7/25/2019 1987 Equilibrium and Noneequilibrium Models in Ecological Anthropology
1/24
Equilibrium and Nonequilibrium Models in Ecological Anthropology: An Evaluation of"Stability" in Maring Ecosystems in New GuineaAuthor(s): Theodore C. Foin and William G. DavisSource: American Anthropologist, New Series, Vol. 89, No. 1 (Mar., 1987), pp. 9-31Published by: Wileyon behalf of the American Anthropological AssociationStable URL: http://www.jstor.org/stable/678746.
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2/24
THEODOREC.
FOIN
WILLIAM G.
DAVIS
University
f
California,
Davis
Equilibrium and Nonequilibrium Models in
Ecological
Anthropology:
An Evaluation
of
Stability
in
Maring
Ecosystems
in New
Guinea
Three
models
ertaining
o
the
tability f
Maring
cosystems
avebeen
roposed.
he
irst
is
the
local
stability
model,
n which
a
population
eeks
ts own
equilibrium
tate;
the second
s
the
regional
tability
model,
n
which ach
opulation
s
ultimately
nstable,
ut
populationsersist
somewheren space;andthe third s thedisequilibriumodel, n whichneithertabilitynor
population
egulation
s attained.
n the
disequilibrium
odel,
xogenous
actorsprevent
pop-
ulation,
which
s
moving
oward
ome
quilibrium
tate,
rom reaching
t. The
arge
number
f
quantitativenthropological
nd
ecological
tudies
n
Highlands
New Guinea
has not
shown
clearly
which
of
these
hree
models
bestdescribes
eality.
Simulation
f shiftingagriculture
n
New Guinea
hows
hat the
Highlands
ystems
re
equilibrium-seeking,
ut
have uch
imited
recovery
ates
rom
disturbance
hateven
mall
perturbations
re
ufficient
o
keep
hemfrom
each-
ing equilibrium.
When
he
nfluences
f technological
nnovation,
nvironmental
hange,
ndso-
cial-cultural
volution
re taken
nto
account,
he
disequilibrium
odel
s the
model
of
choice.
These
ystems
emain
way rom
their table
quilibrium
oints
most
of
the
ime,
f
those xist
at
all. Thus,New Guinea groecosystemsanbestableor unstable ependingponhowstabilitys
defined.
THE
STABILITY
PROPERTIES
OF
SYSTEMS
n which human
populations
are
a
major
part
have
long occupied
the attention
of
anthropologists
and human
ecologists.
Eco-
logical anthropology
has
moved
from
neofunctionalism,
focused
on
systems
properties
that lead to homeostasis
(i.e.,
stability)
(Vayda
1971;
Rappaport
1984)
to
greater
and
greater
emphasis
on the
effects
of
particular
components
and disturbance
on the behavior
of
the
system
(the
processual approach,
see Orlove
1980).
A
thorough
analysis
of the
stability
properties
of
any system
must
emphasize
the effects of both
stabilizing
and desta-
bilizing
processes.
Harris
(1968:424)
has
emphasized
this
requirement
most
emphati-
cally.
The
study
of
stability
is
not,
however,
a
trivial,
straightforwardprocess.
This has been
true
in
both
anthropology
and
ecology.
One
problem
is that the
term
stability
has
a
number
of
meanings,
some
of
which
are
mutually
exclusive.
Thus,
the definition
of sta-
bility
used
is
clearly
important.
Ecologists
have
progressed
further
than
anthropologists
in
defining
the various forms.
Stability
can mean
(1)
resistance
to
perturbation,
such that the
population
remains at
equilibrium
unless the disturbance
is
severe;
(2)
the
ability
of a
population
to return
to
equilibriumfroma disturbance, no matter how long it may take; (3) the rate of returnof
the
population
to
equilibrium,
following
a
disturbance,
and
assuming
that
(2)
is
true;
and
(4)
recovery
of
a
disturbed
population
to
some,
not
necessarily
the
same,
equilibrium
point.
The first of these
is
commonly
termed
constancy
and is
marked
by
the
minimi-
THEODORE
.
FOIN
is
Professor,
ivision
of
Environmental
tudies,
University
f California,
Davis,
CA 95616.
WILLIAM
G.
DAVIS
s Associate
rofessor,
epartment
f
Anthropology,
niversity
f California,
Davis.
9
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3/24
10
AMERICAN
NTHROPOLOGIST
[89,
1987
zation
of
population
fluctuations;
the second is one form of
qualitative
stability;
the
third
is
quantitative stability;
and
the last is
another form of
qualitative stability
termed
per-
sistence,
or
resilience.
The
opposition
of
constancy
and
resilience is but
one
example
of mutuallyexclusive definitions of stability (May 1975).
A
second
problem
is
that field
investigation
of
stability
is
very
difficult,
since it is
often
impossible
to
know,
a
priori,
what the relevant measures
are,
irrespective
of
the
length
of
investigation
needed to
develop
precise
estimates
of
stability
properties
(for
a
recent
and
fuller
discussion of both of these
issues,
see Connell and Sousa
1983).
The
magnitude
of the field
measurement
problem
has
meant that
many
of the
pioneer-
ing
studies
in
stability analysis
in
ecology
have
placed
heavy
dependence
on
models
and
model
ecosystems
as the
only
tool available for
stability analysis
(May
1974;
Pimm
1981).
This
situation does not seem
likely
to
change
much
in
the near
future because of
the
lim-
itations
of field
ecology.
The study of stability in human ecosystems suffers from exactly the same kinds of de-
fects;
if
anything,
they
seem even more difficult
to overcome.
Ecological
anthropologists
have
been
interested
in
the measurement of
stability
for
some
years
(Moore
1957;
Sahlins
and
Service
1960;
Piddocke
1965;
Vayda
1961, 1969;
Leeds
and
Vayda
1965;
Rappaport
1968,
1979,
1984;
Thomas
1972),
but have not
given
much
attention to
the
details
of
measurement
and definition. Human
ecosystems
are
characterized
by
a
rich,
complex
feedback
loop
structure,
even
in
simple
models
(Forrester
1972),
and
by
limited
human
population growth
rates
compared
to
other
populations. Together,
these two
factors
en-
sure that
it
will
be
very
difficult to
determine what factors
regulate
stability
in
human
ecosystems,
and it
will
take
a
great
deal of
effort to
estimate
stability
with
any
degree
of
precision.
The shifting agricultural systems of Highland Papua New Guinea probablyhave been
studied
by
more
investigators
than
those
in
any
other
place
in
the
world
(Vayda
1971;
Rappaport
1968;
Clarke
1971;
Strathern
1971;
Buchbinder
1973;
Moylan
1973;
Salisbury
1975;
Manner
1977;
Meggit
1977;
Lowman
1980;
Boyd
1985).
