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URBAN POPULATION DENSITY
GRADIENTS IN PORT OF SPAIN,
TRINIDAD

BY
Mary Bliss Seepersad

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF ART

Department of Geography
1982

ABSTRACT

URBAN POPULATION DENSITY GRADIENTS IN
PORT OF SPAIN, TRINIDAD

BY

Mary Bliss Seepersad

This Thesis attempts to reveal the existence of a city
which shows a transition between the non-western and western
urban population density patterns. Using regression tech-
niques, both the Clark and Newling Models will be tested as
to their fit in Port of Spain. The data needed was pOpula-
tion density by district, distance to the city center and
distance squared. The analysis of this data using both of
the models mentioned above, showed that it is possible to
identify a transition density pattern. This is of particu-
lar significance since the trend in developing and develOped
nations is not dichotomous over time, but rather reflects
the changing needs of the city as economic development pro-
ceeds. The work done in developed nations will prove to be
a valuable source of information for planners and policy
makers of the developing world in the planning, directing,
ameliorating and anticipating the direction which urban

growth will take.

DEDICATION

To my father and mother who

stood by me.

ii

ACKNOWLEDGMENTS

This thesis would not be complete if I did not recog-
nise the assistance given to me by many individuals. Among
them are Kathy Frohnert who worked on the maps and figures
used in this research and Jo Cornell who typed the finished
product. Of special note are Dr. Joe Darden and Dr. Bruce
Wm. Pigozzi under whose guidance this thesis was written.
Special thanks must go to Dr. Pigozzi.who patiently went
through the numerous draft copies I produced -- your encour-
agement, comments and criticisms were deeply appreciated as
it encouraged me to work that much harder. In addition to
the assistance given to me by these individuals, I must also
thank my sister Dawn, for her help in the laborious tasks
of copying out the raw data I needed from those dusty vol-

umes of statistics.

iii

LIST OF
LIST OF
LIST OF
Chapter

I.

II.

III.

IV.

TABLE OF CONTENTS

TMLES C O O O O 0 O O O O I O O O O C O
FIGURES O O O O O O O O O O O O O O O O O

MAPS O O O O O O O O O O O O O O O O O 0

INTRODUCTION. . . . . . . . . . . . . . .
The Problem. . . . . . . . . . . . . .
The Models . . . . . . . . . . . . . .
Transition Density Patterns. . . . . .
Hypotheses and Thesis Overview . . . .
Footnotes. . . . . . . . . . . . . . .

STUDY AREA AND FACTORS AFFECTING DENSITY

FUNCTIONS . . . . . . . . . . . . . . . .
Age of City and Mode of Development. .
Timing of Development. . . . . . . . .
Density Gradient . . . . . . . . . . .
Preference for Central Locations and

Non COngested sites. . . . . . . . .
Dicotomy of Patterns . . . . . . . . .
Footnotes. . . . . . . . . . . . . . .

DATA PREPARATION AND METHODOLOGY. . . . .
Data Preparation . . . . . . . . . . .
Areal Computation. . . . . . . . . . .

Distance Computation . . . . . . . . .
Generation of an Objective Surface . .
Limitations. . . . . . . . . . . . . .

Footnotes 0 O O O C O C O O O O O O I 0

RESULTS OF THE STATISTICAL TESTS. . . . .

Restatement of Hypotheses. . . . . . .
Clark Model- . . . . . . . . . . . . .
Explained Variance . . . . . . . . . .
Deviant Areas. . . . . . . . . . . . .
New Regressions. . . . . . . . . . . .
Footnotes. . . . . . . . . . . . . .

iv

Page
Vi
vii

viii

Chapter
V. CONCLUSIONS . . . . . .
Recommendations. . .
Footnotes. . . . . .
APPENDICIES
I. Data Sources. . . . . .
II. Areal Computation using

III. Data Base . . . . . . .

BIBLIOGRAPHY . . . . . . . . .

