Environs: The Superniches of Ecosystems1

AMER. ZOOL., 21:845-852 (1981)
Environs: The Superniches of Ecosystems1
BERNARD C. PATTEN
Department of Zoology and Institute of Ecology, University of Georgia, Athens, Georgia 30602
SYNOPSIS. Evolution proceeds by natural selection of heritable variations of individual
organisms based on direct influences of environment. However, indirect effects probably
vastly outweigh direct ones in ecosystems. Therefore, why is evolution based on direct
effects only? The ecological niche represents the point of direct contact between organisms
and their environments. To encompass indirect influences, niches are extended to new
structures, environs, which are units of organism-environment coevolution. The motive
force for coevolution is closure of outputs back upon inputs of the organism members of
ecosystems. Closure is achieved by biogeochemical cycling and feedback interactions,
direct and indirect, between organisms. To the extent that closure does not occur, there
is no imperative for organism-environment coevolution. Coevolution at the system level
based on indirect effects is compatible with normal evolution at the individual organism
level based on direct effects. The organism is the unit of the latter, but environs are the
unit of coevolution.
INTRODUCTION
tion is responsive to indirect effects, but
The ecological niche represents the the imperative for it is a system design
points of direct contact of organisms with characteristic, namely, the existence of
their environments. The classical concepts feedback loops in ecosystem coupling netinclude the habitat niche of Grinnell works. To develop these points, a system
(1917, 1928), the role or functional niche theory of organisms and their niches is
of Elton (1927), and the fundamental and formulated, then applied to represent the
realized niches of Hutchinson (1957). concept of environs and their coevolution.
Niches are non-systems constructs, that is,
OBJECTS
they pertain to the local environment of
organisms, but they do not extend into the
In mathematical system theory, abstract
world of indirect influences, which mod- objects are open systems that interact with
ern ecosystem ecology increasingly asserts their environments through inputs and
that environments really are.
outputs. A determinate (i.e., unique) relaEvolution takes place through the nat- tionship between inputs and outputs is esural selection of heritable characteristics by tablished through state. The law of the obthe direct properties of environment ject, which determines its dynamic behavior
which impinge on organisms. Yet it can be through time, is expressed in the form of
shown that the influences of greatest mag- two functions, a response function and a
nitude in ecosystems are those which come state transition function (Zadeh and Deto the organism indirectly, over indirect soer, 1963; Mesarovic and Takahara,
pathways in the ecosystems' coupling net- 1975). Consider object H, a system at some
works (Patten, 1981). Thus, a paradox level in a hierarchy of levels of organizaarises. If indirect influences are the most tion. If Z is its set of admissible stimuli (inimportant, why is evolution based on di- puts), Y its set of responses (outputs), and
X its state space, then its response p and
rect effects only?
In this paper, niches are extended to transition r functions are
their counterpart systems constructs, enZx X
Y
virons, and environs are shown to be units
(1)
X.
Zx X
of system-level coevolution. This coevoluNote that writing functions in this manner
the same as in ordinary functional
means
1
From the Symposium on Theoretical Ecology prey = p(z,x) and x = T(Z,X). The
notation,
sented at the Annual Meeting of the American Sofirst function takes input and state uniqueciety of Zoologists, 27-30 December 1980, at Seattle,
Washington.
ly into simultaneous output, and the sec845
846
BERNARD C. PATTEN
ond takes these same two arguments into
the next state.
Abstract objects may be anything, from
rocks to organisms to ecosystems, etc. The
fact that they have inputs and outputs
means they also have environments. Let
H* be the environment of H. Then this
system can also be described in the same
manner as (1),
(heat, light, etc.) so that it is not these but
integrated environments that are perceived. That is, physical inputs Z underdetermine environment, and subjective
entities must be inserted between these
and the organism to derive environmental
complexity (e.g., Turvey and Shaw, 1979).
