individuality biology can show, or the sophistications of features of individuality in many sciences, there is a theoretical concept of individuality that is provided by evolutionary biology: to be an individual is to be something upon which natural selection acts, i.e., an individual is a unit of selection. This concept of individual is theory-based. It has been challenged by other theory-based views of individuals, such as views based on physiology—be they developmental views (e.g., Nuno de la Rosa 2010), or immunology-centered views (Pradeu 2010). However, the evolutionary perspective is at least the most encompassing regarding biology (in the sense that evolutionary principles apply more univocally to any living entity; people still fight about whether unicellulars display development or immune systems).

It allows one to discriminate the individuals of (evolutionary) biology. Genes and organisms can both be individuals, provided that they are units of selection. There may be, of course, controversies about the application of this concept—related to controversies over the units of selection—but this does not contradict the fact that we have a concept to apply to the actual systems under study in order to pick out the genuine individuals. Yet the fact that selection may act at many levels simultaneously may raise an issue for this view. However, interestingly, if one adopts Hull’s view of natural selection as the differential replication of replicators according to the interactions of interactors (Hull 1980), it enables one to make sense of the nestedness of individuals. Replicators and interactors can exist at any level: e.g., meiotic drive is a case where interactor and replicator are genes; group selection sensu Wilson and Sober and Wilson (1998) is a case where replicators may be genes but interactors are groups, etc. As a consequence one can easily find nested individuals. As Bouchard (2010) also shows, this view of individuality accommodates cases where genuine individuals are multispecies individuals, as in the case of obligated symbiosis (the Vibrio Fischeri-squid symbiosis being the most famous example (Nyholm and McFall-Ngai 2004)). Acknowledging multilevel selection, as it is involved in the evolutionary transitions research programs, clearly leads to accounting for nested individuals.

But what does this mean for ecology, and the individuality of ecosystems and organisms? Obviously, in this approach an ecosystem or a community is an individual if it is a unit of selection; yet, this status is actually very controversial. Orthodox evolutionary biology would not allow ecosystem selection, to the extent that ecosystems include abiotic entities that do not respond to selection. As to community selection, this is quite controversial too. The most liberal biologists in general accept high-level selection at the level of species (Gould and Lloyd 1999) or clades (Williams 1992); but communities are by definition made up by many species. While the fitness of species can be understood as the number of daughter species or the speciation rate (Damuth and Heisler 1988), and analogous measures even exist with clade selection, it is not easy to see what the fitness of communities would be.

Van Valen (1991); Goodnight (2011) and Goodnight and Stevens (1997) considered community selection; however, another and maybe the most crucial problem is that this is rather a logical possibility, not yet documented. Williams (1966) claimed that it may be possible that there is in principle selection at levels higher than the gene or the organism, but this would in any case in nature be swamped by low-level selection. Others had the same argument with species selection. Concerning community selection, one could argue in the same way—the lack of evidence being so interpreted. Granted, Swenson et al. (2000) as well as Williams and Lenton (2007) have shown some ecosystem selection—however it was artificial selection of mud, not in the field. Even if one accepts that their results indeed show selection at the level of ecosystems and not only the ecosystem-level effect of selection of organisms or even species, there is still no answer to the Williams-style objection.

Therefore, in any case, applying the evolutionary concept of individual to solve the question of the individuality of species or ecosystems is a difficult task, since it seems that at least for the moment none of them passes the test. Therefore, we are left with the task of finding a meaning under which it is plausible to say that some communities or ecosystems are individuals. The next section turns to this task.

The Weak Concept of Individuality as Quasi-Independence

Assuming that no ecosystem or community is an individual sensu the evolutionary concept of individual, there are reasons to think that another concept should exist, to discriminate between communities or ecosystems as individuals, and “indexical communities” or so. A reason for that is that we can not exactly pick out communities in any arbitrary way. Just picking some species, forming a set, and calling it a community is less a community than what ecologists deal with under this name; and the same with ecosystems. Therefore it seems that some ecosystems and communities may be more individuals than just arbitrary sets of species. I am now looking for a concept to capture this intuition more rigorously.