Page’
63

67
70

71
72
75
77

LIST OF TABLES

Page

Rate of Decrease of Population From the
City Center Outwards 1960-1980 . . . . . . . . . . 41

Parameters of Equations. . . . . . . . . . . . . . 43
F-test and R2 for the Two Models . . . . . . . . . 46

Areas Over estimated and Under estimated by
the Clark and Newling Models . . . . . . . . . . . 49

Changing Values of the Parameters, F-test
and R2 O O O O O O O O O O O O O O I O O O O O O O 5 9

vi

LIST OF FIGURES

Figure Page

1. Temporal Comparison of western and
Non-Western Cities . . . . . . . . . . . . . . . 10

2. Central Density Over Time in Port of Spain . . . 40

3. The 1960, 1970 and 1980 Residential
Density Curves for Port of Spain and its
Suburbs [Newling Model]. . . . . . . . . . . . . 42

4. The 1960, 1970 and 1980 Gross Residential
Density Curves for Port of Spain and its
Suburbs. . . . . . . . . . . . . . . . . . . . . 45

5. Gross Residential Density Curves for
Port of Spain and its Suburbs: 1960,
1970 and 1980 (123 Observations, Newling
Model. . . . . . . . . . . . . . . . . . . . . . 60

vii

LIST OF MAPS

Study Area - Port of Spain and its Suburbs

Residuals from Regression of Log of Density
with Distance from the CBD - 1960. . . . .

Residuals from Regression of Log of Density
with Distance from the CBD - 1970. . . . .

Residuals from Regression of Log of Density
with Distance from the CBD - 1980. . . . .

Residuals from Regression of Log of Density
with Distance and Distance Squared - 1960.

Residuals from Regression of Log of Density
with Distance and Distance Squared - 1970.

Residuals from Regression of Log of Density
with Distance and Distance Squared - 1980.

viii

Page
19

51

52

53

54

55

'56

CHAPTER I
CHANGING URBAN POPULATION DENSITY OVER TIME

In the recent years since the mid 1940's, geographers
have begun to examine the processes of urbanization and urban
growth. One aspect of these processes has been the changes
in the spatial distribution of the urban p0pulation over time.

It has been suggested that differences exist in the ur-
ban population density patterns which are characteristic
of "Industrial" and "Pre-Industrial"1 or "Western" and "non-
Western"2 cities. These studies have tended to focus on
the cities of the industrially advanced Western nations and
their findings are of considerable value in the planning
and promotion of the orderly growth of cities. However, the
-topic of the spatial distribution of the urban p0pulation
in the developing nations has suffered from a lack of atten-
tion. In addition, quite often the findings of studies
focused on the Western nations has been deemed inapplicable

to the cities of the develoPing world.3

Insight into the
distribution of urban population densities in the developing
nations is needed.

Works on the pattern of urban population densities

seem to suggest that the trend observed in developed and

developing nations is dicotomous. If nations move from an
underdeveloped to a developed state, it is contended that

the pattern of urban population densities should also appro-
ximate the pattern observed in Western nations, as the devel-
opment process proceeds. As such there should be cities
which incorporate features of the density patterns observed
in both developed and developing nations -— an example of a
transition from one stage to another. This Thesis attempts

to reveal such a city which shows this transition.

The Problem

If the disparity in the pattern of urban population den-
sities between developed and deve10ping countries does exist,
the findings of the studies concerned with urban density
gradients in advanced nations will be of limited value for
the developing nation. However, if it can be shown that the
trend in developing and develOped nations is not dicoto-
mous over time but rather reflects the changing needs of the
city as economic development proceeds, the work done in de-
veloped nations will prove to be a valuable source of infor-
mation for planners and policy makers of the deve10ping world
in the planning, directing, ameliorating and anticipating
the direction which urban growth will take. As such it is
my purpose to identify the existence of a transition be-
tween the western and non-western urban population density
patterns through an analysis of the changing form of the ur-
ban density pattern over time in the city of Port of Spain

and its suburbs. The existence of a transition between the

two patterns will be said to exist if features associated
with both types of urban population density structures can

be identified.

