The Niche
Barry Smith
Department of Philosophy and Center for Cognitive Science, SUNY Buffalo, NY

Achille C. Varzi
Department of Philosophy, Columbia University, New York, NY(Published in Noûs 33:2 (1999), 214–238 . Polish trans. in Filozofia Nauki 8:3-4 (2000), 5–30.)

Abstract. The concept of niche (setting, context, habitat, environment) has been little studied by ontologists, in spite of its wide application in a variety of disciplines from evolutionary biology to economics. What follows is a first formal theory of this concept, a theory of
the relations between objects and their niches. The theory builds upon existing work on
mereology, topology, and the theory of spatial location as tools of formal ontology. It will
be illustrated above all by means of simple biological examples, but the concept of nicheshould be understood as being, like concepts such as part, boundary, and location, a structuralconcept that is applicable in principle to a wide range of different domains.

1.

Introduction

In his Axiomatic Method in Biology of 1937, J. H. Woodger seeks to apply thetools of mereology, or the formal theory of part and whole, to the field of biology. More precisely, Woodger seeks to give exact formal specifications of suchbiological notions as gamete, zygote, allele, and so on, and to utilize these formal
specifications in order to illustrate how, on his view, a scientific theory should
be constructed. Woodger’s project is significant because it represents a detailed
attempt to apply mereology in the extramathematical sphere.1 Unfortunately,
however, Woodger’s actual theory is of little interest. Its formalizations rest on
a version of genetic theory that is long since outdated; they involve a confusion
between formal notions (such as part) and material notions (such as cell), all of1Leśniewski’s original 1916 formulation of mereology grew out of an attempt to provide a solution to Russell’s paradox; Whitehead’s formulations in 1919 and 1929 were meant
as a basis for his theory of extensive abstraction; and Tarski’s 1929 application was to thefoundations of geometry.

1which are listed by Woodger among the ten ‘biological primitives’ of his theory; and the theory brings little in the way of conceptual clarification.
What follows is an attempt to take up once again the project of applying
mereology in the extramathematical sphere, but with strict adherence to the ideaof mereology as a formal theory. We see mereology, more precisely, as a formal
or domain-independent ontology along the lines sketched by Husserl in his
Logical Investigations2 —a theory of certain formal structures (namely: structures of part and whole) which are realized or exemplified across a wide rangeof material domains. The tools of formal ontology will be applied not, as inWoodger’s case, to mimic individual special sciences in specific stages of theirdevelopment. Rather, they will be applied to the task of clarifying the basic concepts shared by a range of disciplines, concepts so fundamental that they are notthemselves an object of study in those disciplines.
In order to make way for interesting applications along these lines, however, mereology must be supplemented by other concepts and principles offormal ontology— most notably by concepts and principles of topology and of
the theory of location.3 As mereology is formalized in terms of the single
primitive relation, part of, so mereotopology is obtained by adding a further
primitive relation, boundary for, and the theory of location by adding a third
relational primitive, located at. On this basis, it is possible to define a number ofstructural properties—such as connectedness, compactness, regularity, spatial
coincidence—which prove to be of central ontological importance. Consider, forexample, the task of characterizing individual integrity, the nature of artifacts, orthe distinction between identity and coincidence for events.4 Even domains traditionally outside the scope of ontological theorizing may benefit from suchextensions of mereology to topology and the theory of location. Consider thegeographer’s concern with such questions as the relationship between a nation(a city, a parcel of real estate) and a physical territory; the dependence of these
entities on their borders; or the representation of boundaries which —as in the2

See Husserl 1900/1901, ‘Prolegomena’, Chapter 11. This project of a formal ontology is present also in Leśniewski’s later work on mereology (see his 1927/1931).
3
On the importance of topology for formal ontology, see Smith 1993, 1997 and Varzi
1994. On the theory of location, see Perzanowski 1993 and Casati and Varzi 1996, 1997.
4
On individual integrity see, for instance, Cartwright 1975; on artifacts see Simonsand Dement 1996; on events see Hacker 1982.

2

case of Wyoming, or Utah—may lie skew to any qualitative differentiations or
spatial discontinuities in the underlying territory.5 Of course, not everything issettled once clear definitions of such concepts as territory or border are provided. But further questions cannot even be addressed without agreement as tothe meanings of such fundamental terms.
In order, now, to do justice to a range of further central formal-ontologicalproperties of the world we live in, we shall argue that, in addition to part,boundary, and location, a fourth primitive relation is needed, which we shallcharacterize via the concept of niche. This concept will be illustrated above allby means of simple ecological and biological examples. But it should be understood as being, like part, boundary, and location, a formal concept, one that is
applicable in principle to a wide range of different domains, from economics6 tothe theory of network security. 7 The concept of niche and its cognates are indeed already employed ubiquitously in many disciplines, from evolutionary biology to context-based semantics. Yet the underlying principles have thus far
been investigated not at all from the formal point of view. This is in part because
the mereotopological tools needed for such an investigation have been developed only recently. But it is in part also a consequence of the fact that formal
ontologists have tended to shun holistic structures, preferring to conceive reality
in terms of what can be simulated via (normally set-theoretic) constructions
from out of postulated atoms or Urelemente. The account presented here, incontrast, will be resolutely mereotopological: it will proceed from the idea that
there are structured wholes, including the medium of space, which come before
the parts that these wholes contain and that can be distinguished on various levels within them.
2.

The ecological background

Standard treatments of the relevant categories (of niche, habitat, ecotope,
biotope, microlandscape) in the ecological literature distinguish between theniche as the function or position of an organism or population within an eco5

For some applications of ontology to geography see Egenhofer and Mark 1995,
Smith 1995, Frank 1997, and Casati et al. 1998.
6
See e.g. Milne 1990.
7
See Cardelli and Gordon 1998.

3

logical community and the niche as the particular place or subdivision of an environment that an organism or population occupies.8
The functional conception, associated primarily with the work of Charles
Elton and other more traditional ecologists, is illustrated by phrases like: “Theniche of the Dipper or Water Ouzel (Cinclus sp.) is: fast-running mountainstreams with rapids and waterfalls, where they dive under the water to catch insects on the bottom.” We can think of the functional niche as a way of making
a living in an organic community:
When an ecologist says ‘there goes a badger’ he should include in his thoughts somedefinite idea of the animal’s place in the community to which it belongs, just as if he
had said ‘there goes the vicar’. (Elton 1927, pp. 63f.)

