1987 Equilibrium and Noneequilibrium Models in Ecological Anthropology

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



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



5/24

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



6/24

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-



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-



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



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-



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.



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.



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.



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-



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-



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.



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.



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

Documents

1987 Equilibrium and Noneequilibrium Models in Ecological Anthropology