The very general picture is that ecological interactions in a given space or area occur between a huge number of entities: many species, many organisms, nutrients, etc. Everything is actually likely to interact with everything. Community ecology and functional ecology provide descriptions and explanations of the processes defined by such interactions and the patterns they yield. A community, or an ecosystem, seems to be a set of all these things that interact; yet, it is not any arbitrary set. The idea I will use to account for this nonarbitrariness, or in other words for our discriminating the genuine ecosystems or communities, derives from what Herbert Simon (1980) called “quasi-independence.”

Given a system—e.g., a computer, a brain, etc.—a quasi-independent subsystem is a subsystem within which interactions between elements in this subsystem are stronger than interactions between external elements. Quasi-independent systems are used to define “modularity,” especially in cognitive and computer science. “Stronger” and “external” are quite vague, but I claim that there can be a more precise concept of individuality derived from these general features. With a firmer grasp on such features, one can account for the way we draw the boundaries of the system on the basis of our knowledge of interactions (e.g., Cadenasso et al. 2003), and this is exactly what we need in order to forge a concept of individuality that could be applied to ecosystems or communities.

Clements (1916) argued that communities were “tightly integrated groups of species”; yet, his superorganism-style view of communities seems quite outdated. Later on Hutchinson (1957) said something weaker, namely: a community is “a group of species that at least weakly interact with one another and not others at a time and through time.” The aim of my weak concept of individuality is to make sense of Hutchison’s understanding of individual ecosystems. Hence, besides a strong concept of individual, provided by the evolutionary criterion, I will advocate a weaker concept of individual, based on the knowledge of interactions in a large set of entities of various nature, and which entitles us to pick out individual ecosystems as well as to make a difference between indexical and ecological communities. I will start by giving the formal definition of the concept, below. Then I will characterize its relation to the various scientific theories, stressing a distinction between the formal concept of individuals and its implementation in a specific theory (in the Material Concept of Individuality section, below). The follow-up paper (Huneman 2014b, this volume) will consider the articulation between the strong and the weak concept, some specific questions about ecological individuals that arise in the framework of the application of the weak concept, and then the differences between ecosystems and organisms from the viewpoint of the weak concept.

The Formal Weak Concept of Individuality

Let’s elaborate the idea that among a set of myriad entities’ interactions of which we have a knowledge embedded in a model, some subsets are interacting more cohesively than others. I will consider two ways of formalizing such an idea, indicating the strengths and the weaknesses of each one. In the end, both concepts may have the same extension but they somehow function differently; and it is easier to start with the first, simpler, even though the second one in the end allows more complexities of individuality to be captured. The first version is a static, counting one, considering each interaction as either present or absent, counting links and building equivalence classes on the basis of this counting. The second is a more probabilistic view, that starts by considering a random item and asks what are the probabilities of interacting with others.

Approach 1

The static concept is the following, formalizing the idea that for each possible subset I of a set of entities X we compare the internal interactions in I and the interactions between elements of I and of its complementary subset in X:

  1. (1)

    Let’s consider a set X;

    I is a subset, belonging to the set of subsets of X (written \({\fancyscript {P}}\)(X))

    I′ is the complementary subset of I; i belongs to I

    Ci,j is the presence of a link between I and j (note that Ci,j in {0,1} and that Ci,j = Cj,i)

    Let’s write : ni = \({\sum}\) i in ICi,j/card I

    (this is the proportion of interactions between i and j, for j varying in I) and n′i = \({\sum}\) k in I′ Ci,k/card I′

    (this is the proportion of interactions between i and k, for k varying in I′).

Then amongst the possible subsets I the individuals are the Is such that

$$Individuals = \{ I\, in \,{\fancyscript{P}} (X) / for\, all\, i, n_{i} \gg n_{i}^{\prime}.$$

There is one first obvious problem here: X is discrete, whereas reality is often continuous. However, for many of our scientific purposes and especially ecology, we can consider discrete sets—for example, we count species, individuals, units of soil, etc.; in neurosciences, we consider synapses, neurons, that are countable, or we cut the brain into small equal 3-D pixels named “voxels” (e.g., Bullmore and Sporns 2009).