The
information
available
for
the
Maring
speakers
is
particularly
rich
and
suitable for an
analysis
of
stability
prop-
erties.
These data
permit
simulations
of
Maring
population
dynamics,
which
enable
us
to
gain
further
insight
into
the
meaning
of
the vast
body
of
empirical
data
that
already
exist. In
turn,
this
leads to
an
examination of
the
stability
properties
of the
simulation
model,
and hence
the
system
itself.
In
this
paper
we
present
an
analysis
of
population
stability
based
on
the
Maring
data. We
begin
by
summarizing
the
key
features of each
of
three
population dynamics models that have been proposed for these agroecosystems,
then
analyze
the
behavior of each
in
an
attempt
to
determine which of
the
three
models
best
describes
the
Maring
data.
The
Maring
Agroecosystem
The
Maring
population
consists of
approximately
7,000
persons
who
reside
in
the
Jimi
and
Simbai
River
valleys
in the Bismarck
Range
of
Highlands
Papua
New
Guinea. The
population
is
organized
into
20 more-or-less
politically
autonomous,
local
groups
which
range
in
size from
roughly
100
to
900
persons
(Rappaport 1968).
The main
zone
of hab-
itation lies
between
1,000
and
2,000
m
and is
characterized as
being
more
heavily
forested
than is usual for similar altitudes elsewhere in New Guinea (Buchbinder 1977).
Shifting
cultivation
is the main
source
of
subsistence,
but
pig
husbandry
and
foraging
also
are
economically
important.
New fields
are
cut from
the
forest each
year.
Fields usu-
ally
are
cropped
for 14
to
26
months,
then
returned to
fallow for
8 to
20
years.
Mature
secondary
forest is
favored for
agriculture
over
primary
forest.
The
major
crops
cultivated
are
taro,
sweet
potato, yams,
manioc,
and
various
kinds of
leaves and
grasses
(Buchbin-
der
1977).
Maring
local
populations
are
(or
were)
characterized
by
a
complex
cycle
of
warfare
and
truce. Each
local
population
frequently
is at war
with
some
groups
and allied
with
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4/24
Foinand
Davis]
EQUILIBRIUM
ND
NONEQUILIBRIUM
ODELS
11
others.
Each
group
is
likely
to
be
involved in a
significant
period
of
warfare
approximately
every
8 to
12
years,
alternating
with
periods
of truce.
The
incidence of
warfare s
regulated
by
the
ritual
cycle,
the
kaiko,
he conclusion of
which
releases
the
group
from
taboos
pre-
venting conflict. The active military phase of the warfare-trucecycle usually persists for
several
months,
then
is terminated when
a
few
casualties have
been sustained
by
each
side.
There
is
disagreement
among Maring
scholars
concerning
the
mortality
levels
associ-
ated with these encounters.
The
most serious
killing
occurs when
one's allies
defect,
thus
allowing
the
numerically
superior
enemy
group
to effect
a
rout. At
those times
killing
is
not limited to
opposing
warriors,
but
is extended to women and children.
Houses,
gar-
dens,
and orchards
are
likely
to be
destroyed
after a
rout,
but
vacated
enemy
lands
are
only rarely
occupied
immediately.
Rappaport
(1968)
reported
that routs are
unusual,
but
both
Vayda (1971)
and Lowman
(1980)
suggested
that
they commonly
are the
eventual
outcome of hostilities.
In
the
past
decade
a
number of
important
changes
have occurred
in
the
Papua
New
Guinea
Highlands.
The intervention
of the Australian administration
in
Papua put
a
temporary
end
to
warfare,
but there are
reports
that
fighting
has resumed since
inde-
pendence.
Working
with the
Awa,
Boyd
(personal
communication)
has
reported
that
wage
labor
in
the lowland
economy
has
been
increasingly
important
in
recent
years,
as
young
men have
emigrated
from their native territories
seasonally
to
work
as
laborers.
Degradation
of
the
forest
in
New
Guinea,
especially
conversion to
anthropogenic
grass-
lands,
is also
reported
to be
widespread
and
increasing
(Robbins
1963).
Models of
Population Regulation
In
this
paper
we
evaluate
the
application
of three
conceptual
models of
population
regulation
to the
Maring
of
New
Guinea. These three models
are
(1)
the
local,
single-
population
equilibrium
model;
(2)
the
regional
population
model,
consisting
of a
collec-
tion of
interacting
groups;
and
(3)
the
disequilibrium
model,
in
which
the
population
is
not
normally
at or even near
equilibrium.
These three models are somewhat
arbitrary,
since
gradations
between
any
two of
them are
easily
found
in
the literature.
However,
these three are
the dominant
models
in
the literature and
they
will
be
analyzed
here.
In
this
paper
a
distinction is made between
model,
which
without
a
modifier refers to
these three
conceptual
models
for
Highlands
populations,
and
simulation,
which
refers
to
mathematical simulation models constructed to test
differences between the
concep-
tual
models.
The
Local
Equilibrium
Model
The
model of local
equilibrium
is
easily
identified
in
the work
of
Rappaport
(1968,
1979),
Clarke
(1971,
1977),
and Buchbinder
(1977).
Each
author
has,
however,
proposed
a
different
mechanism for
population
regulation
within the
context
of
the local
equilib-
rium
model. It is
important
to note that with the
Maring,
local
equilibrium
is not
point-
stability;
fluctuations
in
population
size due to the ritual
cycle
and other
factors
produce
something
closer to a
limit
cycle.
Clarke's
model,
most
explicitly
discussed in his 1977
paper,
is the most
conventional
of the
three,
in that it
proposes
that
population
size is
regulated
by
resource limitation.
Clarke
argued
that
productivity
of the swiddens
would limit
population growth
and
keep
each
local
group
in
equilibrium
with its environment.
He termed the
process
of
equili-
bration with
environment
the structure
of
permanence.
This
idea has also
been
in-
voked for other
groups
elsewhere
(Conklin
1957; Kunstadter,
Chapman,
and Sabhasri
1978;
Dove
1981).
Buchbinder's
(1977)
model also
postulates
an
equilibrium
solution for
the local
group,
but she
argues
that the
regulating
variables are to be
found
in
the
interaction
between
nutritional
status
and disease rather than
in
productivity
alone. In her
view,
each local
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12
AMERICAN
NTHROPOLOGIST
[89,
1987
group
moves
through
a
developmental
cycle
in
which
population
density
varies over
time.
Groups
begin
in a
pioneering,
low-density
phase
in
which
environmental
quality
and
nu-
tritional status
are
high.