The Models
The differences in intra-urban population densities

has been a subject of much attention especially since the
work of Colin Clark in 1951.4 The mathematical model devel-
oped by Clark describes the relationship between population
density and distance from the center of the city or Central
Business District. This model states that the spatial dis-
tribution of population densities within cities appear to

conform to the following equatiOn.

where
D = population density at distance x
from the city center
D = population density at the city center
b = density gradient [indicating a negative
exponential decline]

e = the base of natural logarithms.

The value of the density gradient slope (b) indicates
the rate of change in population density with a unit change
in distance (x), when the equation is log transformed. If

the absolute slope value is large, this is indicative of a

rapid decline in population density as distance from the
Central Business District [CBD] increases. A city with a
large SIOpe value would be compact and relatively limited

in spatial extent. [A small absolute slope value would in-
dicate a dispersed and spatially extensive city.]5 A popu-
lation density gradient is a line showing both the population
density at varying distances from the center of the city and
the rate at which population density decreases as distance
from the city center increases.

Clark's model has undergone a series of applications,
evaluations and revisions. These revisions have been aimed
at making the model approximate reality move closely. How-
ever, the general linear's relationship specified by the

equation
ln Dx = ln DO-bx (2)

which is derived from (1) by performing a logarithmic trans-
formation on the density data has been found to be represen-
tative of the distance decay function associated with popu-
lation density in cities around the world.

The first revisions proposed independently by J. C.
Tanner and G. G. Sherratt6 suggested that urban population
densities decline exponentially as the square of distance

where

D = D e (3)

This modification is inadequate as a general rule as it as-
sumes that

"The instantaneous rate of change of den—

sity with distance at the center of the

city is zero and does not recognize the

possibility that the instantaneous rate

of change of density at the center can be

either positive [as when density first

rises and then falls with increasing dis-
tance from the city center] or negative."

8 extended the basic negative exponen-

Bruce E. Newling
tial model by the addition of distance squared [x2] as an ex-
planatory variable. This variable takes into account the
likely fall in population density at the heart of the city
when business and commercial activities preclude these same
sites as locations of residence. Newling's model takes the
following form:
ebx-cx2 (4)

DX = Do

_ _ 2
ln Dx — 1n Do+bx ex (5)

where

ln D the logarithm of the population density
at distance x from the center of the city
ln D = the logarithm of the population density
at the center of the city
b = a parameter which measures the change in

density at the center of the city

a parameter which measures the change in

0
I!

density away from the center of the city.

It has not been decided whether Newling's model is su-
perior to Clark's in terms of data conformance.9 Hideaki
Ishikawa undertook the formulation of a new model in an iso-

10 His model attempts to take into

lated, hypothetical city.
consideration the centrifugal and centripetal forces which
influence population movements in urban areas. Ishikawa also
attempts to present a model for the daytime [or working popu-
lation] and residential population density distributions to
derive the density crater seen in large metropolitan areas.
However, Ishikawa's model was not applied to an actual city
and as such, in this instance cannot be used as the Clark

and Newling models have been to establish the existence of

a transition between Western and Non-Western density patterns.

Bruno De Borgerll used the basic Clark model in the study
of surburbanization in Belgium. However, unlike the research
discussed thus far, De Borger was concerned with the influ-
ence of income and transport costs on the changing values of
the parameters of the urban pOpulation density functions.

The spatialLysystematic relationship between urban
population densities and distance revealed by the Clark and
Newling models have withstood time. However, it has not been
determined whether the Newling or Clark model is superior
in terms of data conformance - this depending on the city
being examined and its develOpment history.