For example, in metaphysics Kant introduced human knowledge between a formless, qualityless, unknowable absolute realp*: Z* x X*
Y*
ity
(noumena) to obtain a known reality
(2)
T*: Z* x X*
X*,
(phenomena). In linguistics, Whorf (1940)
where Z*, Y* and X* are the environmen- inserted language between environment
tal input, output and state sets, respective- and integrated behavior: "We dissect naly. Objects and their environments interact ture along lines laid down by our native
by exchanges of inputs and outputs across languages. . . . we cut nature up, organize
it into concepts, and describe significances
a set of coupling constraints,
as we do, largely because we are parties to
y* = z, y = z*,
(3) an agreement to organize it in this way—
where z £ Z, y £ Y, z* G Z* and y* G Y*. an agreement that holds throughout our
When this occurs, a new system at the next speech community and is codified in the
hierarchical level of organization is creat- patterns of our language" (p. 213). In
ed. It is obvious that the pair of identities physiology sensory perception is limited by
(3) achieves a closed relationship between sense organs, and in psychology cognition
H and H*, i.e., a closed object-environ- is a complex set of reactions to stimuli inment system which can be denoted volving perception, integration, representation, description, thought, language,
{H,H*}.
memory and learning. And in science, a
paradigm or belief system consisting of
ORGANISMS
The formulations (1) and (2) provide symbolic generalizations, particular models,
satisfactory representations of inanimate shared values and concrete exemplars is
objects, but living objects come with an ad- thrown up between objective data and fiditional complication. To illustrate, let H, nal scientific understanding (Kuhn, 1970).
and H2 be two cloned determinate organ- Bats introduced into a dark room strung
isms identical in every way. This means with wires will not strike the wires because
their state transition and response func- they navigate by radar. But if, after a time,
tions are identical. Suppose an experiment a wire or two is changed in position, acciis performed in which two different stim- dents will occur for awhile (Griffin, 1976).
uli, z, G Z, and z2 G Z2, are introduced to With familiarity, the animals move about
these organisms when they are in the same by memory, not radar.
states, i.e., x, = x2, where x, G X] and x2
In each of these cases, some form of winG X2. The outcome of the experiment dow or screen is thrown up between the
should be identical, but it is observed that observer and the real world. In effect, the
it is not. What is the explanation?
observer makes a model which filters physThe explanation is embodied by the ical inputs Z and converts them to phewell-known statement around the biologi- nomenal inputs Z, which are the operative
cal laboratory that under the most care- inputs that generate a response. Thus, for
fully controlled conditions, organisms will at least some classes of biological objects,
do what they darned well please. A big perhaps all, an additional capability must
term, "epistemic mediation," is the culprit. be added to the general systems object (1)
It is necessary to turn to philosophy for a in the form of a modeling function \JL. The
moment. Epistemic mediation is the pro- formulation of determinate behavior for
cess of enriching simple physical stimuli living objects is therefore
ENVIRON THEORY
847
Finally, interpreting Y* to be all possible
outputs from H*, then the realized niche
H: \T: Z X X ^ X
(4) (Hutchinson, 1957) is the set of actual outputs Y*' C Y* from the environment. For
close systems {H,H*}, Y*' = Y* because in
t where Z is the set of admissible physical these H and H* are constrained to interact
A inputs, and Z is the set of admissible phe- consistently, that is, their input and output
nomenal inputs. The latter are the opera- sets must mutually correspond (Y* = Z
tional stimuli. If the environment of H and Y = Z*). In these circumstances realcontains biota, then in a like fashion:
ized and habitat niches are the same.
Thus, the various niche conceptsfitthe
p*: Z * X X M Y*
general systems model of the organism-enH*: \ T*: Z * x X M X*
(5) vironment relationship rather readily. Patix*: Z * x X M Z*.
ten and Auble (1981) should be consulted
for further details.
These two objects then form the closed system {H,H*} by exchanging inputs and
ENVIRONS
outputs, subject to the coupling constraints
From the above, the ecological niche
(3), as before. That is, only physical quanrepresents
that portion of environment
tities are transferred; the phenomenal
with
which
the organism has direct input
variables are internalized.
(habitat, fundamental and realized) and
output (role) contact. But, there is more to
NICHES
environment than its direct contact attriThe classical niche concepts relate to the butes. Environments are whole systems of
preceding system theory formulations as indirect as well as direct effects which enfollows. Grinnell's (1917, 1928) habitat velop and motivate organism dynamics.
niche corresponds to Y*, the physical out- Mason and Langenheim (1957) ruled inputs available to H from H*. Through the direct effects out of the concept of enviinteraction constraints (3), these outputs ronment because of the infinite regresses
from H* become physical inputs Z to H, into the past and future which including
which H perceives phenomenally as its them required. To include infinite time in
habitat Z, and to which it responds. The the concept of environment would be to
role niche of Elton (1927) corresponds to Y, make the idea intractable. Environment is
whose elements through (3) become Z*, not history, nor is it the future. It is the
which represents the role or function of H instantaneous relationship between objects
in the community {H,H*}. Hutchinson's and their niches.