They
mature at
a
high-density
phase
in
which
the
forest
envi-
ronment is degraded, productivitydeclines, and nutritional status is poor. As nutritional
status
declines,
the
population
becomes more vulnerable to
malaria,
which is
the
factor
responsible
for
compensatory
mortality.
Buchbinder's
hypothesis
is
based on data
and is
thus
plausible,
although
some authors
(Scrimshaw,
Taylor,
and
Gordon
1968;
Murray
et al.
1978a, 1978b;
Lepowsky
1984;
see also the review
by
Beisel
1982)
have
argued
that
severe malnutrition
will
halt the
growth
of Plasmodium
nd
prevent
a
serious clinical
man-
ifestation
of
malaria.
These
findings
cast some doubt
upon
the
effectiveness of malaria
as
a
mortality
agent
when nutritional status is
poor.
As a
result,
we
examined
the
influence
of
malarial
mortality
on model behavior more
closely.
The
ritual
regulation
hypothesis
of
Rappaport
(1968,
1984)
is
least conventional
but
is the best known of the threediscussed here. His model is based explicitly on ideas about
population regulation
advanced
by Wynne-Edwards (1962).
Wynne-Edwards
argued
that
many
social
animals,
especially
in
their
optimal
conditions,
practice self-regulation
by
assessing
numbers and
consequently limiting
density
to
average
values below
those
which
would
damage
essential resources.
Self-regulated
populations
are
supposed
to
have
one or
more means for
sensing
excess
density
( epideictic signals ),
and
an
effective
group response
for
limiting
further increase
in
density.
Rappaport proposed
that the
key
epideictic
signal
for
the
Tsembaga
Maring
is
the in-
tensity
of
female labor.
In
the
Maring
division of
labor,
females are
principally
respon-
sible for
pig
husbandry.
Women tend the
gardens,
prepare
the
food,
and feed
the
pigs.
These are
labor-consuming
tasks;
Rappaport
estimated that
immediately
before the cer-
emonial pig slaughter that he witnessed, pigs were consuming 80% of the manioc har-
vested and
50%
of
the sweet
potatoes produced
by
the
Tsembaga.
Gardens
were
36%
larger
before the
pig
sacrifice than afterwards. The
intensity
of
female labor is
directly
proportional
to
pig
density
and thus is an
attractively
simple
index of
environmental
quality.
Rappaport
argued
that as
labor devoted to
pig
husbandry
increased,
complaints
about the
workload would
also,
thus
triggering
a
kaiko
as the
only
response
that
could
relieve
the workload. An
incidental,
but
crucial,
consequence
of the kaiko s
that
warfare
usually
resumes
shortly
thereafter.
Thus,
the ritual
cycle
is
a
means for
reducing
both
pig
and human
numbers,
and
hence
pressure
on the
environment and
resources. The time
required
to
rebuild the
pig
herd
to
the level necessaryto support a ritual festival, on the other hand, preventsexcessive war-
fare. The
net result of
the ritual
cycle,
therefore,
is
establishment
of
population
equilibria.
In
higher-quality
environments
pig populations grow
more
swiftly,
kaikos
are held
more
frequently,
warfare
occurs at shorter
intervals,
and war
mortality
is
higher.
In
lower-
quality
environments,
exactly
the
converse situation
holds.
It follows
that the ritual
cycle
is a
homeostat
that
functions to
regulate
the size
of both human
and
pig
populations,
population
dispersal,
nutritional
states,
and
environmental
quality.
Regional
tability,
Local
Instability
Moylan
(1973)
and Lowman
(1980)
are
the
principal
proponents
of
this
model. A
re-
gional
stability,
local
instability
model is based on
the
notion that local
groups
are
un-
stable (neitherpoint stable nor subject to a limit cycle), but that local
populations
persist
in
time
and
space
at
some
points
in
the
region
and
recolonize.
Moylan
developed
a
gen-
eral,
multiple-causation
hypothesis
of
regional-local
interactions,
rather
than a
more
spe-
cific
proposal
for a
group
of
populations.
His
major
contribution was
to
point
out that
local
instability
is a
necessary
feature of
regional
stability.
Indeed,
it is
unnecessary
to
invoke
regional
stability
if local
stability
is
commonplace.
Lowman
developed
a
more
specific
model,
but one
along
the
same lines
as
outlined
by
Moylan.
She
termed her
hypothesis
the
structure of
impermanence,
in
contrast to
Clarke
(1977).
She
postulated
that
individual
populations
exhibit a
developmental cycle
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Foin and
Davis]
EQUILIBRIUM
ND
NONEQUILIBRIUM
ODELS
13
much like
that
portrayed
by
Buchbinder,
but
differs
in that each
population
ultimately
decreases
to local extinction.
A
complete
life
cycle
for
a
population,
estimated
by
Lowman
to
occur
in
approximately
200
years,
begins
with establishment of a small
group
of
mi-
grants in an unused forest environment. With time, the group expands as new migrants
join
it;
when the
group
reaches
a
critical
minimum
size,
it will have established
effective
self-defense and social
rules.
As it continues to
grow,
partly
through
natural increase and
partly
through
continuing immigration,
forest
regeneration
is
impaired
and the resource
base suffers.
Immigration
becomes
emigration,
fewer resources are available to
reward
allies,
and
a
military
defeat becomes
inevitable.
Each
subsequent
defeat worsens the sit-
uation,
as
the
group
no
longer
can
attract
new brides
or
warriors,
until
ultimately
the
group
is routed from
the
land.
The
group
is forced to seek
refuge
at lower altitudes where
malaria is
endemic,
and
which
ultimately
leads to the
extinction of the social
unit
in
the
lowland environment.
Lowman's
regional
stability
model is
plausible
and overcomes
a
number of the objections that have been set against the local equilibrium model
(MacArthur
1974;
Salisbury
1975).
However,
as
Lowman
points
out,
the data needed
to
confirm
her model
do not
presently
exist,
nor
is
it
clear that
they
ever
will,
given
the
long
time frame of
her
hypothesis.
Furthermore,
a
logical
concern about
the model
may
be
raised here: it is not clear
why
a
population
would
not,
while
it
still
possesses
its
greatest
numerical
strength
and
political
power, simply
use
its
position
to annex
higher-quality
territories
occupied
by
weaker
neighbors,
rather
than
resigning
itself to inevitable de-
cline.
The
Disequilibrium
Model
Several students of
Highland
New
Guinea
ecology
have
expressed
skepticism
about
the
validity
of
equilibrium
models (Watson 1965;Salisbury 1975;Golson 1982). The two
alternative states are
nonequilibrium
(which
refers
to the absence of
any
equilibrium
point)
and
disequilibrium
(which
recognizes
the existence
of an
equilibrium
state,
but
argues
that the
system
is seldom
if
ever
in
this
state).