Two major findings of Clark's model have been the sub-

ject of much discussion. First, where the model has been

used to derive population density gradient parameters for a
given city at different points in time, both the b values
[slope term] and a values [central densities] have been found
to differ. These differences have been taken to be indica-
tive of an increase in the spatial extent of the city and

changes in the concentration of p0pulation in the center of

the city.12

In addition to this Harry W. Richardson noted that:

"Apart from the observation that b becomes
smaller over time [the suburbanization ef-
fect], there has been little systematic
analysis of the behavior of Do and b in
conditions of urban growth. Intuitively,
population growth may be expected ceteris
paribus to increase densities everywhere
and to extend the boundaries of the city,
but this might be associated with either
a higher or lower b. Income growth [asso-
ciated with economic development] will
tend to flatten b, if the demand for space
is income elastic and because higher in-
comes allow households to spend more on
travel. When income and population change
simultaneously, the consequences for
urban spatial structure may be very com-
plex."1

Second, when the density gradient of cities in the eco-
nomically advanced and developing countries have been com-
pared 0ver time, the density gradient slopes for "Western
cities" tend to decrease in value, indicating a suburbani-

14 of the city along with an in-

zation or "decompaction"
crease followed by a decrease in central densities suggest-
ing a deconcentration trend. Slope values for developing
countries on the other hand, have been found to remain rela-

tively constant over time while central densities have

continued to increase. The situation in deve10ping countries
is indicative of overcrowding [increasing central densities]
and urban expansion without suburbanization in the Western
sense. Figure 1 illustrates the differences between "Western"
and "non-Western" cities in terms of density gradients and

central densities over time.

Transition Density Patterns

I contend that the pattern theorised by Berry Simmons
and Tennant for non-western cities will not be found in its
pure form for Port of Spain as:

i) Trinidad is now among the ranks of the more
developed of the less developed countries -
implying that the country is progressing to-
wards greater economic development. Ideally
this process should continue until Trinidad

is considered to be economically advanced.15

ii) In the process of growth, urban centers should
undergo a transition from old morphological
and functional patterns, derived from the
Spanish and British colonial rule, to patterns
commensurate with the goals and capabilities
of the nation's economic plans.

iii) It would seem that to apply the term "non-

western" to the city of Port of Spain is a

mis-nomer, as, Port of Spain is, strictly

speaking not a non-western city.

Figure‘l: Temporal Comparison of Western and Non-
Western Cities.

[Source: B.J.L. Berry, J.W. Simmons and R.J. Tennant,
"Urban Population Densities: Structure and Change,"
Geographical Review, 53, 1963, pp. 403.

10

 

 

 

 

 

 

Western Non-Western
L09 L09
Density Density
3 3
1 2 1 2
Distance Distance

(time periods 1. 2. 3...)

Central Central
Density Density

 

 

 

 

Time Time

 

Figure 1. Temporal Comparison of Western and Non-Western Cities

 

11

iv) It is hypothesized by the researcher, that
the pattern of urban pOpulation densities is
not dicotimous; one pattern in less devel-
Oped nations and another in advanced coun-
tries. Rather, there should be an interme-
diate_pattern as the country moves towards
the ranks of the economically advanced stage
of economic development. Just as there is
a continum of examples of countries at vari-
ous stages of economic deveIOpment, there
should also be a continum of urban density

patterns.

As such, Port of Spain should be an example of a tran-
sition from the non-western to the western urban density pat-
tern. Through an examination of the urban density pattern
in Port of Spain for 1960, 1970, and 1980, it is anticipated
that features of both the western and non-western models
will be found which would support the contension that the
city represents an "intermediate pattern," a hybred which can-
not be strictly classified as either a "western" or "non-

western" pattern..

Hypotheses and Thesis Overview
This study is an attempt to identify a transition be-
tween the dicotimous western - non-western density patterns.

To this end the following hypotheses will be tested.

12

H1 - The rate of decrease of population density from the
central city or "city proper" outwards has decreased

over time between 1960 and 1980.

H - The pattern of urban population density in Port of
Spain is indicative of the city's transition from a
"non-western" type of city to a "western" type, incor-

porating features of both.