A second problem is that by applying such a scheme by-products of the subsystems considered will be counted as the individual—for example, the external secretions of an organism may have more frequent interactions with the organism than with some other things, but actually they are not part of it. This would be taken care of in the second view. For now, I just mention that “interaction” is a primitive view of the theory; it has a very abstract meaning, namely “A interacts with B if some variables in the set of variables that describe A are modified by a change of variables in the set of variables characterizing B.” In some contexts, one may add requisites for interactions relevant to the theory: often it will be a clause of reciprocal interactions; it can be a request for direct interactions—or, more often, a distinction between direct and indirect interactions will be taken into account while weighting the strength of interactions (a perspective taken in the second approach below).

A third problem is that some entities may interact through one or several intermediaries, as in many networks, which would lead to problems of double-counting (also handled in the next approach).

But the main problem is that estimating the frequency of interactions is not enough. Obviously, some interactions are not so frequent but very strong: if a fox eats a rabbit, it is a less frequent interaction than the rabbit’s feces altering the soil, but it might be as relevant for the ecosystem. So the frequency should be weighted by the strength of the interaction, and we need some other measure. The proper variable (instead of ni) involved in the comparative estimation (1) would be a mix of ni and the strengths of the interactions. We could do this by switching from the current view, where each interaction is a link, hence Ci,j scores 0 or 1, to a view where Ci,j belongs to [0,1], its value being precisely the strength of the interaction. Estimating strength of interactions is attempted in Ulanowicz (2002), which also provides clues to define individuals. The move here is the same as when ecologists move from graphs of interactions to oriented graphs and then weighted graphs (see Fig. 1). This integration of interaction weight is now taken up in the second approach, which is a more probabilistic view that may also address the third problem listed above.

Fig. 1
figure 1

a Graph; b oriented graph; c weighted graph. From Ulanowicz (2011)

Full size image

Approach 2

The probabilistic view elaborates the basic intuition that if you are part of an individual, the chances that something that is strongly interacting with you is also part of this same individual are higher than the chances that it is something external. This is intuitively valid for metazoan organisms: consider a cell in such an organism—the chances that some cell in strong interactions with this cell is part of this organism are higher than chances that it is a cell from another organism. Then it may be valid for ecological communities, in the sense that some could display this property and therefore be characterized as genuine individuals. Having such a property would thereby imply the following: considering a set S of individual organisms, if A is an organism in S, then “S is a community” means that the chances of A to have one of its strong ecological interactions (i.e., predation, mutualism, etc.) with an individual of a species within S are higher than the chances that it is in interaction with an individual of an organism of a species outside S.

The general definition of an individual can therefore be written as:

  1. (2)

    Consider S a set of entities; i a given entity in S.

    xi,j is a link between i and j (namely, any kind of interaction; j is in S)

    H, n are constant values defined in advance (n between 0 and 1; the variable h is the value of the strength of interaction, n is a significance threshold)

    P(xi,j, h): probability that a link xi,j, has strength h

    We define the set of i-centred strong interactions: Hi = {xi,j/P(xi,j, H) > n}

    We define the set of i-strongly-interacting entities: Ji = {j/xi,j ∈ Hi}

    If S is an individual system then for all i in S, Ji is included in S.

One problem with this definition is that n is an arbitrary fixed value, but it is very likely that some value between 0.7 and 0.9—or in general the value of significance in a traditional statistics framework, like 0.95—in many cases will yield a result close to our intuitive ascriptions of individuality. The other problem is the arbitrary value of H, i.e., the strength of “strong” interactions; however it is reasonable to choose a quite high value for H, defined for example by the threshold defining the first quintile of interactions when all interaction strengths are measured. Granted, such an approach deals in the same way with interactions that can be of very different types; however, the only way to elaborate a concept of individuality on the basis of interactions that can be valid for different ontological and theorical domains, within each of which there are distinct types of interactions, is to assume the possibility that there is a way to define a measure according to which all relevant types of interactions can be combined and compared.