We know of no authors who
argue
for
nonequilibrium
as defined
here. Of those
authors cited
above,
Salisbury
comes
closest
to
presenting
a
comprehensive
qualitative
model for
disequilibrium
for
Highlands
pop-
ulations. He
begins
by
explaining
how cultural
rules and environmental
reality
on which
they
are based
can be
seriously
out
of
phase.
He
argues
that culture consists
essentially
of
sets of
rules,
each of which
may
permit
a
variety
of
behavioral
outcomes,
with no al-
teration
in
the rules themselves.
As
many
aspects
of culture are sensitive to resource avail-
ability, any given set of rules may be expressed in manifold ways, depending upon pop-
ulation
density.
Thus,
retention
of the
categories
of
traditional
culture
by
a
population
may easily
conceal the fact that the
actual behavior associated with those rules has under-
gone
profound
transformation
as
density
or resource
availability
varies.
Having
shown that cultural
stability
does not
necessarily
imply
population
stability,
Salisbury
outlines
a
model to
explain
disequilibrium.
The essence of the model is that
exogenous
inputs,
typically
new
technologies
for
food
production
or more efficient
orga-
nization,
can
be
expected
at
a
frequency
such
that resource limitation
is
rarely
a
serious
factor. Even a
temporary
limitation
serves
mainly
to increase the likelihood of a
techno-
logical
or
organizational
innovation.
Furthermore,
occasional
episodes
of
disease,
war
mortality,
or deaths from other causes occur.
Consequently,
the
population
receives no
selective
pressure
to stabilize.
Salisbury's
model, then,
is a
nonequilibrium
and a dise-
quilibrium
model: the
population
never
reaches
a
true
equilibrium
because of continuous
change,
nor is it
possible
to define what the
equilibrium population
size is-if
indeed
there is one.
Golson
(1982)
has
provided
one
example
of the
impact
of an
exogenous
factor on
the
Maring.
He
showed that the sweet
potato
had
a
dramatic and
lasting
impact
on
Maring
culture,
since it was
so
highly
productive,
was
good
for
feeding pigs,
and could be
grown
at
higher
elevations than
traditional
crops.
The
sweet
potato opened
new environments
and modes of
existence for the
Maring
and is
but
one
illustration of the effects of
exoge-
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7/24
14
AMERICAN
NTHROPOLOGIST
[89,
1987
nous
factors on social
systems.
Other
examples
include
the intervention
of
Australian
authority
and the
introduction of
market
agriculture
and
commercial
forestry
to
New
Guinea.
Using
Simulation
to
Evaluate
Stability
The
empirical
difficulties
associated with the field
assessment of
stability
properties
in
human
ecosystems
suggest
that mathematical models of the
Maring
are
appropriate
tools
for
the
problem.
Mathematical
modeling
of
Highland
New
Guinea
agroecosystems
ad-
dresses both the time
and multivariate
problems,
and
simulating
the
dynamics
of
shifting
agroecosystems
permits experimental
manipulation
of the
simulation.
By
identifying
the
predictions
of
each
stability
model,
it is
possible
to
compare
them
to the
predictions
of
the
simulation
model
in
order to determine which
stability
model best
describes
reality.
The Local Equilibrium Simulation Model
The
Maring
simulation
is
based
upon
a
synthesis
of the
literature,
particularly
Buch-
binder's
work
and
many
of the
provisions
included
by
Shantzis
and
Behrens
(1973)
in
their
simulation. The local
system
is defined as the
population
or
social
group
that
acts
as
a
unit
in
warfare,
and is
most
commonly
seen
as
a
village
or
group
of
villages.
The
causal-loop diagram
for this
system,
displaying
the
main
variables
and their
relation-
ships,
is shown
in
Figure
1. The main
sectors are:
1.
The
population
sector,
which
contains
provisions
for
an
average
net
growth
rate,
death
rates
set
by
war
and
by
disease
mortality,
and
negative
feedback
on birth
rates.
The
major
interactions of
the
population
sector are with the
forest
succession
and the
food
production/diet sectors; the latter mediates the severity of disease mortality. In this
model the
population
was not
disaggregated
by
age
or
sex,
following
the
practice
of
Shantzis
and Behrens
(1973).
Although
we
recognize
that
significant
effects
on the
local
population
are
traceable to
age
and sex
(e.g.,
labor
available
for
specific
tasks),
close
inspection
of the
results of the
simulations
indicated that our
conclusions
about
stability
properties
would not
be affected
by
further
disaggregation
of the
population
sector. For
this
reason,
we
chose not to
do so.
2.
The
forest
succession
sector,
which
tracks
the
composition
of
forest,
forest
produc-
tivity,
productivity
of the
swiddens,
and
changes
in
productivity
and
recovery
rates
de-
pending
on
swidden
practice
and
population
size.
The
major
function of
this
sector is
to
account forchanges in forestsuccession and its impacts upon restoration of productivity.
The
succession
sector is
sensitive to
various
human
actions,
such as
forest
cutting
rate
and
delayed
abandonment
of
gardens.
3.
The
food,
diet,
and disease
sector,
which
translates
productivity
into
caloric
output,
calculates
caloric
availability
per
capita
and sets the
level
of
malarial
impact
on
the
pop-
ulation.
4.
The
pig
population
sector,
the main
functions of
which
are
(1)
to
serve as a
sink
for
some
part
of
the
productivity
of the
system
and
(2)
to
serve as a
trigger
mechanism
for
the
ritual
festivals
characteristic of
Maring
society.
5.
The
festival
sector,
which
is
the
trigger
for a
period
of
warfare
with
neighbors.
In
this
simulation
warfare
never
leads to a
rout from
the
territory;
its
role is
restricted to
being a source of mortality.
The
principal
causal
loops
in
this
simulation were
developed
from a
variety
of
sources,
but
the
simulation
constructed
by
Shantzis
and
Behrens
(1973)
was the
original
source
of
the
structure of
the
program.
This
simulation
was
reprogrammed
without
substantial
change
and its
behavior
investigated
in an
earlier
paper (Foin
and Davis
1984).
Although
the
general
orientation
of
the
original
simulation was
retained,
the
present
one
differs
in
several
important ways:
1.
The
population
sector has
specific
loops
for
malarial
effects.
As
the
populationgrows
and
experiences
declining
food
supplies
per capita,
the
death
rate due
to
malaria in-
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8/24
Foin
and
Davis]
EQUILIBRIUM
ND
NONEQUILIBRIUM
ODELS
15
SWIDDEN
SWIDDEN
PRODUCTIVITY
LANDS
FOOD
SUPPLY FOREST CUTTING
PER CAPITA
DECISIONMAKING
MALARIAL
DISEASE
IMPACTS
HUMAN
POPULATION FOREST
SUCCESSION
DYNAMICS
AND PRODUCTIVITY
WARFARE
FESTIVAL-WARFARE
TRIGGER
PIG POPULATION
DYNAMICS
Figure
1
The
principal
causal
loops
of the
local
simulation model.