From Elton’s point of view the world of functional niches might be conceived
as a giant evolutionary hotel, some of whose rooms are occupied (by organisms
which have evolved to fill them), some of whose rooms are for a variety of reasons unoccupied but can become occupied in the future.
More recently however, primarily as a result of criticisms of the functional
conception by Richard Lewontin (see Lewontin 1979, Sterelny and Griffiths
1999), the environmental niche conception has come to enjoy a position of
dominance in the ecological literature. In the formulation advanced by G. E.
Hutchinson (1978, p. 159), the environmental niche is a volume in an abstract
space determined by a range of physical parameters pertaining to food, climate,predators, parasites, and so on.
Our theory in what follows will take as its starting point the environmental
niche conception as defined by Hutchinson. We shall aim, however, to be more
explicit than is customary in the ecological literature as concerns the ontologicalmarks of the entities with which we have to deal. Specifically, we shall focus ourattention on the concrete niche (token)—the habitat, location, or site—that is
actually occupied by a given organism or group of organisms on a given occasion. We shall hereby assume that each functional niche, to the extent that it isrealized at all, is realized in (or as) some concrete environmental niche or habitat. The niche or habitat occupied by a given organism is thus to be understood
not as a mere location, but rather as a location in space that is defined addition-

8

See Whittaker and Lewin (eds.) 1975.

4ally by a specific constellation of environmental variables such as degree ofslope, exposure to sunlight, soil fertility, foliage density, and so on.
How, then, are we to set about providing a theory of the niche as thus conceived? The ecological psychologist J. J. Gibson provides one important indication as to the nature of the task in hand:
According to classical physics, the universe consists of bodies in space. We are tempted
to assume, therefore, that we live in a physical world consisting of bodies in space andthat what we perceive consists of objects in space. But this is very dubious. The terrestrial environment is better described in terms of a medium, substances, and the surfaces that separate them. (Gibson 1979, p. 16)

Gibson seeks accordingly, in the section entitled “Surface and the EcologicalLaws of Surfaces,” ‘a theory of surface layout, a sort of applied geometry thatis appropriate for the study of perception and behavior’ (p. 33). This theory
would investigate concepts such as: ground, open environment, enclosure,detached object, attached object, hollow object, place, sheet, fissure, fiber,
threshold, and so on. It would take account not only of the systems of barriers,
doors, pathways, to which the behavior of human beings is specifically attuned,but also of the many different sorts of phenomena—for example, temperature
gradients and specific patterns of movement of air or water molecules—that
produce surface layouts with which the behavior of other organisms iscorrelated. Note that some of these concepts refer to what we might call‘positive’ features of the environment (to predators or prey, to dials and leversin the airline cockpit, to obstacles like rivers or mountains); but some of themrefer to what we might more properly think of as negative features: to gaps inspace, or in some medium (e.g., hollows for shelter, escape, protection; chasms,
corridors, conduits, thermoclines).9What Gibson attempted informally for humans, Jakob von Uexküll conceived in relation to the entire range of animal species. The ‘first principle’ of
Uexküll’s Umweltlehre (1934) reads as follows: all animals, from the simplest
to the most complex, are fitted into their unique worlds with equal completeness. A simple world corresponds to a simple animal, a well-articulated
world to a complex one (p. 10). Unfortunately, Gibson, von Uexküll, and their

9

The theory envisaged by Gibson would thus be closely related to the mereotopological ontology of holes presented in Casati and Varzi 1994.

5

followers were not in a position to make use of the tools made available by recent work in formal ontology in describing the environments or worlds in whichorganisms live. Some applications of such tools may be found in certain areasof artificial intelligence and the information sciences,10 but the legacy ofthe strong association between these disciplines and concern with human reasoning has meant that these tools have not been utilized for the formalontological investigation of non-human animal behavior and cognition. The
simulations of ecological structures of the type generated by Artificial Life programs11 are similarly of no use for our present purposes, since they yieldnothing in the way of conceptual explication.
More positive guidance is provided by the anthropological literature on thephenomenon of territoriality, a phenomenon that arises whenever there obtains atype of relation between an individual or group and an area of space which is ofsuch a sort that the former will seek to defend the latter against invasion byother conspecific individuals or groups.12 Anthropologists have shown that in
the case of both human and non-human animal species, a nested hierarchy oftypes of site must be distinguished around any given individual or group. The
force of territoriality then diminishes with increase in group size and spatialarea. In the first place there are territories in the narrow sense, the characteristically tiny areas in relation to which the occupying individual or group demands
exclusive use. This central area is then extended to comprehend various attachedregions, for example watering holes, where desirable resources are available ona routine basis. Finally we have the home range, that larger surrounding area
within which the group spends almost all of its time.13 This idea —that niches(territories, settings) form a nested hierarchy around an individual or group at its
center—will play a crucial role in the theory that follows.
3.

Places

One philosophical progenitor of our theory is the ontology of places sketched10

See e.g. Guarino (ed.) 1998.
Hraber et al. 1997.
12
Sack 1986. Compare also the related psychological phenomenon of ‘personal space’discussed in Hall 1966.
13
See Taylor 1988, pp. 21f.
11

6

by Aristotle in his Physics. What is it for a substance to be (or to fit snugly) ina location or context? Each substance has its place, Aristotle tells us, and theplace of a substance is ‘neither a part nor a state of it, but is separable from it.
For place is supposed to be something like a vessel’ (209b26f). Place cannot bea type of body, however, for if it were, then two bodies would be in the sameplace, and this Aristotle holds to be impossible. Place has size, therefore, but not
matter. It has shape or form—exactly the shape or form of the thing that is located in it—but it lacks divisible bulk.
What, then, is place?
We say that a thing is in the world, in the sense of in place, because it is in the air, andthe air is in the world; and when we say it is in the air, we do not mean it is in every
part of the air, but that it is in the air because of the surface of the air which surrounds it; for if all the air were its place, the place of a thing would not be equal to thething—which it is supposed to be. (Physics 211a24-28, italics added)