In general, several parameters have to be estimated within the computation of h, the strength of a given interaction. For instance, if we take as an example a set of models, we consider that all the entities are in a network of entities as in the case of networks in community ecology (Montoya and Solé 2002; Dunne 2006; Montoya et al. 2006), and can be represented in a graph (each interaction being a link), then the main parameters would be:

  • The number of various pathways between entities (the more pathways, the stronger the interactions);

  • The number of steps between i and j (the less steps, the stronger the interaction);

  • The number of supplementary necessary conditions needed (if the interaction is conditional upon some other interactions, for example when a predator switches prey in case of scarcity of the main prey).

Once the set of entities is represented, there should be ways, along those lines, to define the strength of interactions and compute it for each of them. Yet it is not obvious that there could be a general method for computing this strength for all cases of putative individuals. However, restricting the problem to communities and ecosystems ecology—where network approach are often available (Ulanowicz 2002, 2011)—the framework here roughly sketched seems plausible.

Now, the fact that we take n as a constant, plausibly reflecting high chances of strong interaction, can be alleviated by another option: considering the average value of P(xi,j, H), written \({\fancyscript {P}}\). Then the sets Ji so defined will be sets where the probability of interactions between entities is clearly higher than average, and therefore could be considered as individuals. Then the clause about defining the sets Hi can be rewritten as:

$$ {\text{H}}_{\text{i}} = \, \{ {\text{x}}_{{{\text{i}},{\text{j}}}}/{\text{P}}\left( {{\text{x}}_{{{\text{i}},{\text{j}}}} ,{\text{ H}}} \right) > {\fancyscript {P}}\} . $$

The interest of such a method consists in having a statistical threshold of significance defined by the system itself. Applying this scheme onto our models of interactions allows one to discriminate subsystems that are indeed more cohesive, self-contained, and distinguished than the rest of the set of entities; it is reasonable to say that these subsystems or subsets are individuated through their interaction patterns. The scheme for identifying individuals focuses on mean values of interaction strength; however, given that often we have statistical descriptions of interactions, and probabilistic laws of interactions, an even more general scheme would take into account not only the mean value, but the variance of the interaction strengths (and possibly even statistical moments of higher order). This is left for future work—for the moment it seems that the picture of “weak individuality” given here is enough to deal with some of the questions concerning ecology and biology I addressed in the beginning.

Some Consequences

This formal notion of individuality bears several consequences.

First, the problem of by-products as counted within an individual seems answered. Actually, suppose an entity i that is a by-product of a putative individual S, such as the smoke emitted by a cigarette or the wastes of an earthworm. Granted, these entities have strong interactions with the focal individual; but still, the probability that the link—interaction (i,j) is very high seems not necessary to be higher when j is something that is already part of the cigarette or the earthworm, than when j is a part of something else around: smoke is dispersed by the wind and is possibly breathed, wastes secreted by earthworms are nutrients for many other organisms, etc. Moreover, if directedness enters into characterizing interaction, which occurs in directed graphs, then one may find here an argument against including these wastes in the focal individual.

A second important consequence is that when n and H are given (or when only H is given, in the variant approach that focuses on the average \({\fancyscript {P}}\)) a set of individuals is univocally given. It means in turn that individuals are relative to the choice of H. The higher that H is, the fewer individuals one will find on the basis of the models of interactions occurring in the reality under focus. This could be seen as a radical flaw of the approach, since it seems that no objective list of individuals can be eventually provided; however I see it rather as a strength, meaning that what counts as individuals depends upon a theoretical decision about what counts as high interaction threshold: it is a consequence of the weak concept being a theory-based concept (as will be developed below).