The
arrows indicate
the
major
causal
flows
in
the
model.
By
convention,
the variable at
the tail of the arrow has
one
or
more
specific impacts upon
the
variable
at the head of the arrow.
creases as
a
consequence
of
reduced host resistance
and
increased local
endemicity
of the
mosquito
vectors,
following
the work
of Buchbinder
(1973)
and Lowman
(1980).
In
ad-
dition,
malaria
also
reduces
vigor
such that
fertility
and
early
infant
mortality
also
in-
crease
(Buchbinder
1973,
1977).
Malaria acts as a
classic
regulatory
mechanism,
oper-
ating
on
population
density
through
the effects of
dietary
adequacy.
Samuels
(1982)
has
developed
a
simulation
for
the
Maring,
which
also
depends
upon
a
significant
role
for
disease in
population
control.
2.
The
forest
productivity
sector was
completely
reconstructed.
Shantzis
and
Behrens
built
in
strong sensitivity
to
overuse of the
forest
such
that
collapse
was
inevitable
once
forest
degradation
reached
a certain
point.
In
this
simulation
we
have
developed
a
succes-
sional
sequence
in which the forest is
partitioned
into a number of
categories.
Overuse of
the forest
affects
recovery
both
quantitatively
and
qualitatively,
but does not
necessarily
lead
to
irreversible
forest destruction.
The evidence
available on Asian
montane forests
strongly
supports
this
view rather
than the
more
extreme
scenario
put
forward
by
Shantzis
and
Behrens
(Paijmans
1976;
Manner
1981;
Dove
1981).
3.
The forest
succession and
cutting
sector features
explicit decision-making
behavior
absent
from
the
Shantzis-Behrens
simulation. The
behavioral variables include a
pref-
erence
function
for
forest
type
and
age;
limits on
per capita ability
to
clear
forest;
adjust-
ment of
cutting
rate as a
function
of
dietary quality;
and control over
swidden
retention
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9/24
16
AMERICANNTHROPOLOGIST
[89,
1987
and fallow
period
intervals.
According
to the
literature,
flexible decision
making
is
com-
monly
associated
with
shifting
cultivation
(see,
in
particular,
Conklin
1954,
1957;
Dove
1981).
4. The ritual festival-warfarecycle differsbetween the two simulations. Shantzis and
Behrens followed
Rappaport
(1968)
in
utilizing
pig/human
ratios and incidents of
pigs
raiding
gardens
as
ritual festival
triggers.
Both
of
these
triggers depend upon
pigs
becom-
ing
nuisances.
The
present
simulation
views
pigs
as
a valuable
economic
commodity;
the
ritual festival
is
triggered
only
when there
are
sufficient
numbers of
pigs
to
support
an
adequate
festival
(Salisbury
1975;
Peoples
1982;
Boyd
1985).
The warfare
phase
is sub-
stantially
the same
in both
simulations,
differing
principally
in the rate of
mortality
per
episode
(Foin
and
Davis
1984).
Detailed Structure
of
the
Simulation
Model
Population egulation
The
Maring population
grows
or
decays
exponentially
when rates
are fixed. The
equa-
tion
is
(1)
H,
,=
H,+
r-H,-
(D,
+
D)
where
H
is
the
Maring
population,
rH
is
the net
growth
rate,
D.
is the number of deaths
in
the
interval t
to
t
+
1
due to
warfare,
and
Dd
is
the number
of deaths due to
disease.
The
parameter
rHis
calculated from
a
range
of
variables
(-
15%
to
1.5%),
using
a
TA-
BLE function based
upon
dietary
adequacy
and
forest
stocks,
equally
weighted.
Dietary
adequacyis normalizedon 742,000 kcal/capita/annum, the number used by Shantzis and
Behrens. The forest
stock function
is
%
total
mature forest
as fraction
of
total
territory.
Denters
episodically
with warfare
at 3% of
the total
population.
Ddis
also
calculated
with a
TABLE function
based on
dietary
adequacy;
the
mortality
rate
ranges
nonlinearly
from 0.0% to
20%.
There are
no
data
to
support
these
values,
so
they
were
subjected
to
extensive
sensitivity analysis.
Forest
uccession
The forest
succession
sequence
consists
of
three
categories:
mature
primary
forest,
ma-
ture
secondary
forest,
and
immature
forest. The distinction
between
primary
and sec-
ondary
forest is
principally
one
of historical
use:
primary
forest
has
not been
cut within
recent
memory,
while
secondary
forest
is cut on
a
regular
rotational
cycle
(Dove 1981).
Botanical differences tend
to be
quite
minor
(Whitmore 1975).
Immature
forest refers to
early
stages
of
regrowth
and recolonization
of abandoned swidden
plots.
This is estimated
to be 8 to 15
years following
abandonment;
in the simulation the
longer
time was
used.
There is also
provision
for an
anthropogenic
grassland
succession
when
swiddens
are
kept
in
production
too
long.
Succession
is
an
input-output
process
for
any
one
vegetation
group.
In
mathematical
form
succession
is
(2)
F, ,= F,
+
(I
-
O)(t)
where Fis
the
number of acres of
vegetation type
F,
I
is
the sum
of
the
input
rates
(succes-
sion
from less
mature
vegetation types),
and
O
is the sum of the loss rates
(succession
into
the next
higher
category
and losses to
cutting
for
swiddens).
All
vegetation
categories
are
transitory
in this
simulation
except
for
primary
mature
forest,
which
will
persist
indefi-
nitely
in
the absence of
cutting.
Normally
succession is from old swiddens to immature
forest,
as the forest invades
the site.
However,
with extended use of
the
swiddens
(subject
to a maximum of four
years),
some
proportion
of the abandoned swiddens
will
convert
to
anthropogenic
grasslands
typified
by
Imnperata
ylindrica.
f
such
grasslands
are scat-
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10/24
Foin and
Davis]
EQUILIBRIUM
ND
NONEQUILIBRIUM
ODELS
17
tered,
they
represent
only
a
temporary
delay
in
return to forest.
Dove
(1981)
found
that
grasslands
in
Kandep territory
n
Kalimantan
would
be
overtopped
by
forest and
shaded
out
in
four
years).
Under
very
heavy
cutting
rates,
when
acreage
under
total mature
for-
est is depressed,then grasslandsare more persistentas a consequenceof diminished abil-
ity
of the
forest to recover.