A place contains its body, in Aristotle’s view. The body relates to its place insomething like the way the liquid in an urn relates to the urn, or the hand relates
to the glove, or a precisely engineered Russian doll relates to the immediately
circumjacent Russian doll. A place exactly surrounds the thing, but the placedoes not depend specifically upon the thing, since the latter can be replaced byanother thing, which is then said to be in the same place. A place exactly surrounds the thing, but not in the sense in which the white of an egg exactly surrounds the yolk, for the two are here such as to form a single continuous whole.
A place exactly surrounds the thing, rather, where the thing is separate from but
yet in perfect contact with its surrounding body, the latter being therefore
marked by a certain sort of interior cavity or hole. The external boundary of thething then exactly coincides with the internal boundary of that which surrounds
it. Thus when a thing is in a surrounding body of air or water ‘it is primarily in
the inner surface of the surrounding body.’ The boundaries of the two—the
outer surface of the thing and the inner surface of its surrounding body—exactly coincide (211a30-33).
This, then, is place, on Aristotle’s view: the place of a substance is the inner boundary of the immediately surrounding or containing body. There are anumber of problematic consequences of Aristotle’s theory. For one thing, it is
topologically incoherent, at least on standard views of contact and separation,
since the boundaries of distinct things never coincide in the way required by7

Aristotle’s theory.14 Moreover, the theory implies that proper substantial partsof bodies (for example: your leg, my arm) are not, in fact, in place—they are
only potentially so: they will actually be in place only if they are transformed
into substances in their own right by separation. For these reasons, the accountof niche that we are after will deviate in crucial respects from Aristotle’s accountof the relation of place and body.
4.

Physical-behavioral units

Another important progenitor of the theory that follows is the account of settings elaborated in great detail by the ecological psychologist Roger Barker.
Think of a performance of a Wagner opera, a lecture on Hegel, a garage sale.
Wholes of these types, which Barker calls physical-behavioral units, are of importance not least because almost all human behavior occurs within one (or inwhat turns out to be a nested hierarchy of such wholes).
Consider, on the one hand, the recurrent settings that serve as the environments for the everyday activities of persons and groups of persons. Examples
are: my swimming pool, your favorite table in the cafeteria, the 5pm train toLong Island. Each of these is marked by certain stable arrays of physical objects and physical infrastructure, by ‘surface layouts’ in Gibson’s terms. But
each recurrent setting is associated, on the other hand, with certain stable patterns of behavior on the part of the persons involved. Physical-behavioral units
are the conjunct of these two aspects. They are built out of both physical andbehavioral parts.As Barker puts it, physical-behavioral units
are common phenomenal entities, and they are natural units in no way imposed by aninvestigator. To laymen they are as objective as rivers and forests—they are parts of theobjective environment that are experienced directly as rain and sandy beaches are experienced. (Barker 1968, p. 11)

Each physical-behavioral unit has two sorts of components: human beings be-

14

For something like Aristotle’s theory to work, we would need to recognize a deviant
topology of boundaries of the sort described in Smith 1997 and Smith and Varzi 1999, where
topological connection is defined in terms of boundary coincidence. In classical topology, bycontrast, connection between two things is explained in terms of intersection (overlap) between one thing and the closure of the other. See section 7 below.

8having in certain ways (lecturing, sitting, listening, eating), and non-psychological objects with which behavior is transacted (walls, chairs, paper, electricity,etc.). Each physical-behavioral unit has a boundary that separates an organizedinternal (foreground) pattern from a differing external (background) pattern.
This boundary, too, though it may be far from simple, is an objective part ofnature, though it may change according to the participants involved or according
to the nature or phase of the relevant activity. Each unit is further circumjacent
to its components: the former surrounds (encloses, encompasses) the latter: thepupils and equipment are in the class; the swimmers are in the swimming pool.
Many units occur in assemblies, as a chick embryo is constructed as anested hierarchy of organs, cells, nuclei, molecules, atoms, and subatomic particles.
A unit in the middle range of a nesting structure is simultaneously both circumjacentand interjacent, both whole and part, both entity and environment. An organ—the liver,for example—is whole in relation to its own component pattern of cells, and is a partin relation to the circumjacent organism that it, with other organs, composes; it
forms the environment of its cells, and is, itself, environed by the organism. (Barker
1968, p. 154)

Physical-behavioral units, too, may be nested together in hierarchies in this way.
There are typically many units of each lower-level kind within a given locality,
and these are typically embedded within larger units, as a game is embedded
within a match. Conversations, hunt meets, weddings, each of these arephysical-behavioral units in Barker’s sense. By contrast, a randomly delineatedsquare mile in the center of a city is not a physical-behavioral unit, and nor isthe mereological sum of its Republican voters; the former has no self-generated
unity; the latter has no continuously bounded space-time locus.15
5.

Towards a formal theory

We can now summarize the ontological marks of environmental settings orniches as Aristotle and Barker might conceive them, as follows:(i) An environmental niche takes up space, it occupies a physical-temporal locale, and is such as to have spatial parts. Within this physical-temporal

15

See Barker 1968, pp. 11f., 16; 1978, p. 34.

9locale is a privileged locus—a hole—into which the occupant of the niche fits
exactly.
(ii) Environmental niches are unitary. A typical niche enjoys a certain natural completeness or rounded-offness, in contrast to its arbitrary undetachedparts and to arbitrary heaps or aggregates of niches.
(iii) An environmental niche has an outer boundary: there are objects whichfall clearly within it, and other objects which fall clearly outside it.
(iv) Environmental niches may have actual parts that are also environmental
niches, and they may similarly be proper parts of larger, circumcluding environmental niches.
(v) An environmental niche is not simply a location in space; rather, it is alocation in space that is constrained or marked by certain functional properties(of temperature, foliage density, federal jurisdiction, etc.).
(vi) An environmental niche may overlap spatially with other environmental
niches with which it does not share common parts.
We may now proceed to setting forth a formal theory.
6.

Mereology

For simplicity, we shall assume a standard mereological background.16 The
primitive relation ‘x is part of y’ we symbolize by ‘P(x, y)’, which we take to betrue when x is any sort of part of y, including y itself. The relation of properpart can be defined accordingly:
D1

PP(x, y) := P(x, y) ∧ ¬ x = y.

proper partIt will be understood that variables range over individuals—individual bodies,
individual boundaries, and individual instances of a range of other categories, aswell as the individual parts and aggregates of these.
The ‘is’ in ‘x is part of y’ is to be given a tensed reading. Thus our mereological framework embodies a synchronic theory, a theory of the part-whole
relations existing at some given time. If we now define overlap as the sharing ofcommon parts:

16

For an introduction to standard mereology and its variants, see Simons 1987. Ourpresentation here follows that of Smith and Varzi 1999.

10

D2

O(x, y) := ∃z(P(z, x) ∧ P(z, y)),overlap

then the axioms for standard mereology can be formulated as follows:17
A1
A2
A3
A4
A5

P(x, x)P(x, y) ∧ P(y, x) → x = yP(x, y) ∧ P(y, z) → P(x, z)∀z(P(z, x) → O(z, y)) → P(x, y)∃x(φx) → ∃y∀z(O(y, z) ↔ ∃x(φx ∧ O(x, z))).