H1 - Those areas whose population density is either under-
estimated or over estimated by the density functions,
can be regarded as indicative of the co-existence of
old morphological urban structures with the new as the

city develops.

The following chapters present a more detailed descrip-
tion of the study area - Port of Spain, the data needs and
preparation, and statistical analysis involved in the test-
ing of the hypotheses. Chapter II introduces the study area
and deals with the factors influencing the form of density
functions. Chapter III covers the data needs and manipu-
lation necessary to carry out this study. The final chap-
ter presents the results, conclusions and recommendations

based on this study.

10.

11.

12.

13.

13

Footnotes

G. Sjoberg, "The Pre-Industrial City," American Journal
of Sociology, 60:5, 1955, pp. 438-445.

 

B.J.L. Berry, J.W. Simmons and R.J. Tennant, "Urban
Population Densities: Structure and Change," Geographi-
cal Review, 53, 1963, pp. 389-405.

 

Berry, Simmons and Tennants, op. cit.

Colin Clark, "Urban Population Densities," Journal of
the Royal Statistical Society, ll4:A, 1951, pp. 490-
496.

Colin Clark, op. cit.

J.C. Tanner, "Factors Affecting the Amount of Travel"
and G. G. Sherratt, "A Model for General Urban Growth,"
cited by Bruce E. Newling, "The Spatial Variation of
Urban Population Densities," Geographical Review, 59:2,
1969, PP. 243.

Bruce E. Newling, ibid, pp. 243.
Bruce E. Newling, op. cit, pp. 242-252.

H. Morikawa, "The Spatial Distribution and Changing
Pattern of Urban Population Density: A Case Study of
Hiroshima City," Journal of Geography, 85, 1976, pp.
237-254.

Hideaki Ishikawa, "A New Model for the POpulation Den-
sity Distribution in an Isolated City," Geographical
Analysis, 12:3, 1980, pp. 223-235.

Bruno De Borger, "Urban P0pulation Density Functions:
Some Belgian Evidence," Annals of Regional Science,
13:3, 1979’ pp. 15_24e

Colin Clark, cp. cit. A. Guest, "Population Suburban-
ization in American Metropolitan Areas 1940-1970,"
Geographical Analysis, 7:3, 1975, pp. 267-283. Ishikawa,
op. cit.

 

Harry W. Richardson, "A Note on the Dynamics of POpu-
lation Density Gradients," Annals of Regional Science,
10:3, 1976, pp. 15.

14.

15.

14

Berry, Simmons and Tennants, Op. Cit.

W.W. Rostow, Stages of Economic Growth: A Non-Commu-
nist Manifesto, Cambridge University Press, Cambridge,

 

1960.

CHAPTER II
STUDY AREA AND FACTORS AFFECTING DENSITY FUNCTIONS

The city of Port of Spain and its suburbs was chosen as
being representative of a city in the developing world which
would display a transition from the non western, underde-
veloped density structure to a western type of urban popula-
tion density form. The population in the city and its suburbs
has increased from 134,105 in 1960 to 255,345 in 1970 and
287,075 in 19801 which represents a 47.48% increase between
1960-1970 and 11.05% between 1970-1980. The changing dis-
tribution of population density over time and space will be
examined to reveal the existence of a "hybred" density form.

The models which have been discussed thus far, have con-
sidered three variables in describing the differences in the
form of density gradients in different countries: - central
population density, distance and distance squared. In con-
sidering Port of Spain as an example of a city displaying a
transitional density form, it would be falacious not to take
into consideration other factors which have been put for-
ward to account for the differences in the form of density
gradients.

While Clark believes that differences in Transportation

15

16

systems are the reason for the disparity bewteen Western
and Non-Western cities,2 Berry, Simmons and Tennant dis-
agree. They contend that sociocultural differences between
"western" and "non-western" societies affect the demand for
land, with non-western societies preference for central city
residential location reducing the demand for land on the

3 These preferences restrict the horizontal growth

periphery.
of cities so necessitating increasing central population den-
sities.