(1957) fundamental niche N' is a subset of
The flaws in such a limited concept of
Z, as follows. For each z £ Z, let z be the
environment
are readily apparent. If one
minimum and z the maximum values of z
a
radiotracer
at some point A
introduces
that H can tolerate without dying or othit
will
travel
through the
in
an
ecosystem,
erwise becoming inviable. Let V C Y be
ecosystem
network
and
show
up
some time
the viable responses of H. Then, with N'
the set of tolerable inputs, the viable be- later at point B. Thus, a future is traced
out in the course of the movement, and
havior of H is
viewing it retrospectively from just having
detected the first radioactivity at point B,
p: Z X X ^ V
one would be concerned with the history
H: T: Z X X ^ X
(6) of movement from its point of introduc/j.: N' x X ^ Z ,
tion. Environment is history and is the future, but the question is where to cut off
and the inviable behavior is
the infinite regresses in finite time.
[p:ZxX^(Y-V)
The answer is, it is done automatically.
(7) Every object which has an environment is
a member of some system. Its environi: (Z -N')xX-»Z.
Ip: Z x X-> Y
848
BERNARD C. PATTEN
--
0
o
Z30B9
/
\
-»
0
r
167 0
H
l
285 0
B882O
H2
H3
1166
35794
2000
751
»A
S700
H5
170
600
_
r
t
0
0
0
Vr
0
0
0
0
TV
I
-
FIG. 1. Static energy flow model of a cold water
spring ecosystem (detailed description in Patten et.
al, 1976, p. 512 ff.). The components are H, plants,
H2 detritus, H3 bacteria, H4 detritivores, and H5 carnivores. Storages (boxes) in kcal m"2, andflows(arrows) in kcal m~2 y"1.
7_
O-
A
I
933
ment, therefore, has a within-system portion which can be structured, and an extrasystem portion which is unstructured
(a characteristic of system level environments is that they are everything one does
not wish to define), and which extends to
infinity in the past (input side) and future
(output side). Thus, systems of definition
automatically truncate the infinite regresses to which Mason and Langenheim took
exception. As these systems are partially
interconnected sets of member objects, the
environments of the latter can be known
explicitly in terms of the system's internal
structure out to the latter's input and output boundaries. The within-system environments of subsystem level components,
including the components themselves,
constitute environs. Each object has two of
n V
n
0 8
\[1169
\
933, w//////,
1207
''/////////-
038
1 169
001
1
039
018
0
°21 \
1
'//,?/////
1039
/
\
0
°21 \
\
1018
\
0
FIG. 3. Input environs H ' , , . . . , H ' 5 of Figure 1
model. Flows (arrows) responsible for one unit of output in each case, together with summed inflows (boxes) to each compartment. Realized niches N ' , , . . . ,
N' s shown as darkened boxes and arrows with control
symbols.
them, an input environ and an output environ (Patten, 1978).
\
Environs are the superniches of ecosys1 r
794
199
031
434
956
10
tems because they represent outward extensions (through the niches in the case of
\F
\
living objects) into the ecosystem structure,
and backward and forward in time, from
the point of interactive contact between
255
things and their environments. To the ex039
039
251
564 0 2 6
tent that an object's output environ H"
does not close around to its input environ
/
H', the object-environment relation is not
FIG. 2. Output environs H", and H"2 of the Figure closed, {H,H*}, but open {H',H,H"}. In
1 model. Flows (arrows) generated by one unit of this case, the coupling constraints are
1
193
m
m
input in each case, together with summed outflows
(boxes) from each compartment.
y' - z, y = z",
(8)
849
ENVIRON THEORY
where y' E Y', z E Z, y E Y and z" £ Z",
and the inputs z' £ Z' and outputs y" £ Y"
are understood to be from and to, respectively, the system level environment of the
system to which H belongs. As before, if
)
H' or H" contain living elements, then
w modeling functions /A' and /J." will be required in their description.
Each environ encompasses a unique microcosm of direct and indirect interrelations within the system in which its defining object is a member. Environs are
relativistic structures in two ways: they are
determined by both their defining object,
and by this object's system. Niches are the
restrictions of environs to the portions
which participate in direct interactions
with H.