Parthood is, accordingly, reflexive, antisymmetric, and transitive, a partial ordering. In addition, A4 ensures that parthood is extensional (two things cannot
consist of the same parts) and the schema A5 guarantees that for every satisfied
property or condition φ (i.e., every condition φ that is true of at least one individual) there exists an entity consisting precisely of all the φers.18 This entity iscalled the sum or fusion of the φers and will be denoted by ‘σx(φx)’. It is defined as follows:
D3

σx(φx) := ιy∀z(O(y, z) ↔ ∃x(φx ∧ O(x, z))),sum

where, for simplicity, the definite descriptor ‘ι’ is assumed to be contextually
defined in Russellian fashion:
D4

ψ(ιx(φx)) := ∃x(∀y(φy ↔ y = x) ∧ ψx).

The mathematical properties of this mereological theory are well known
and correspond to those of a Boolean algebra with the null (zero) element removed. Given D3, the analogues of the ordinary Boolean operators are easily
defined:
D5
D6
D7
D8

x+ y := σz(P(z, x) ∨ P(z, y))x×y := σz(P(z, x) ∧ P(z, y))x–y := σz(P(z, x) ∧ ¬O(z, y))–x := σz(¬O(z, x)).

17

binary sum
binary product (intersection)differencecomplement

Here and in the sequel initial universal quantifiers are to be taken as understood.
‘φx’, again, is to be given a tensed reading. Hence, the entity in question will consistof those things that satisfy φ at some given time, not of those things that satisfy φ at sometime or other .
18

11In addition, we can associate the general sum operator σ with a general productoperator π: the product of any number of overlapping φers is the sum of all
those things that are part of every φer:D9πx(φx) := σz∀x(φx → P(z, x)).

product (intersection)

Of course, since A5 is in conditional form, this operator may fail to be defined
if the φers have no parts in common. The operators introduced in D6–D8 may
likewise fail to be defined for some of their arguments. This is because there areno null individuals in our theory, no analogues of the empty set.
7.

Topology

We should like to talk of things that are connected, or of a piece, on the one
hand, and distinguish them from scattered groups or aggregates and othergerrymandered beings, on the other. It is impossible to account for this difference on the basis of mereology alone. More generally, mereology cannot account for some very basic spatial relations, such as the relationship of continuity
between two adjacent parts of an object, or the relation of one thing’s being
entirely inside or surrounded by another. To provide a systematic account ofsuch relations will require a topological machinery.
We shall assume here an apparatus closely corresponding to ordinary topology, though constructed on a mereological basis.19 The central concept is theconcept of boundary as illustrated by the outer surface of a sphere, the edge of atable, or the borders of Japan. As a primitive, we assume ‘x is a boundary for y’,which we symbolize as ‘B(x, y)’. We say boundary for, rather than boundaryof, to allow for boundaries that are not maximal (corners, edge segments, partsof surfaces). The maximal boundary of x is then immediately defined, using
AP5, as the sum of all the boundaries for x:
D10b(x) := σyB(y, x).

maximal boundary

Again, note that this notion may not be defined for every value of ‘x’. Some

19

Here we confine ourselves to a brief review. For more on mereotopology, we refer toSmith 1993, 1997, Varzi 1996a, Cohn and Varzi 1998, Smith and Varzi 1999. For a standard
reference on ordinary topology, see Steen and Seebach 1970.

12objects, for instance the universal object (definable as the sum of all selfidentical things), may lack a boundary.
For the sake of perspicuity, it is convenient to introduce also a closure operator:
D11c(x) := x + b(x).

closureThis is a mereologized version of the standard, point-set-theoretic operator of
topological closure. We may then formulate our axioms by mereologizing thestandard Kuratowski axioms (1922), in the obvious way, as follows: 20
A6
A7
A8
A9

P(x, c(x))
P(c(c(x)), c(x))
P(c(x), c(x+ y))P(c(x+ y), c(x) + c(y)).

(In view of D11, axiom A6 is actually derivable from A1 but we list it here forease of reference.) The axioms imply that ‘B’ satisfies certain familiar conditions. In particular, boundaries are always transitive and dissective (i.e., they
only have boundaries as parts):
T1
T2

B(x, y) ∧ B(y, z) → B(x, z)
P(x, y) ∧ B(y, z) → B(x, z).

They are also symmetric, in the sense that a boundary for a given entity is also aboundary for that entity’s complement:
T3

B(x, y) → B(x, –y).

The axioms also allow us to define:
D12
D13
D14

IP(x, y) := P(x, y–b(y))
interior partC(x, y) := O(x, y) ∨ O(c(x), y) ∨ O(c(y), x)
connection
EC(x, y) := C(x, y) ∧ ¬O(x, y)
external connection (touching)

20

These axioms are to be understood as holding whenever c(x) is defined. In other words,
we read each axiom as involving a tacit antecedent asserting the existence of denotations for
its defined terms. For instance, A6 amounts to the conditional ∃y(y = c(x)) → P(x, c(x)). We
shall rely on a similar convention in stating all our theorems and axioms below.

13

D15
D16

Cn(x)
:= ∀y∀z(x=y+ z → C(y, z))CP(x, y) := Cn(x) ∧ P(x, y).

self-connectedness
connected part

Note that ‘IP’ and ‘CP’ are both transitive and antisymmetric, while ‘C’ is reflexive and symmetric and ‘EC’ is irreflexive and symmetric. We then require,for self-connected boundaries, the existence of self-connected wholes which
they are boundaries for:
A10

∃yB(x, y) ∧ Cn(x) → ∃y(B(x, y) ∧ Cn(y) ∧ ∃zIP(z, y)).