A specific difficulty for this approach is actually the definition of the variable h that appears in our formula. As indicated, it is made up of several parameters that only exist within a theory, and whose combinations are also definable and tractable within this theory. In the examples I gave, h is not something that could be easily reduced to the addition of several parameters, since actually these parameters do not have a common unit of measure; yet there should be a way to combine them in a significant way. But this is not as much a real problem as the main consequence of the fact that this is a purely formal concept of individuals in general, and that the complete concepts to discriminate between individuals and nonindividuals in a specific domain—what I call below “material concepts”—are intrinsic to a theory. h actually functions a bit like indices do, in many theories. I mean that h is supposed to combine many specific features of interactions as they are determined within a specific theory into one indicator of interaction strength, in the same way as community ecology’s diversity indices (e.g., Simpson diversity, or Shannon diversity, or Hill’s index (Gosselin 2006)) are indices of the diversity of ecosystems that combine, each in a particular way, several measures such as species richness, species evenness, absolute abundances, etc. Hence, for instance, theories whose models include networks will involve considerations about number of links, redundancies, connectance, etc., within their h indices (e.g., Guimera et al. 2007; Fletcher et al. 2013); theories with thermodynamic models will include considerations about fluxes of matter within the constitution of h, and so on. In some theories it may be harder to define a specific indicator whose evolution would track individuality, yet we can interpret it as a fact that “individuality” may not be a relevant concept for those theories (this may be the case for quantum physics; see French 1989).

Having multiple options to define h in a satisfactory way would not be a dramatic objection against this approach—it only means that some theories may yield several kinds of individuality ascriptions. One of the aspects of this concept being a weak concept is that it involves some pluralism, which should not be confused with pure arbitrariness. However, another kind of pluralism characterizes such a concept, a pluralism that actually accounts for a feature of the usual notion of individuality, namely, allowing nested individuals (see also below on pluralism). What individuals are indeed relies on the significance threshold n and the “high interaction” threshold H. Increasing values of H define individuals that are nested: with a high H, fewer individuals will exist than with a lower H, but the interactions characterizing the former will ipso facto enter into the specification of parts of individuals according to the latter, therefore we will have nested individuals.

Other Difficulties

Another difficulty for this approach consists in the context-dependence regarding measuring instruments. In many cases interactions are indeed reported through our measure of interaction strengths (think of microarrays in molecular genetics, of particle detectors in fundamental physics, of devices that track the life history of animals, etc.). These interactions with measuring devices may be quite strong. Therefore, given that such devices should not be included in the definition, some clauses have to be added in order to discriminate against this possibility. Actually, averaging the strength of interactions across several (experimental) contexts would lead to averaging out the influence of measuring devices. Hence, at least in principle the definition of individuals in terms of the knowledge of interactions allows for decoupling the signature of measuring devices’ influence and the signature of objective individuals by using averaging protocols.

A different difficulty obviously concerns time. Actually, it is trivial to say that biological and ecological objects are in constant flow, being always crossed by various fluxes, parts of systems being always replaced by other parts that are in some sense their equivalents, etc. Hence, at least in the biological and ecological domains, a hallmark of individuality is the persistence through time of identical features. This is of course one of the major concerns for the philosophical literature about personal identity (Parfit 1984; Ricoeur 1992). And more generally being likely to be reidentified as “the same” in time is a feature definitional of individuals in Strawson’s classical analytic philosophy work (Strawson 1959; see also Wiggins 2001). Yet it seems that in the sections above I gave a wholly synchronic definition of individuality, leaving aside all this temporal aspect, which would just avoid the main theoretical problems of individuality.

However, the view suggested here has resources to deal with diachronic individuality—for the sake of simplicity it just began with synchronic individuals. But “synchronic” does not mean instantaneous. The links defined by the interaction involve time—namely, the time proper to the relevant processes, e.g., in ecology predation, competition, etc., take time. Therefore, the opposition between diachronic and synchronic in this context is not an opposition between instantaneous and temporally extended, since the above scheme of individuality concerns a set of entities that indeed extends in time. But some interactions are rapid, others are slow, and the entities are indeed changing through time at different rhythms, as well as the interactions themselves. The actual difficulty, here, is that the set of relations and interactions used to apply the scheme (2) above is changing across time: at one timescale, it can be assumed as approximately stable, at another timescale, it will be variable. Hence what’s important here are the timescales: not all entities and interactions have the same timescales. A question therefore arises about reidentifying within a larger timescale an individual determined at a small timescale.

Let’s divide time in “time-slices,” in the sense of a duration in time scale a that can be seen as instant in time scale b (think of the timescale of a cell compared to the timescale of the physiology of an elephant). The formal concept of individual provides criteria to discriminate individuals within a time-slice. We need a further criterion to capture the persistence of these individuals through successive time-slices.