Literature
estimates on
succession
rates
are not
very
precise.
Succession
to mature
sec-
ondary
forest was
estimated to be 15
years,
but it could be as
short as
8
years
(Davis
1973;
Sabhasri
1978);
it is
unlikely
to be
very
much
longer
than
20
years.
The
least certain
time
is
for
succession
into
primary
forest,
estimated
in
this
simulation to
require
100
years.
Swidden
Cutting
nd
Decision
Making
In
the
simulation,
swiddens are
cut
according
to
certain
decision
rules. Each
member
of
the
population
is
assumed to share a
preference
function for
forest
type.
Thus,
Iban
areprimaryforest swiddeners (Freeman 1955)while Karen and
Maring
prefersecondary
forest
(Kunstadter,
Chapman,
and
Sabhasri
1978;
Clarke
1977).
The
cutting
preference
for
the
population
is
easily
modeled
by
postulating
various
forms of
relationships
between
the
preference
for
type
and
proportion
of
secondary
in
mature
forest. The
Maring
prefer
secondary
forest
and
will
switch
to
primary
forest
only
when
secondary
forest
is rare
com-
pared
to
the former
type.
This
preference
was
established
using
a
TABLE
function in
the
simulation.
The
acreage
cut
in
the
simulation
depends
upon
dietary
quality
in
the
previous
time
step.
If
the
harvest
(measured
in
calories)
at time t
-
1
is
adequate,
the
simulation
only
replaces
the
swiddens
returning
to forest.
If
caloric
intake is not
adequate,
then
more
forest is cut, subject to a maximum of 0.085 ha per capita which, following Dove (1981),
we
take as the limit
set
by
labor.
This is
an
action
taken to
restore caloric
output
from
the
forest
to
adequate
levels.
Cutting
rates
ultimately
affect the
average
fallow
time for
the
average
plot
of
forest.
Finally,
the
simulated
swiddeners also can
control
the time
period
in
which
they
use a
given
plot
(swidden
retention
time).
This
generally
occurs
simultaneously
with
expansion
of
cutting,
since it is
also
a
function
of
dietary
quality,
subject
to
a
maximum
retention
period
of
4
years.
As
noted
above,
the
longer
the
retention
time,
the
greater
the
subse-
quent
environmental
degradation,
expressed
in
delayed
forest
recovery
and
grass
inva-
sion
of the
swiddens.
Swiddens can
be
cut from
any
forest
type
and/or
from
grassland.
Swiddens from
each
type
are accounted for
separately,
since each
type
has a differentinitial value for
produc-
tivity.
In
the
present
simulation these values
(in
106
kcals/acre/yr)
are
5.2
for
primary
forest,
4.4
for
secondary
forest,
2.2
for
immature
forest,
and
0.5 for
grassland-derived
swiddens.
These
values are
assumed to
hold for
1.5
years,
the
base
value for
retention
time,
but to
decrease as
average
fallow
times
decrease.
This
provision
incorporates
the
effect
of
declining
soil
fertility
known
to affect
swidden
productivity (Nye
and
Greenland
1960;
Sanchez
1976),
although
not
directly.
The
literature
suggests
that
productivity
is a
function
of
vegetative
biomass
(Pelzer
1978;
Harcombe
1977;
Manner
1981).
Pig Populations
nd
Ritual
Festivals
The
pig
population grows
exponentially
at rates
ranging
from6% to
14%.
It will
grow
at
lower rates in
the absence
of human
husbandry,
but
achieves
maximum rates
only
when a
portion
of
garden
produce
is
fed to the
pigs.
The
specific
forms
of
mortality
im-
posed
upon
the
population
are
(1)
a
low annual rate
of
killing
(1%)
for
use as
sacrifices
during
illnesses
and for
those
pigs
caught
raiding gardens;
and
(2)
catastrophic
mortality
(75%
to 90% in
the
literature)
when a ritual
festival
is
staged.
A
ritual
festival is
staged
only
when the
pig
population
meets or
exceeds 100
animals
(an
imprecise
figure
but
ap-
proximately
the same
argued
by
Rappaport
1968).
If
the herd is
slaughtered,
75% of the
herd
is
killed,
the
remainder
being
reservedas a
starter
herd for the
next
generation.
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11/24
18 AMERICANNTHROPOLOGIST
[89,
1987
Simulation
Strategy
The simulation was used to evaluate the inherent
stability
of the
agroecosystem.
Thus,
we constructed the simulation as described above with data taken from the cited litera-
ture,
supplemented
as
needed
by
our own estimates.
The model
output
obtained with
the
best
estimates for
parameter
values is
referred to
as
the baseline
version. Once
the
simulation
was
debugged
and
verified,
it was further modified to
include a
standard
set
of
response
variables
(behavioral indicators),
in
addition to state variables
already
pres-
ent in
the
outputs.
The additional
response
variables are the
derivatives of
selected
var-
iables.
The
simulation
strategy
used was standard for simulations of this
type.
We
compared
the
effect of
a
specified
change
in
simulation structure or
parameter
values
by
comparing
the
response
variables
of
the
experimental
run
to the
baseline,
and
where
appropriate,
by
normalizing using
the baseline
version,
in
a fashion similar
to that used
by
Miller
(1974) and Miller, Butler, and Bramell (1976).
All
runs of the swidden simulation were carried out
using
a
period
of 400
years,
with
integration
step
size of
1
year
and
print/plot
intervals of 10
years.
Simulating Regional Equilibrium
Evaluation of Lowman's
(1980)
regional
stability
model
requires
a
simulation that is
sectored into several local units. The
simplest
model that
accomplishes
this
would consist
of
several local units that are
dynamically
equivalent.
The
regional
simulation was
con-
structed
by
linking
four of the local
equilibrium
models with a
set of
explicit migration
provisions.
Each local unit was
subject
to
immigration
and
emigration
rules
developed
fromLowman's
hypothesis,
i.e.,
when forest stocks were
large
and
productivity
high
in a
given
local
unit,
that
unit would attract
immigrants
from
the
pool
or
potential migrants
from
other
groups.
The
immigration
rule
draws from
the
pool,
and
all
units
with net
outmigration
potential
contribute
equally
to that
pool. Conversely,
when
population
den-
sity
is
high,
productivity
is
down,
and forest
stocks are
limited,
a
local
group
shifts to
net
emigration,
corresponding
to the
hypothesis
that it
loses its
attractiveness
both to
out-
siders
and local
residents.
In
essence,
local
groups
are
attractive when
forest
stocks are
good
and diets
are
adequate,
and
unattractive when
forests
decrease and
dietary
quality
declines.