This corresponds to the Aristotelian thesis that boundaries are ontologicallyparasitic on (i.e., cannot exist in isolation from) their hosts, the entities theybound—a thesis which stands opposed to the ordinary set-theoretic conceptionof boundaries as, effectively, sets of independent points, each one of whichmight exist though all around it be annihilated.21
Finally, we define:
D17
D18
D19
D20
D21
D22
D23

i(x) := x–b(x)e(x) := i(–x)Op(x) := x = i(x)Cl(x) := x = c(x)Ro(x) := x = i(c(x))Rc(x) := x = c(i(x))Rg(x) := Ro(i(x)) ∧ Rc(c(x)).

interior
exterior
open
closedregular open
regular closed
regular

These definitions provide a natural mereotopological analogue of standard topological notions.22 For instance, the notion of regularity captured by D23 corresponds to that of a regular set. We shall impose on niches and their occupants
the constraint of regularity in order to exclude from the orbit of our theory
space-filling curves, deleted Tychonoff corkscrews, and other topological mon21

A more general statement of the dependence thesis would assert that the existence ofany boundary is such as to imply the existence of some entity of higher dimension which it
bounds. Here, though, we shall content ourselves with the simpler formulation. For moredetails, see Smith 1993 and Smith and Varzi 1999.
22
Recall that we are assuming a Russellian treatment of definite descriptions (D4).
Thus, ‘Op(x)’ will be false not only when x is non-identical with its interior, but also when x
lacks an interior altogether, i.e., when i(x) is not defined; and similarly for the other definitions listed here and below.

14

sters. A regular object is, roughly speaking, an object which does not possess
outgrowing boundary “hairs,” it does not lack a single interior point, it does
not consist of two or more voluminous parts connected by interiorless filaments, and so on.
Note that it follows from D14 that two entities can be in contact (externallyconnected) only if one of them is not closed:
T4EC(x, y) → (Cl(x) → ¬Cl(y)).

Thus, if Bill and Monica are topologically closed, then genuine contact between
them is impossible if contact is understood in terms of external connection(EC). In general, the surfaces of distinct physical bodies cannot be in contact
topologically, though bodies may of course be so close to each other that they
appear to be in contact to the naked eye.23
8.

Location

Before proceeding to the formal theory of niches proper, we still need to draw adistinction between the part-whole relations that apply to entities in space andthose that apply to the spatial regions these entities occupy. This distinction
would not be necessary if we could assume that the relation of spatial location is
exclusive—that no two entities may share the same spatial location at the sametime. We shall, in fact, assume that this principle holds of organisms; but it is
not true in general. There are relations of spatial overlap which do not imply
corresponding relations of mereological overlap. If you put a stone in a hole,then the stone occupies a region of space which is also occupied by the hole;and yet the stone and the hole do not share any parts.24 Likewise, we want to
say that there may be objects located inside the region where a niche is locatedthat are not part of or connected to the niche. The niche around the sleeping

23

There is a compacting of molecules where Bill and Monica kiss, but no part of Bill isever in contact with any part of Monica. This is in agreement with standard topology, andalso with standard physics, but see again Smith and Varzi 1999 for a more detailed account of
the underlying issues.
24
See Casati and Varzi 1994, ch. 7. Our talk of ‘spatial regions’ and ‘locations’ here
should not be taken as expressing commitment to an absolutist conception of space: analogous remarks would apply on a relationist conception.

15

bear is full of flies, but the flies themselves are not a part of the niche.25 We
also want to say that a niched object does not overlap its niche, not only in the
mereological sense of not sharing any part with the niche, but also in the purely
spatial sense of not sharing any common location. This, too, cannot be expressed in purely mereotopological terms. Finally, the ecological literature
makes it clear that niches are bounded not just spatially, and not just via physical material (the walls of the cave), but also via thresholds in quality-continua(for instance, temperature). Distinct niches, therefore, may occupy the same
spatial region. And we may want to say that different organisms, or organisms of different types, are able to find niches within the same spatial region
without thereby implying that they share a niche. A niche for the fly on the
bear’s nose is not a part of the niche for the bear (or at least: we need not assume that it is).
All of this suggests that we introduce, in addition to our mereotopologicalprimitives of part and boundary, a primitive concept of spatial location. We shalluse the notation ‘L(x, y)’ to indicate that ‘x is located at y’, that x stands to y in
the primitive relational tie of exact location. Other locative relations, such as
partial and interior location, can easily be defined in terms of this primitive together with our mereotopological apparatus, but we shall have no use for themfor our present purposes.26
As basic axioms for L, we assume the following:
A11
A12

L(x, y) ∧ L(x, z) → y = z
L(x, y) → L(y, y).

By A11, a single entity cannot have two distinct locations: L is a functional
relation. By A12, L behaves as a reflexive relation whenever it can: all (andonly) those things are located at themselves at which something is located. We
shall assume, further, an axiom to the effect that every entity has a location:
A13∃y(L(x, y)).

25This suggests a distinction between the narrowly defined concept of niche and a wider
concept of environment, defined as the mereological sum of all that lies within the spatial
location of an object’s niche. The environment of the sleeping bear would then include theflies as proper parts.
26
See Casati and Varzi 1996, 1999 for details.

16This is obviously very strong: it implies that entities lacking spatial location(such as numbers) are excluded from the domain of our theory. It brings however the compensating advantage that it allows us to speak of regions as justthose things at which something (not necessarily something else) is located:
D24

Re(x) := ∃y(L(y, x)).

regionThe region at which an entity x is located we shall call the location of x:
D25l(y) := ιx(L(y, x)).

location

The uniqueness of l(x) follows directly from the functionality postulate, A11,
while A12 ensures further that l is idempotent:
T5l(l(x)) = l(x).

On the other hand, nothing guarantees that the domain of regions is mereologically well-behaved in the sense that every part of a region is a region, and thatthe sum of any regions is itself a (possibly disconnected) region. To this effect,
the following axioms must be added explicitly:
A14
A15

Re(x) ∧ P(y, x) → Re(y)∀x(φx → Re(x)) → Re(σx(φx)).

At this point we obtain a more adequate theory of location by adding principles connecting the axioms for L with our basic mereotopological apparatus:
A16
A17l(x+ y) = l(x)+l(y)l(b(x)) = b(l(x)).

These two principles ensure that the mereotopology of things is mirrored in theappropriate way in the mereotopology of their corresponding regions. By A16
the location of a sum of parts is the sum of the locations of the parts, and by
A17 the location of an entity’s boundary is the boundary of the entity’s location. This implies that the locations of a thing’s parts are parts of the thing’s location, and the locations of a thing’s boundaries are boundaries of the thing’s
location:
T6
T7

P(x, y) → P(l(x), l(y))
B(x, y) → B(l(x), l(y)).
17Moreover, A17 implies that a similar result holds when ‘b’ is replaced by theclosure or interior operators:
T8T9l(c(x)) = c(l(x))
l(i(x)) = i(l(x)).

A16, in turn, can be strengthened to cover infinitary sums—the location of asum of φers is the sum of the locations of the φers:
A16'9.

l(σx(φx)) = σz(∃x(φx ∧ z = l(x))).