Given a set of interacting entities at the time-slice t, and S an individual (characterized according to (2)), that includes a part x, consider the next time-slice t′. The question of diachronic individuality (as individuality that spans several time-slices) amounts to a criterion to reidentify S at t′. Suppose x is part of S and persists across timescale b (t and t′ are part of the same time-slice in b). Actually, there are individuals at t′ that comprise x′, which was x at t. Hence there is some probability that an individual S′ of which x′ is a part, was S at t′, since x has a probability to persist into the same individual across timescale b. This probability gets higher as other parts y′ of S′ can be reidentified with parts y of S at t.

This means intuitively that there is an overlap between S and S′, because some parts x of S can be reidentified across time in the timescale b, and these parts are indeed making up a significant component of S′. “Significant” should of course receive a more formal definition, and this should be done in term of relevance and strength of interactions within S′. Such definition can indeed be made along the same lines as definition (2). Moreover, the reidentification across time, in the theories pertaining to evolutionary biology, will rely on mechanisms of inheritance.

Now, if x does not exist at t′, then one can consider other parts y of the same individual S with which x was closely interacting, and reiterate the same protocol for y′, defined as a reidentification of y. Along these lines there are ways to diachronically define individuals, assuming the plausible claim that there is a significant overlap between S at t and S′ at t′ (the overlap being defined by parts such as x, that exist at two different time-slices).Footnote 1

Up to this point we have the sketch of a formal concept of individuality, understood as the scheme through which our knowledge or models of interactions enable us to pick individuals in a set of many interactions, according to a criterion defined by the above equations. To apply this scheme in order to uncover genuine individuals, a theory is requested, one that provides us with a content for the variables in the scheme—especially h, which denotes generally the strength of interactions.

Material Concept of Individuality

The weak concept of individuality is blind in the absence of any well-corroborated theory, whose set of models allows one to define the variables in the definition scheme (2) above; it is therefore just a formal concept. When these theoretical components are plugged into the definition, it becomes a material concept likely to be used to pick up genuine individuals.

The theory should encompass a model for the interactions on the basis of which individuals are identified. The formal sketch here has to be variously instantiated by the theories proper to the ontological kind the purported individual belongs to (namely, instantiating h). Regarding ecosystems, community ecology or functional ecology could provide such a theory. The variable h is defined by integrating the strengths of interaction, their reliability, their regularity, etc. The interest of such a view of weak individuality is that proper instantiations of the scheme allows individualization criteria for ecological systems as well. It does not settle the question of whether communities are “local ecological communities” (sensu Sterelny), or ecosystems “individuals,” but it provides a concept enabling researchers to empirically ask the question.

As an example, let us consider research in ecological interaction networks (Dunne et al. 2002a, b; Pimm 2002; Montoya and Solé 2002). Whereas the network approach first focused on food webs (e.g., Andrewatha and Birsh 1984; Pimm 2002), allowing researchers to prove interesting results about the way connectance and diversity can yield stability properties (Huneman 2010 for a philosophical account of the explanatory regimes involved), recent theoretical approaches are trying to merge several kinds of networks, not only focusing on trophic interactions (Olff et al. 2009; Kéfi et al. 2012; etc.). Interactions can be distinguished along two axes: mutualistic versus antagonistic (e.g., fig-wasp mutualism versus predation), and high vesus low intimacy interactions (e.g., ant-plant versus fig-wasp mutualism). Considering the kinds of interactions therefore leads to interesting conclusions about which kind of network emerges by combining interactions of a same kind—and later, by combining kinds of interactions network. Especially,

from low to high intimacy, network architecture changes from highly connected and weakly modular to weakly connected and highly modular. Although empirical evidence remains scarce, these results strongly support the conclusion that high interaction intimacy leads to compartmentalization in both mutualistic and antagonistic network. (Fontaine et al. 2011, p. 1173).