To illustrate environs and their relation
to niches more concretely, Figure 1 shows
a simple compartment model of energy
flow in a cold spring ecosystem (Tilly,
1968). There are five components, two
with inputs from the system level environment, and all have outputs to this environment. The two output environs associated
with each component object with input are
illustrated in Figure 2, scaled to one unit
of input in each case. The five input environs associated with one unit of output
from each component are shown in Figure
3. In every case, the environ's defining object is identified by a bold input or output
arrow. In Figure 3, realized niches within
each environ are indicated by darkened
boxes and the arrows with control symbols.
Environs partition their systems, i.e., divide them up into mutually exclusive and
exhaustive subsystems. Thus, in Figure 2,
if the unit inputs are multiplied by the actual inputs which appear in Figure 1, and
all the numbers in each environ are scaled
accordingly, and if then both absolute environs are added, they will sum to the Figure 1 system. Similarly, in Figure 3 scale
all the numbers according to the respective
absolute outputs in Figure 1, then sum the
environs, and the original system will be
produced. Output environs form one partition of systems according to inputs, and
input environs constitute a second partifc
™ tion according to outputs. Hence environs
trace the fate of inputs and the origin of
FIG. 4. Food web for a subcommunity of the continental shelf ecosystem of the Gulf of Mexico (Patten,
1981). Arrows denote carbon flows. Input processes
are detritivory, and outputs represent excretion. The
intrasystem flows are trophic.
outputs between system input and output
boundaries.
INDIRECT EFFECTS
The study of evolution should consider
environs rather than only direct effects on
organisms because indirect influences are
important in systems. This can be illustrated with another example. Figure 4 depicts carbon flow in the food web of a marine subcommunity, and Table 1 is a
matrix of direct effects in this web from
the column elements to the row elements.
Each column in Table 1 represents the daily food ration of the corresponding row
elements as a fraction of the carbon within
each column compartment. The entries
are thus probabilities, and imply unit daily
inputs to the compartments heading each
column.
Table 2 is the matrix of corresponding
total effects (Patten, 1981). Each column
represents the total carbon flows to each
row compartment in the unit output environ of the compartment at the head of
the column. These total effects are seen to
vastly exceed the direct effects in Table 1.
If such a simple model can generate such
contrasting differences, indirect influences
must be overwhelmingly predominant
over direct ones in real ecosystems. This
850
BERNARD C. PATTEN
TABLE 1. Matrix of daily carbon flows, as fractions of standing crops of donor compartments, from column compartments
to row compartments. These feeding links represent direct effects.
From
l
1
2
To
3
4
5
6
7
8
9
.900-^,
.029
.012
.002
.005
0
0
0
.009
2
3
4
5
6
7
0
900
.021
.001
.004
0
0
0
0
0
0
;930
0
0
0
0
0
0
0
0
0
0
0
0
0
~^~950^_
0
'
.003
0
.011
.003
0
.003
.007
.003
1971
.002
0
.006
0
0
0
0
0
0
^~.95O^
0
0
'
.012
.009
.004
0
0
8
.040
.009
.003
0
0
0
0
-.825 ^
.008
9
0
0
.001
0
.002
.013
.002
0
.979
phenomenal set is maintained, but its elements correspond to fewer physical inputs
than before; and (3) Z1 < Z, modeled inCOEVOLUTION
puts also become reduced. The first case
Consider the closed organism-environ- is unlikely, the second case somewhat likement system {H,H*}, in which both H and ly, and the third case most likely, most
1
H* are modeling systems as described in times. Thus, for the operative inputs, Z1 C
(4) and (5). Let H* change, causing a dif- Z occurs, and a reduced output set Y C1
ferent set of outputs Y*1 to be generated. Y is generated by H. The inputs Z1 - Z
There are four possibilities for the relation and corresponding outputs Y — Y have
of Y*1 to Y*: Y*1 n Y* = <j> (the empty set), been lost, and H has become restricted:
1
1
Y *i n Y* T^ </>, Y* C Y* and Y* C Y* .