NichesWe are now ready to proceed to the basic principles of the theory of niches.
Formally, this may be thought of as a theory of certain sorts of neighborhoods.
We shall formulate it with the help of a new primitive predicate ‘N(x, y)’, to beread: ‘x is a niche for y’ (we shall call y the tenant of x). Again, the ‘is’ here is
to be given a tensed reading: we are concerned with the panoply of nichetenant relations at a given time. For simplicity, we shall initially suppose that
all tenants are compact, in the sense that they have no internal cavities. Later
we shall see how the account can be extended to the case of tenants with cavities.
The mereotopological conditions on niches are fixed by the following setof axioms, which we shall explain and justify in the sequel.
A18
A19
A20
A21
A22
A23
A24
A25

N(x, y) → ¬O(l(x), l(y))
N(x, y) → IP(l(y), l(x+ y))N(x, y) → C(x, y)N(x, y) → Cl(y)N(x, y) → Cn(x)N(x, y) → Rg(y)N(x, y) → Rg(x)N(x, y) ∧ N(x, z) → y = z.

disjointness
spatial containment
connection of nicheclosure of tenantconnectedness of niche
regularity of tenant
regularity of nichefunctionality

The first three axioms fix the basic spatial relationships between niches andtheir tenants. A niche is a type of perforated or deleted neighborhood of its tenant. Thus, we require that the location of the niche should not overlap (A18) but
rather surround (A19) that of its tenant, and that the niche itself sould be con18

nected to its tenant (A20). It follows that a niche is always externally connected
to its tenant and therefore that N is irreflexive (since nothing is externally connected to itself):
T10
T11

N(x, y) → EC(x, y)¬N(x, x).

A result stronger than T10 is in fact provable, namely, that every boundary of atenant is also a boundary of its niche:
T12

N(x, y) ∧ B(z, y) → B(z, x).

(It is here that our supposition concerning the lack of interior cavities becomes
explicit. The presence of a cavity would split the boundary of the tenant into two
disconnected parts, only one of which—the exterior one— can be shared by theniche. We shall come back to this in Section 11 below.)
We also assume, by A21, that all tenants are topologically closed, hence
that they contain their boundaries as parts:
T13

N(x, y) ∧ B(z, y) → P(z, y).

This is motivated by our ecological interpretation of ‘N’: the boundaries of atenant are its surfaces, which face out toward the niche. It also follows that every
niche has an interior (has divisible bulk), and therefore that the categories ofniche and boundary are mutually exclusive:
T14

N(x, y) → ¬B(x, z).

This is so because, since niches are externally in contact with their tenants (byT10), and since tenants are always closed (by A21), a niche must always be
open in the region in which it makes contact with its tenant (by T4, which tells
us that, where two entities are externally connected, one must be open and theother closed).
Given T4 and T10, A21 also implies that the tenant of a niche cannot itself
be a niche:
T15

N(x, y) → ¬N(y, z).

This in turn implies that N is not only irreflexive (T11) but fully asymmetric
and—more generally—that niches cannot themselves be niched:
19

T16
T17

N(x, y) → ¬N(y, x)N(x, y) → ¬N(z, x).

This does not exclude an organism from being such as to constitute a niche or
natural setting for another entity, for example a micro-organism inside a humanbody. What it does rule out is that the hosting organism might serve this hosting function by itself. To see what is at issue here, note that, if every organism isclosed and every niche open (in the relevant contact area), then it follows that a
micro-organism lodged inside your body as a niched entity is not topologicallyconnected to your body: there must be some distance between them, however
small. The niche for the micro-organism is thus not your body itself (which is
closed), nor a proper part thereof, but rather an entity including also the area
immediately surrounding the micro-organism and separating the latter fromyou.
By A22, all niches are connected. Moreover, the regularity axioms A23 andA24 rule out niches and tenants with strange topologies, for example niches or
tenants with outgrowing interiorless boundary hairs. There are, to be sure, organisms that have a quasi-fractal structure (sponges, mosses) and niches whose
porosity is important to their ecological role. The hole-part structure of such
entities is enormously complex, but they are nonetheless regular in the sense atissue here.
Our last axiom, A25, says that niches are exclusive environmental settings:
they cannot be shared by distinct entities (though distinct entities may haveoverlapping niches, both in the mereological and in the spatial sense of ‘overlap’). Consider the inside of an ant’s nest. This is, no doubt, a niche for a clutchof eggs when they are laid (a disconnected tenant). But is it not also a niche foreach separate egg? To see why this is not so, consider that the surrounding environment of each single egg includes, or is determined by, the boundaries of its
neighbors. The surface layout of the collective niche is quite different from thesurface layout of the niche for each egg taken singly. Similar considerations
apply in relation to a pair of twin fetuses inside a mother’s womb. Each fetus
helps to determine the niche for its neighbor. The womb as a whole serves asniche for the twinned pair.
Note that our axioms do not guarantee that niches are closed under the basic mereological operations of sum and product. If an object has two niches,
their sum need not be a niche, for it might lack the sort of homogeneity that20

typically characterizes a niche. Likewise, if an object has two niches, their intersection need not be a niche. Consider a group of cows in the middle of a large
field with a water tank at each of the two extremities A and B. The whole field isa niche for the cows, as is the middle plus A and the middle plus B. But the intersection of the latter is not a niche, since the cows need water. This asymmetryof behavior with regard to the mereological operations is one respect in which
the concept of niche would seem to deviate from the purely topological conceptof neighborhood.
There are many other properties of neighborhoods whose analogues forniches have an uncertain status. For instance, should we assume that every twoniches of the same tenant have a common part? Should we assume that every
niche for a given tenant has a proper part that is itself a niche for that tenant?
Should we assume that every niche has a compact part that is a niche for its tenant (a niche with no internal holes except those occupied by the tenant)? Theseare questions that we can hardly address at this stage, and we shall content ourselves, here, with the basic apparatus defined by A18–A25.
10. VaguenessOur axioms do not imply that niches are dissective: a niche for an entity y
may have proper parts that are not niches for y, even if those proper parts
fully envelop y. Thus, for instance, no non-regular proper part of a niche everqualifies as a niche. Our axioms do not imply, either, that niches may be arbitrarily large. Thus, in particular, the mereological complement of an organism (the result of imagining the organism as having been deleted from the remainder of the universe) need not be a niche, according to the axioms here
listed.27
What, then, is to be said about the outer boundaries of niches? In somecases the surface layout of the surrounding physical environment provides anupper limit to the niche extension (the worm in its wormhole, the scholar in hercell). In other cases, however (the fish in the ocean, the bird in the sky), no such

27

The axioms do not however rule this out. Indeed, a straightforward consistency proof
for the theory defined by A18–A25 can be obtained precisely by taking ‘N(x, y)’ to be true if
and only if x is the mereological complement of y.