It also appears that antagonistic interactions yield more modularity than mutualistic interactions. Modularity of course relates exactly to weak individuality, as is indicated when it is defined: “Modularity occurs when groups of species interact more within groups than among groups“ (p. 1173). Figure 2 displays the way these kinds of network differ in terms of the modularity they yield. According to scheme (2), it seems that in the cases of intimate antagonistic interactions dominating, we have more individuals, and in the cases of domination of mutualistic low-intimate interactions, we will have fewer individuals with more species included.

Fig. 2
figure 2

Kinds of interactions according to high versus low intimacy character, and mutualism versus antagonism character. A Examples of ecological interactions varying in their type (mutualistic versus antagonistic) and intimacy (high versus low) of interactions; (a) plant–pollinator, (b) acacia–ant, (c), ant–spider, (d) bird–parasite. B Schematic representation of nested (a) and (c) and modular (b) and (d) bipartite networks. (a) and (b) Matrix representation, where each row and column represents a species, and the intersections of rows and columns are black when the species interact. (c) and (d) Network representation, where each circle (or node) represents a species, which are connected by edges when the species interact. (From Fontaine et al. 2011)

Full size image

When it comes to organisms the individuating theory can be physiology, which models all kinds of interactions between cells, tissues, etc., at all levels; it can also be immunology, and competing theories allow one to distinguish what is part of an individual (Burnet 1959; Moulin 1991; Pradeu 2010). It is obviously in the context of such theory that a threshold for strong interactions can be seen.Footnote 2

Developmental theory also studies interactions at all levels, between genes, epigenes (Helantera and Uller 2010), proteins, transcripts, etc. It uses several theoretical schemes, including Gene Regulatory Network (e.g. Revilla et al. 2003), and it is very plausible that such an approach allows defining the proper variables to distinguish individuals. It may be that during the developmental process several transient individuals exist—some involving symbionts, some involving specific sets of cells, etc.—that give rise to what we call an organism. Mostly, this approach would bridge our view of usual individuals such as large metazoans and other forms of life where individuality ascriptions are not so easy to make, because in both cases there are specific transient individuals taking place and playing a role in the developmental process (for example, Dictyostelium cells or multi-organisms that make up a Portuguese man-of-war can both have the status of a transient individual within development that developmental theory could discriminate).

Turning to the diachronic perspective emphasized above, it appears then that the persistence of individuality in time can be understood on the basis of the various kinds of robustness the models may identify for each putative weak individual. In community ecology, stability, under various modes—constancy of species effectives, constancy of some properties like biomass (Tilman 1996), or conservation of the same species across time even if their abundances vary a lot (“persistence,” in a technical sense; Middleton and Nisbet 1997)—has been the focus of many models (e.g., McCann 2000). Many complex relations between species diversity, species richness or evenness, functional diversity, connectance, etc., in a community, have been shown to beget various kinds of stability (Ives and Carpenter 2007). The intuitive idea that diversity begets stability actually disappeared (May 1974) and has been replaced by modeling vast arrays of relations between the values of some variables instantiating a kind of diversity, and some types of stability (e.g., Tilman 1997; Doak et al. 1998; Frank and McNaughton 1991; Gravel et al. 2011). The whole point of these researches for us is the fact that specific ways of enduring in time are in fact proper to specific interaction patterns in an ecological setting, and when an ecological individual can be picked up using the scheme of weak individuality, a further question arises about the type of robustness it is capable of. Clearly, in many cases, inheritance—which provides a way to reidentify parts of individuals across time, as indicated in the preceding section—will play a major role in such robustness. This connects overall with the question of measuring persistence and acknowledging its status within evolutionary theory (Bouchard 2014, this issue).

The same models of interaction may allow answering this robustness question, which means that as soon as we can pick out weak individuals in ecology on the basis of a theory of ecological interactions, we can also investigate the persistence in time of these individuals, and eventually rank their persistence abilities, which can be seen as a further degree of individuality. However, this scale of degrees of persistent individuality may not be in principle conflated with the scale of nestedness that I linked to the graded values of the H threshold, and which defined a type of pluralism (discussed above). In principle, weaker individuals (in the scale of nestedness) can be higher on the scale of persistence, and reciprocally.