However, Berry, Simmons and Tennant did not take into
consideration the fact that the Western pattern is not ex-
clusively western nor non-western exclusively non-western.
For example,4 New York had a constant density gradient from
1910 to 1940; Brisbane, Australia and Christchurch, New
Zealand had increasing central densities with almost con-
stant gradients from 1933 to 1947 and 1936 to 1951 respec-
tively: Poona, India had a non-western pattern between 1822 -
1881 followed by declining central density and density gra-
dient and Okayama, Japan revealed a "western" pattern of
urban density change from 1939 to 1953. Thus, the notion of
dicotimous density patterns for developed and developing na-
tions has been subject to serious question.

Using the city of Port of Spain as a case study, I
hope to be able to show that features of both a western and
non-western type city can and does co-exist over time and

space. This would in effect take the argument for the non—

exclusivity of the western - non western dicotomy a step

17

further by identifying features of both types of cities in
one city over time. Such a city would be an example of a
hybred or "transitional density type."
Four major factors have been cited as affecting cen-
tral density gradients over time and space: -
i) Age of city and mode of development
ii) The controlling influence of timing of deve10p-
ment on subsequent form
iii) The density gradient
iv) Centrality preference and a preference for non-
congested sites by the resident population.5

Using these four factors it is possible to structure the

description of Port of Spain and its suburbs.

Age of City and Mode of Development

The original city of Port of Spain was established by
the Spanish as a port and administrative center. In the Span-
ish tradition, as distance from the core of urban activity ’
increased, the social and economic status of the residents
decreased. This stemed from a desire by the more prominant
citizens to be near to the seat of power, and the access to
paved highways and services that such a location gave them.
Such "relic" low density areas continue to exist today close
to the CBD, where according to the Clark and Newling models,
population density should be high.

In addition to this is the dying practice of entre-
preneurs living on the premises of their business establish-

ments in the CBD. As these entrepreneurs leave the central

18

city, their movement out is reflected by declining central
densities. The repelling influence of lower socio-economic
groups on the location of elite residence is also reflected
in the location of the elite St. Clair area and the poorer
East Dry River on either side of the CBD as shown on the

map of the study area [Map 1]. These patterns will influence
the density gradients on either side of the central city

area.

' Timing of Development

The form of the city is the result of its "laws of
growth up to that moment" [Growth creates form, but form
limits growth].6 Once a city has been established, the form
it takes dictates its future development. In the case of
Port of Spain, the importance of this is brought out by the
co-existence of features of the original Spanish form and a
more Anglo-American type of urban development today around
the original city structure. In some instances the force
of sentimental attachment and tradition are strong enough
to perpetuate patterns which would otherwise not continue
to exist. The physical form of the heart of the city was
established in the past and continues to exist as it would
appear to be the most expedient policy to follow at the pre-
sent. To institute a radical change in the distribution of

population could involve undesirable social dislocation.

19

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20

Density Gradient

Central Density is related to the density gradient
which is in turn influenced by a variety of additional fac-
tors such as the size of the city, pattern of residential
location displayed by the higher and lower socio-economic
groups in the city. In Port of Spain, over tima there. has
been a reversal of the situation where the most affluent
favour a location close to the center of the city and the
less well off being delegated to the periphery, to one simi-
lar to North America [i.e. wealthy suburbs and poorer class-
es close to the center]. However features of the older
trend still exist along with the wealthy elite who move out-
wards to the periphery of the city, and poorer classes 10-
cate close to their place of work in the CBD.

Model assumptions of a circular city and the city center
located at the center of the circle is somewhat idealistic.
Few cities conform to these assumptions as asymmetry, lop-
sidedness, elongations and crenulations are common. Theoreti-
cally, density gradients should decrease as shape distor-
tions increase, implying that areas which would normally be
occupied by certain levels of densities are no longer avail-
able. Thus residents who prefer these densities must move
outwards to the nearest available sites.