There
are three
equations
governing migration
behavior:
(3)
PMS(i,t)
=
MF(i,t)/MF(t)
when
PMS is the
propensity
to
migrate
for
an
individual
in
the
ith
group
at time
t,
MF(i,t)
is
the
proportion
of
standing
mature forest in
the ith
group
at
t,
and
MF(t)
is the
total
mature forest in all
groups
at
t;
(4)
CMP(i,t)
=
DT(i,t)*HP(i,t)
where
CMP
is the
contribution of the ith
group
to
the
migrant
pool
at
t,
HP
is
the
popu-
lation
size of
group i,
and DT is
the
proportion
of
the
group
that will
migrate.
DT
is
specifiedas a TABLE function which outputs the proportionof the population that
joins
the
pool
as
a
function of
diet
(range
of
output:
23% to
98%);
and
(5)
M(i,t)
=
PMS(i,t)*MP(t)
where
M
is the actual
number of
migrants
and
MP
is the
size of the
migrant
pool
at
t.
The
migrant
pool
is
emptied
at each
step
of
the simulation
by
allocating
all
individuals
in
proportion
to
the
forest
stock
available
locally.
Simulation
control
parameters
for this
model
were
the same
as for
the local
stability
model
above.
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12/24
Foin and
Davis]
EQUILIBRIUM
ND
NONEQUILIBRIUMODELS
19
Complete
listings
of
both
simulations,
including
lists
of the variable
names,
are
avail-
able on
request
from
the senior
author. The
DYNAMO
language
and simulations
are
implemented
on
the DEC
1173
system.
Results
Behavior
f
the
Baseline
Simulation
Inspection
of
the
outputs
of the
baseline simulation
(Figs.
2-6)
shows
that the
system
is
inherently
stable
with the
parameters
chosen,
in
the
sense that
the derivatives of im-
portant
variables
go
to
zero,
even
though
the
equilibrium
values of
these variables are
not
the same as the
initial ones.
The
Maring
population
initially grows
rapidly, approach-
ing
an
asymptotic equilibrium
at
295
individuals
approximately
170
years
into the
sim-
ulation
(Fig. 2). Simultaneously
mature
secondary
forest
declines
from -700 acres
to
200
acres,
to be
replaced
by
successional
forest
(coded
as immature
secondary
forest,
IMF
in
Fig.
3).
All
vegetation types
reach
steady
state
in
less than 50
years.
The baseline sim-
ulation
predicts
very
little
grassland
invasion into old swiddens because
plots
are
aban-
doned
quickly
enough
to
permit
the forest
to
regenerate
normally. Average
utilization
times
(UT,
Fig.
4)
fluctuate
around
2
years,
which is insufficient to
trigger
much
reversion
to
grasslands.
Return
times
(RT),
defined as
the time between use of
a
particular piece
of
land,
fluctuate more
widely
but seldom
fall
below 15
years.
Both estimates
compare
favorably
to the
literature,
although
RT
may
be
slightly
too
high.
The
derivatives associated
with
population
pressure
on the land
(Fig.
5)
all fall
to zero
asymptotically
or
go
to
a
limit
cycle
as a
consequence
of the
diet-disease
loop.
Disease
incidence rises as population pressureon the forest reduces productivity, and ultimately
forces the
population growth
rate to zero.
In
turn,
reduction of
population
growth
deriv-
atives
permits
the derivatives associated
with
the
state of the forest
(Fig.
6)
to
go
to zero
as
well. The
process
of stabilization
by
increased
impact
of disease occurs
only
after di-
400
P
0
P
U
L
300HP
A
T
I
o
N
S
I
200
z
E
100
0
100
200
300
400
TIME IN
YEARS
Figure
2
The
population
growth
curve
for
the
baseline
simulation.
HP
=
human
population.
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13/24
20
AMERICAN NTHROPOLOGIST
[89,
1987
800
F
0
R
E
- -~ -
. -
- - - . ..--- - -.-
T
600
C
I
v
E
R
400
I
N
A
C
200
EXXX
_X._X
X_
$
R
X
X
X
XXX
X
X
X
Sxxxx
xx
xx
xx
X
xx
x
cp
S
0-
0
100 200
300
400
TIME IN YEARS
Figure
3
Growth curves for four
vegetation types
in
the baseline simulation.
P
=
mature
primary
forest;S = maturesecondaryforest; I = immatureforest;and G = anthropogenicgrass-
lands.
etary
quality
begins
to
fall,
which
means
that
the forest resources are
under increased
pressure
when disease
increases,
in
accord with the field observations
made
by
both
Buchbinder and
Lowman.
Consequently,
most of the
response
measures show
limited
fluctuations as the
system
moves toward
equilibrium
(e.g.,
food
per capita,
return
time,
utilization
time,
and
ephemeral appearance
of
grass
invasions
in a
small
proportion
of
the
swiddens).
The
exceptions
are the behavior of the
pig population,
which is
expected
to show
continuing
variation due to
harvesting
for the
ritual
festival,
and the
group
of
variables associated with quality of the diet. Since the diet variables control system reg-
ulation,
this
variation is to be
expected.
Extensive
simulation with
different values
of the
malarial
mortality
vector
showed that the
critical
rates are
those
operating
when
diet is
80% to
100% of the desired
value.
This is
due to the low
potential
rate of
population
growth;
not
many
deaths are
required
to limit
population
increase,
so even low
mortality
rates
are sufficient.
Thus,
the amelioration of malaria
by
malnutrition
may
be a
real
phe-
nomenon,
but should have
only
limited
effects on the
stability
of the
system.
These
results
suggest
that
local
stabilization is
a
reasonable model for
the New
Guinea
Highlands,
but it is
important
to remember that
the model has
very
limited
ability
to
choose
from the
number of
competing
mechanisms
for
regulation.
Nevertheless,
the sim-
ulation
model
supports
the
feasibility
of malarial
mortality
as
a
control
agent
in
the Mar-
ing
ecosystem,
and
it
rejects
the
Rappaport
model.
The baseline
simulation,
as
well as a
number
of
variants,
all
show that
disease
mortality
is
about ten
times
greater
than
war
mortality
in
the
system.
War
mortality
becomes
important only
under
extreme
condi-
tions. In
the
simulation,
at
least,
it is malarial
mortality
stimulated
by
malnutrition which
imposes
control on
population growth.
Behavior
f
the
Regional
tability
Simulation
Linking
four identical
groups
having
equal territory
sizes
using
simple migration
rules,
in
accord with
Lowman's
hypothesis,
fails to
produce
local
disequilibrium
(Fig.
7).