1
Except in the case Y* C Y*, some of the
new environmental outputs, Y*1 = Y*1 (9)
Z, will be inadmissible as inputs to H. Others, Z1 = Y*1 - Y*\ will be admissible, but
except in the unlikely case Y* C Y*1, the
admissible input set will be reduced com- Now with Y1 C Y, Z* becomes restricted to
pared to the original, Z1 C Z. One of three 2*i Q 2*, then the phenomenal inputs also
possibilities will then prevail for the phe- become restricted by the same argument
nomenal input sets: (1) Z1 > Z, H compen- as above to Z*1 C Z*, and thus Y*1 becomes
sates by increasing the variety of its phe- still further reduced, to Y*2 C Y*1. Therenomenal inputs; (2) Z1 = Z, the original fore, H* becomes restricted:
fact needs to be reconciled with normal
evolutionary theory.
TABLE 2. Matrix of total effects (direct, Table I, plus indirect) propagated from column compartments to row compartments. *
From
•
To
1
2
3
4
5
6
7
8
9
9.097--^
2.964
2.833
.852
1.957
2.872
.532
0
5.933
2
.013
9.004^
3.017
.340
1.008
.391
.127
0
.646
3
0
0
13.286_
0
0
0
0
0
0
* See Patten, 1981 for detailed discussion.
4
5
6
7
.311
.201
0
1.472
.091
.059
0
.432
.536
.418
0
2.444
.920
0
20.298^.
6.032
0
5.861 """20.239.^
5.141
0
9.243
5.982 ~~42.704
2.796
3.289 — 19.000
2.019
0
0
0
o ~-- •
5.765
12.971.
0
15.302
8
9
.906
2.359
.266
1.217
1.115
1.881
4.137
.394
5.570
.745
26.894
1.853
4.042
.305
4.714
0
3.939"^^"57.310
ENVIRON THEORY
H*
1
p*: 2*i
T*:
u*:
X
2*i X
2*i X
X* —» Y*2
X* - » X *
X* ^ • Z * 1
(10)
The original environmental change has
initiated a contracting process which, with
each cycle around the {H,H*} loop, progressively attenuates the behavioral ranges,
i.e., the input and output sets, of both H
and H*. Thus, organism and environment
move toward, first stentotopy, then extinction. To halt this process H must alter its
input set to admit the new outputs Y*1
generated by the initial change in H*. A
mutant H1, with input set Z1 = Y*1 rather
than Z1 = Z*1 - Y*1, which reestablishes
consistency, Y*1 = Z1 and Y1 = Z*1, is required. Thus, H and H* must coevolve, or
their input and output sets will contract to
the point of vanishing.
In the case of the open {H',H,H"} system, if H' undergoes a change, then output at the system boundary will change in
response. But as there is no feedback to
H', alteration of H" will carry no impetus
for a coevolutionary response of the remaining system. If H' changes, however,
its output set changes to Y'1, some of
whose elements Y" = Y'1 - Z will be inadmissible as inputs to H. Again, except in
the unlikely case where Y' C Y'\ the set
of physical inputs to H is reduced, Z1 C Z,
and by the tendencies of the modeling
function as discussed above, so also the
phenomenal inputs Z1 C Z. The result is
a reduced output set Y1 from H. But a contracting process is not initiated because Y1
is not propagated back to the input set of
H'. It leaves the system as output from H".
Thus, the behavior of H will be narrowed
due to its exposure to a restricted environment H', but the resultant stenotopy is
persistent. There is no force, the movement toward extinction, for a coevolutionary response of the {H',H,H"} system.
CONCLUSION
Thus, the principal conclusions of this
paper are: (1) To the extent that organismenvironment systems are closed, {H,H*}, '
environmental change evokes a coevolutionary response. (2) To the extent, how-
851
ever, that they are open, {H',H,H"},
change in the input environment will lead
to stenotopic but stable organisms, and
their associated environs and niches.
In the last case appears to lie an answer
to the question, why are there so many
species, and why are so many of them
rare? Most species occur in the tropics,
where narrow endemism is very common.
Environments may be disturbed in two
ways, physically and biotically. The latter
situation prevails in tropical ecosystems,
where species come into and go out of existence relatively rapidly. Each addition or
subtraction amounts to a perturbation of
many input environs, and the species
whose environs these are will tend to narrow specialization to the extent that their
environmental systems are not closed.
Thus, the proliferation of narrow (and
rare because of the specialized environments) but persistent forms occurs since in
the {H',H,H"} case there is no force for
extinction.