Port of Spain is not a circular city - rather it is
linear in form. This is a reflection of the relationship
between urban structure and intra-urban transportation,7

and the influence of the Northern Range on the north and by

21

the ocean and swampy land to the south, which is shown on
Map 1. Population density in this urban area, decreases
with increasing distance from the CBD having a directional

bias or long axis.8

Thus Port of Spain and its suburbs

will have an elliptical rather than a circular pattern of
urban densities - which is typical of oceanside [or lakeside]
cities.9 The movement outwards by residents to sites with

prefered residential densities has the effect of also flat-

tening the density curve over time.

Preference for Central Locations and Non-congested Sites
10

 

Emilio Casetti has shown that a central preference
and a preference for non-congested sites can account for the
exponential decline of residential densities with distance
from the city center. This would hold where individuals

are free to maximize their locational utility; and when a
collective maximal locational welfare is enforced provided
that the places of work are sufficiently clustered around the
city center.

However, in a real world situation, individuals are not
free to maximize their locational utility as there are many
factors to be considered which could force a suboptimal lo-
cation. These factors include such things as economic and
physical constraints.

Dennis Conway11

has found that Port of Spain and its
suburbs is atypical in that the high rent areas [such as St.
Clair, Ellerslie Park and Federation Park] did not pull the

growth of the entire city in the same direction. Rather,

22

the city grew to the east by "leap frogging" low grade bar-
riers such as East Dry River and Morvant to the available
land beyond. [Valsayn is a product of this process.] In
addition, the middle class areas of the north-west [Maraval]
and north-east [St. Anns and Cascade] have maintained their
middle class exclusivity. This growth by a leap frogging
process has resulted in a discontinuous development of the
suburbs as "hostile" areas are avoided. These areas are

generally swampy or steeply sloping and show up on Map l.

Dicotomy of Patterns

Bearing in mind the differences noted between Western
and Non-Western cities with regard to the relationship be-
tween population density and distance from the city center,
it is expected that the population density models will re-
veal the existance of deviant areas. These deviations re-
sult from the transitional stage that Trinidad is going
through, local detail and the influence of the factors dis-
cussed above. This suggests that there should be a reflec—
tion of the economic growth and development in the pattern
of urban population densities. For eXample, population
density at the center of the city should decline as a result
of the predominance of business and commercial activities
at the center. [in keeping with an increasing specialization
of land use as development proceeds.]

With the intension of confirming or refuting the views

12

of Berry, Simmons and Tennant; John E. Brush analyzed the

patterns of Indian intra-urban population distribution in

23

several cities. Berry et al. theorised that non-western
and particularly Indian cities have a pattern of urban growth
characterised by rising residential concentration in the
city center concurrently with outward expansion and peripher-
al population increase. The pattern Brush observed differ-
ed depending on whether the city was an indigenous one or a
"British" city. This points to the existence of non-western
and western type patterns at the same time in one country.
The distinction made here depends on a difference in culture
and functions as accounting for the difference in population
density patterns. In the case of the Indian cities, Brush'
found that a non-western pattern was characteristic of the
indigenous cities while the western pattern typified the
cities established by the British - so pointing to cultural
factors as underlying the differences observed.

Like Brush, I am also concerned With the distinction
drawn by Berry, Simmons and Tennant. Through an analysis
of the changing form of the density gradients and the exis-
tence of "mis-fit" areas in one city - Port of Spain and its
suburbs, I will show that there are not two separate pat-
terns which can be expected for "western" and "non-western"
areas (or cultures). Rather, there should be a movement
from a non-western pattern to a western pattern as economic

growth and development proceeds.

10.
ll.

12.

24

Footnote 5

 

Based on data aggregated from the enumeration districts.

Colin Clark, "Transport - Maker and Breaker of Cities,"
Town Planning Review, 28, 1957-58, pp. 237-250.