21physical limit may be provided: the outer boundary of the relevant niche is thenin some sense vague. We face, here, a range of options which are counterpartsof options we face in any account of vagueness. Thus, on the one hand, wemight assert that these cases involve a more or less open-ended continuum of
nested environments, each of which is in itself perfectly determinate and each ofwhich may claim (possibly to different degrees) to serve as niche for the entity
in question. The structure of this continuum would then suggest a postulate ofopen-endedness along the following lines:
A26

N(x, y) → ∃z(N(z, y) ∧ PP(x, z)).

An even stronger axiom would be density: the nesting of niches always yields
mereological intermediates that are themselves niches:
A27

N(x, y) ∧ N(z, y) ∧ PP(x, z) → ∃w(PP(x, w) ∧ PP(w, z) ∧ N(w, y)).

On the other hand, however, we might assert that there is a single niche forthe entity in question, but that this niche has an outer boundary that is literally
vague or indeterminate. There would then be spatial regions for which there isno objective, determinate fact of the matter about whether they overlap the location of the niche.28 This alternative brings ontological problems of its own andwould induce a fuzzification of our basic mereotopological and locative framework. But some might insist that these problems must in any case be solved inan account of the semantics of natural language expressions such as ‘downtown’, ‘Mount Everest’, ‘the hurricane that destroyed the village’, and so on.
We shall here remain neutral with regard to this general issue. Precisely
because it is not a problem peculiar to the concept of niche, the theory of niches
should not force one account or the other. If there are vague objects, someniches will be among them. If (as we would be inclined to argue) all vagueness is conceptual, then the niche concept will in some cases have vague applications.
11. Cavities
A different sort of question relates to the inner boundaries of niches—the28

Niches would thus be vague entities in the sense of Tye 1990.

22

boundaries that niches share with their tenants. In presenting our basic axioms,
we have assumed that tenants involve no internal cavities. This allowed us tocharacterize the idea that a niche surrounds the tenant simply by requiring thatthe location of the mereological sum of niche and tenant includes the location of
the tenant as an interior part (A19). However, a tenant may itself have interior
cavities, and if tenants are to be closed (by A21) and niches connected (by A22),
this means that A19 falls short of capturing the relevant sense of ‘surrounds’ in
the general case: the boundary around an internal cavity belongs to the tenant
and it therefore cannot be in the interior of the sum constituted by the tenant
together with its niche (though it would be in the interior of the threefold sum
made up of tenant, niche, and cavity).
A19 (and T12) may seem threatened also in cases where the tenant has aconnected boundary. All animals are torus-shaped entities, yet it hardly seems
reasonable to suppose that every niche of John would snake through his digestive tract. Here three sorts of cases can be distinguished: (i) Cases where theputative hole is, in virtue of the intimate causal interconnection of processes oneither side of its boundary, analogous to an organ within the interior of the organism in question. (ii) Cases where the putative hole is a genuine hole, analogous to the hole inside a wedding ring. (iii) Cases which involve a combinationof (i) and (ii), perhaps of the sort illustrated by the womb conceived abstractly
as dilation in the uterine tract. In type (i) cases, now, the walls of the putative
hole are not part of the boundary of the object; their not being in contact with
the niche therefore does not contradict T12. Cases of type (ii), in contrast, do
indeed allow penetration by a niche into the interior of the tenant (thus we may
naturally suppose that the finger through Mary’s wedding ring is part of thering’s niche). Type (iii) cases, finally, bring us back once more to the issue ofinterior cavities, and in order to resolve this issue we need to amend A19 as
follows.
Suppose, first, that the tenant is a connected object. In that case, the tenant
has a cavity if and only if it has a disconnected boundary: the cavity has no contact with the rest of the object’s complement, hence its presence splits the object’s boundary into two parts. (Equivalently, the presence of a cavity splits theobject’s mereological complement into two disconnected parts: the one inside,
the other outside the object.) Consider now the entity that results (intuitively)
when we take the object together with those parts of its complement that lie on
its inside—the mereological sum of the object together with its cavities. This23

can be defined, more technically, as the compact closure of the object—thesmallest entity whose boundary is connected and which includes the object
as part:29
D26

k(x) := πy(Cn(b(y)) ∧ P(x, y)).

compact closure

It is easy to verify that this operator is well-defined whenever x is connected.
Moreover, the compact closure of a closed object is always closed, and thecompact closure of a regular object is always regular:
T18
T19

Cl(x) → Cl(k(x))Rg(x) → Rg(k(x)).

Using this notion we can now reformulate axiom A19 in such a way as to allow
for niched objects with cavities. To capture the idea that the niche surrounds theobject, i.e., envelops it from the outside, we require the niche to be a deleted
neighborhood of the compact closure of the tenant:A19'

N(x, y) → IP(l(k(y)), l(x+k(y))).

Of course, this reduces to A19 whenever the tenant has no internal cavities, forin that case the tenant has a connected boundary and thus coincides with its
compact closure:T20

Cn(b(x)) → x = k(x).

On the other hand, given our requirement that niches be always connected(A22), A19' guarantees that, if the tenant of a niche has internal cavities, thenthese cavities are not a part of the niche. Not every deleted neighborhood is acandidate niche for an entity, but only those that surround the entity in the mostliteral sense.
Note that if we replace A19 by A19', theorem T12 to the effect that every
boundary of the tenant is also a boundary of the niche will fail, though the following will still hold:29

In a more sophisticated analysis we would define the compact closure of an object as
the sum of the object with its holes (Varzi 1996b). This, however, would require an explicit
treatment of the relation ‘x is a hole in y’, which cannot be defined in terms of standard
mereotopological primitives of the sort available here.

24

T12'

N(x, y) ∧ B(z, k(y)) → B(z, x).