In the closed organism-environment
complex {H,H*}, however, the movement
is to extinction unless H mutates and selection chooses an appropriate form better
matched to the output set of the new environment. Thus, coevolution of the entire
organism-environment complex, in which
environment of course contains other organisms, appears to be a system design
phenomenon. To the extent that feedback
closure is achieved, coevolution of the
{H,H*} complex will occur. The establishment of closure may be local, as in the direct feedback interactions between organisms of many varied kinds known so
well in ecology, or it may come about by
indirect pathways established in ecosystem
networks. Mechanisms for the latter include biogeochemical cycling and the general circular causal structuring of complex
food and other interaction webs. Such a
web was shown in Figure 4 for a simple
model system, and Patten (1981) should be
consulted for a discussion of the large numbers of alternative paths involved in this
network for the movement of carbon from
one place to another.
The close mutuality between organisms
by direct interactions is already under-
852
BERNARD C. PATTEN
stood in evolution in terms of group selection and related phenomena (e.g., WynneEdwards, 1962). But coevolution in response to mildly indirect effects is just
beginning to be explored (e.g., Wilson,
1980). That characteristics of ecosystem
structure involving predominantly indirect
influences (e.g., Tables 1 and 2) are now
seen also to contribute to whole system coevolution closes the gap, certainly, between
ecosystem and evolutionary ecology.
Moreover, system level coevolution in response to indirect influences does not conflict with the normal evolutionary mechanism. For indirect effects, wherever they
might originate in the ecosystem, ultimately come to a focus at the point of direct
input contact with the organism, the realized niche. Selection at this locus is by normal mechanisms, and the individual organism is the unit. The environ—
superniche—is the unit of coevolution,
however.
Hutchinson, G. E. 1957. Concluding remarks. Cold
Spring Harbor Symp. Quant. Biol. 22:415-427.
Kuhn, T. S. 1970. The structure of scientific revolutions.
Univ. of Chicago Press, Chicago.
Mason, H. L. and J. H. Langenheim. 1957. Language and the concept of environment. Ecology
38:325-340.
Mesarovic, M. D. and Y. Takahara. 1975. General
systems theory: Mathematical foundations. Academic
Press, New York.
Patten, B. C. 1978. Systems approach to the concept
of environment. Ohio J. Sci. 78:206-222.
Patten, B. C. 1981. Environs: Relativistic elementary
particles for ecology. Amer. Nat. (In press)
Patten, B. C. and G. T. Auble. 1981. System theory
of the ecological niche. Amer. Nat. 118:345-369.
Patten, B. C., R. W. Bosserman, J. T. Finn, and W.
G. Cale. 1976. Propagation of cause in ecosystems. In B. C. Patten (ed.), Systems analysis and
simulation in ecology, Vol. 4, pp. 457-579. Academic Press, New York.
Tilly, L. J. 1968. The structure and dynamics of
Cone Spring. Ecol. Monogr. 38:169-197.
Turvey, M. T. and R. Shaw. 1979. The primacy of
perceiving: An ecological formulation of perception for understanding memory. In L.-G. Nilsson
(ed.), Perspectives on memory research: Essays in honor of Uppsala University's 500th anniversary, pp.
167-221. Erlbaum, Hillsdale, N.J.
Whorf, B. L. 1940. Science and linguistics. Technol.
ACKNOWLEDGMENTS
Rev. 42:229-231, 247-248. In J. B. Carroll (ed.),
University of Georgia, Contributions in
Language, thought and reality; selective writings of
Systems Ecology, No. 53.
Benjamin Lee Whorf. MIT Press, Cambridge,
Mass.
REFERENCES
Wilson, D. S. 1980. The natural selection of populations
and communities. Benjamin/Cummings, Menlo
Elton, C. 1927. Animal ecology. Sidgwick and Jackson,
Park, Calif.
London.
Griffin, D. R. 1976. The question of animal awareness. Wynne-Edwards, V. C. 1962. Animal dispersal in relation to social behavior. Oliver and Boyd, EdinRockefeller Univ. Press, New York.
burgh.
Grinnell.J. 1917. The niche relationships of the California thrasher. Auk 34:427-433.
Zadeh, L. A. and C. A. Desoer. 1963. Linear system
Grinnell, J. 1928. Presence and absence of animals.
theory: The state space approach. McGraw-Hill, New
Univ. Calif. Chron. 30:429-450.
York.