In-
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14/24
Foin and
Davis]
EQUILIBRIUM
ND
NONEQUILIBRIUM
ODELS
21
30
E220
I
4
I
IY
R
10
IS
TII
E
I
E
0 100
200 300
400
TIME IN
YEARS
Figure
4
Changes
in
return
(RT)
and
utilization
(UT)
times
indicate
changes
in the
stability
of
the
agroecosystem.
Neither return nor utilization time exhibits
any significant
trend.
stead,
all four
groups
converge
to
equilibrium
values
(2-375
persons)
which
are
held
thereafter.Differences
in initial
conditions
do not affect the
final
outcome.
The
failure of the model to
reproduce
the
hypothesized
developmental
cycle
with
the
simple
migration
rules used
can
be
explained
as follows. For
a
group early
in the
devel-
opment,
with low
population
densities
and
abundant
standing
forest,
early
population
growth
will
be
rapid
due to the influx
of
immigrants
from other
groups
with
limited
forest
stocks.
However,
growth
rates
will slow as the
surplus
of
forest is used.
Groups
that
have
reached peak densities and may have begun to decline will experience net emigration,
which
initially
will
accelerate
their
decline;
but as
densities
fall
and forest
regeneration
begins,
the
probabilities
of
emigration
and
immigration
will
converge
and
densities
will
stabilize.
Thus,
it
is
obvious
that each
group
can
be
expected
to reach an
equilibrium
density.
One
way
to destabilize each local
group
would
be
to make
migration
behavior
more
complex.
For
example,
it
is
possible
that
at the
early
phase
immigration
should be
strong,
but
that
at
or after
the
peak population
is
reached,
that
emigration
should be
limited
by
some
combination of social and
political
factors. This
supposition
has
a
problem,
how-
ever;
if
emigration
is
limited,
then that
group
will
remain
large enough
to
survive chronic
warfare
and
will
dominate
neighboring groups
indefinitely.
We
require
emigration
to
weakenthat group relative to others, but emigrationmust cease before that group simply
disperses.
In
any
case,
simulation
of these rules
produces
no
change
in
outcome;
each
group
still reaches a
stable
equilibrium.
We were
unable to find
any
combination
of
mi-
gration
rules that
produces
the desired
cyclic
behavior.
Lowman's
model
embodies the
implicit
assumption
that the resources
controlled
by
each
group
are
approximately equal.
Groups
that are
founded
in
small territories
(lim-
ited,
for
example, by
steep slopes,
small
size,
or low soil
fertility)
should not
be as suc-
cessful as
groups
with
greater
resources,
if
only
because their maximum
population
size
will
be limited. If
the
population
is small
enough
and not
successful
in
gaining
depend-
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15/24
22
AMERICANNTHROPOLOGIST
[89,
1987
15
D
E
R
10
I
\
V
\
A
T
-\R
V
5-
A
L
FP
100
200 300 400
TIME IN
YEARS
Figure 5
Three
system
derivatives:
human
population
growth
rate
(R),
change
in
population
size
(HP),
and caloric intake
per capita
(FPC).
able
allies,
it will be
defeated
in war
sooner
or
later,
never
having
attained
enough
pop-
ulation
and
power
to reach
the
peak
of the
developmental
cycle.
Simulation
of this alter-
native
was
easily
achieved
by
simply
changing
the
parameters controlling territory
size
for each of the four
groups.
The results
of
this
change
(Fig.
8)
show that the
dynamics
of
the
four-group
system
are not
fundamentally
altered,
except
to
change
the
equilibrium
level of each group to reflect the resource base (measuredby territorysize) of each group.
We
also examined the two criteria for
a
rout to occur. The
principal
criterion is that
there be
a
numerical
disadvantage
of about
2:1
for
the
group
in
degraded
forest
(following
Rappaport
1968).
Although
it
was
easy
to simulate
small
groups
they
would not
be de-
feated
routinely
unless their territorieswere so small
that
a
neighbor
in
a
larger territory
could
fulfill
the
2:1
rout criterion most of the
time,
or
nutritional state
so
poor
that
net
emigration
reduced the
population
size to the critical
proportion
compared
to
hostile
neighbors.
The
original
criterion for
emigration
was that
the
average
diet was
only
60%
of
normal,
but
it did not create sufficient
outmigration
to
ensure
a
defeat. When
the sim-
ulation
model was
changed
to
permit
outmigration
at
90% of normal
caloric
intake,
routs
did occur, but far too frequently to permit a newly founded, small group to undergo the
hypothesized
developmental
cycle
(Fig.
9).
The
village
with
the smallest
territory
cannot
grow large
enough
to
escape frequent
routs
by
its
larger
neighbors,
while the other
three
groups
are
unaffected. This
points
out how sensitive
the
dynamics
of
the
cycle
are to
small
differences
in
parameters.
This
analysis
casts
doubt
upon
the
veracity
of
Lowman's
hypothesis
as a
model for
Maring
population dynamics.
There
must
exist
conditions under which a
200-year
cycle
can
occur,
but
they
are
empirically
unrealistic.
Our
simulations show
that,
as
intuitively
appealing
as
Lowman's model
is,
it
is not
very
likely
to
exist
in
nature.
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16/24
Foin
and
Davis]
EQUILIBRIUM
ND
NONEQUILIBRIUM
ODELS
23
20
D
E
R
10
I
V
A
-
UT
I
*
*
.
.
.
0
- -
-
- -
-
-_- - - - -
- -.
.
-
.
..
.
.
-
-.--
-M.-
-
E PSL
V
A
L
U
E
-10
E
PSF
-20-
0
100 200
300
400
TIME
IN
YEARS
Figure
6
System
derivatives for
UT, RT,
and PSF
(%
secondary
forest).
500
P
400
L-D
T
B
0
N
-
/
200 C/
S
I
0-
D
0
100
200
300
400
TIME
IN
YEARS
Figure
7
Population
growth
curves for
four
villages
with
initial
values of A
=
450,
B
=
300,
C
=
150,
D
=
20.
This content downloaded from 185.2.32.141 on Fri, 20 Jun 2014 18:14:34 PMAll use subject to JSTOR Terms and Conditions
http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp7/25/2019 1987 Equilibrium and Noneequilibrium Models in Ecological Anthropology
17/24
24
AMERICAN
NTHROPOLOGIST
[89,
1987
D
P
0
P
U
4
00
A
A
E
II I
N
s
I 200
z A
100 200
300
400
TIME IN
YEARS
Figure
8
Behavior of the
regional equilibrium
simulation model
with
the
same initial
populations,
but also with differences in territory sizes. Territory size of A = 400 acres, B and C = 1,000,
and
D
=
1,600.
Estimates
fReturn
Times n theLocal
Simulation
Model
Elasticity,
or
return
time,
may
be defined as the time
required
for selected
response
variables
to return to their
equilibrium
values
after a
perturbation
of known
timing
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