A19' is still not general enough, however, since it rests on the supposition
that tenants are connected entities. This need not always be the case (think of
the niche surrounding John and Mary as they enjoy a romantic candle-lightdinner). A tenant may have a disconnected boundary even if it has no cavities,
which would make our reference to its compact closure illegitimate. (There is nosmallest entity whose boundary is connected and which includes John andMary as parts.) To capture the idea that a niche surrounds its tenant without requiring that the tenant be connected, we must further require the conditional in
A19' to hold, not of the tenant itself, but of each maximally connected part (or‘element’) of the tenant. The relevant definition is as follows:
D27

E(x, y) := CP(x, y) ∧ ∀z(CP(z, y) ∧ O(z, x) → P(z, x)).

element

Informally: an element is a connected part that is maximal in the sense thatit contains every connected part that it overlaps. We can finally amend A19 byrequiring the niche to surround every element of its tenant, as follows:
A19" N(x, y) ∧ E(z, y) → IP(l(k(z)), l(x+ k(z))).
The analogue of T12 is then provable in the following form:
T12"

N(x, y) ∧ E(w, y) ∧ B(z, k(w)) → B(z, x).

12. Ecological subjects
Return, now, to the rest of the axioms. We have seen that the sum x+ y of twoniches for an object z need not be a niche for that object. Likewise, we may observe that our axioms do not support the dual principle to the effect that a niche
x for a sum y+ z is ipso facto a niche for each of the summed parts. For instance, if y+ z is an individual substance (the head plus the rest of John’s body),
then it typically has a niche of its own even though the two parts y and z (thehead and torso) do not.
We can now distinguish various different sorts of niched entities which arenatural units in the sense described:
D28

Ct(x) := Cn(x) ∧ ∃yN(y, x)25

connected tenant

D29
D30

Su(x) := Ct(x) ∧ ∀z(Ct(z) ∧ O(z, x) → P(z, x)))Av(x) := ∃yN(y, x) ∧ ∃y(Su(y) ∧ PP(y, x)).

substance
avatarA connected tenant (D28) is a niched entity which is at the same time not scattered (is not an aggregative or collective tenant). A substance (body, thing) is a
maximally connected tenant (D29), a tenant which is such that no larger connected tenant includes it as a proper part.30 You are in this sense a substance,
but your heart is only a connected tenant within your interior. (Two connectedsiamese twins are also not substances in the sense of D29, though their sum is.)Finally, an avatar (D30) is a tenant including substances as proper parts. Examples of avatars might include: a shoal of fish in a lake, a herd of buffalo. These
are causally integrated and more or less reproductively isolated subpopulationsof conspecifics. They play an important role in evolutionary theory in light of
the fact that it is avatars, and not whole species, that are the most plausible candidate subjects of selective pressures at the group level.31
Note that a connected tenant need not be an element (in the sense of D27),
since it may not be maximal. However, every niched element is a connected tenant, and every connected tenant is included in some substance:
T21
T22

N(x, y) ∧ E(y, z) → Ct(y)Ct(x) → ∃y(Su(y) ∧ P(x, y)).

In terms of the concept of niche (along with the underlying mereotopologicaland location-theoretic primitives) we are now able to prove counterparts of anumber of propositions central to the metaphysical treatment of substances inthe tradition, as also to the treatment of groups or communities and of the associated concepts of natural unit and social whole. For instance, it follows from
D29 that substances have a regular topology, that they are closed (i.e., containtheir boundaries as parts), and that no two of them can share any parts:
T23

Su(x) → Rg(x)30

D29 presupposes that every substance is always in a niche. This may be disputable: adiver crossing the boundary between water and air is arguably not in a niche but rather moving from one niche to another. The issues raised by cases such as this, however, are part andparcel of the general problem of motion and change, which goes beyond the limits of thepurely synchronic framework presented here.
31
See Damuth 1985 and Eldredge 1989.

26

T24
T25

Su(x) → Cl(x)Su(x) ∧ Su(y) ∧ O(x, y) → x = y.

Thanks to D29, the theory of niches provides the resources also for a moresatisfactory formulation of the Aristotelian dependence principle for boundaries(A10). This can now be expressed by requiring every self-connected boundary
to be a boundary of some substance:
A10'∃yB(x, y) ∧ Cn(x) → ∃y(Su(y) ∧ B(x, y)).

Likewise, one may want to strengthen our requirement that substances be
maximally connected tenants by further assuming that no substance can be partitioned into connected tenants (otherwise it would be a mere aggregate):
A28

Ct(x) ∧ Ct(y) ∧ ¬O(x, y) → ¬Su(x+ y).

More generally:
A28'∀x(φx → Ct(x)) ∧ ∀x∀y(φx ∧ φy ∧ ¬x=y → ¬O(x, y))→ ¬Su(σx(φx)).

We believe that these and related principles can aid conceptual clarification
in a number of important areas of metaphysics. They can aid our thinking not
only in relation to issues pertaining to the nature of species and to the problemof specifying the unit of selection in evolutionary theory, but also, for instance,in the treatment of the metaphysics of the fetus and of the question as to thestatus and category of the summed fetus+mother pair.
13. Concluding remarks
The theory of niches presented above is of course no more than a first, provisional chapter of a formal ontology of ecological phenomena. It provides a synchronic account only: we still need to introduce the important factor of dynamics and change, and above all to address the issue of the identity of niches andniched objects over time, and issues relating to the movement and interaction oforganisms within and between their respective niches. We need to find a place
for the special types of causal integrity that characterize niches and niched entities, and for the special types of niche assembly-structure that arise for example
when groups of individuals collaborate. We need to consider also the question27

as to how niches for given objects are determined by the properties of their surroundings. What determines the shape and size of a niche? How do animal
niches in this respect relate to those of organisms of other types?
Another important family of problems relates to the question of the statusof niches when tenants are absent. Are niches essentially dependent entities, as
Lewontin would have it? Do we need to distinguish different types of niche,
some of which will survive the temporary or permanent departure or replacement of their tenants? What is the relation between my niche and your niche
when you occupy a position within my niche and I within yours? What is therelation between my niche and yours when we are in conflict, for example when
we compete for occupation of a given territory, or when you are predator and I
am prey? What, finally, is the biologically very important relation between theindividual niche or habitat of a single organism or population of organisms andthe niche-type of the corresponding species? The formal theory outlined in theabove will, we hope, provide at least a starting point for providing answers tothese questions.32
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32

Thanks to David Mark and the National Center for Geographic Information andAnalysis (an Organized Research Unit of the University at Buffalo) for valuable support in
the present project, and to Ling Bian of the University at Buffalo Geography Department,
whose work on fish ecology inspired it. Thanks also to Roberto Casati, Andrew Frank, Michael Ghiselin, Kevin Mulligan, Barbara Nunn, Kim Sterelny, Graham White, Jan Woleński
and the referees of Noûs for their comments on earlier drafts.

28

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