A similar pattern existed in Spanish colonial cities -
see for example Ernst Griffin and Larry Ford, "A Model
of Latin American City Structure," Geographical Review,
70:4, 1980, pp. 397-422.

Bruce E. Newling, "Urban Population Densities and Intra-
Urban Growth," Geographical Review, 54, 1964, pp. 440-442.

Berry, Simmons and Tennant, op cit., pp. 396-399 and
Emilio Casetti, "Urban Population Density Patterns: An
Alternative Explanation," Canadian Geographer, 11, 1967,
pp. 96-100.

Berry, Simmons and Tennant, op. cit., pp. 394.

D.E. Boyce, "The Effect of Direction and Length of
Person Trips on Urban Travel Patterns," Journal of'
Regional Science, 6, 1965, pp. 65-80.

Kingsley E. Haynes and Milton I. Rube, "Directional Bias
in Urban Population Density," Annals of the Association
of American Geographers, 63:1, 1973, pp. 40-47.

 

Haynes and Rube, op. cit.
Emilio Casetti, op. cit.

Dennis Conway, "The Use of Remote Sensing to Investi-
gate Structural Change in Social Area Differentiation
in Port of Spain, Trinidad," paper presented at the
4th General Session of the Conference of Latin Ameri-
canist Geographers, Calgary, Alberta, June 27-30, 1073.

John E. Brush, "Spatial Patterns of Population in Indian
Cities," Geographical Review, 58:3, 1968, pp. 362-391.

CHAPTER III

DATA PREPARATION AND METHODOLOGY

In order to illustrate the existence of a city which
shows a transitional density pattern over time, it is neces-
sary to obtain population density figures over time for the
variOus districts and their distance from the city centers.
This data can then be analysed using regression techniques
to illustrate the changing form of the density gradient over
space and time. This chapter is concerned with the neces-
sary data manipulations and methodology used in the analysis

of population density in Port of Spain and its suburbs.

Data Preparation

To analyse the changing form of the urban population
density functions over time for Port of Spain and its suburbs,
it is necessary to obtain data for each enumeration district.
The data needed to conduct this study consists of the popu-
1ation density by districts and the distance from each dis-
trict to the city center. In addition the density at the
city center was also needed. The raw data used in this study
were obtained from the Central Statistical Office in Port
of Spain, Trinidad. The pOpulation by enumeration districts,

was obtained from the census reports of 1960 and 1980.

25

26

[The figures for 1970 were included in the 1980 report.]1
The boundaries of the sub areas in this study were defined
on the maps of the census enumeration districts for 1960
and 1980.

Port of Spain was chosen as it represents a city which
Berry, Simmons and Tennant would have classified as a "non-
western" type of city. [Non-western being synonymous with
underdevelopment.] However, over time, Port of Spain has also
displayed some of the features associated with a western type
city - such as the development of a suburban, professional
elite, increasing specialization of land use particularly
in the CBD and the movement to the periphery of the CBD
[as opposed to the city as a whole] of the poorer classes.

As such features of a western and non-western city should
be found in Port of Spain and its suburbs.

This city was chosen because data was available for
1960, 1970 and 1980 - which incorporates a time period when
the country was considered to be very underdeveloped. It
also covers the period following the economic development
and growth fostered by the oil crisis of the early 1970's.

As such, not enough time has passed to completely obliterate
the old "non-western" morphological structure, yet changes
associated with economic development have had time to es-
tablish themselves. A second reason is my own familiarity
with the study area which would aid in the explanation of

the deviant cases and density pattern.

27

Areal Computation

 

Having obtained a map of the study area and the popula-
tion for each district for 1960, 1970 and 1980, it was ne-
cessary to calculate the area of each of the districts. This
was done using a Polar Planimeter with a fixed pole arm and
adjustable tracer arm. The technique used was measuring
with the pole outside the figure. This method is a common,
simple and precise method of measuring areas.2 The computed
areas of each of the enumeration districts were used to de-
rive the gross residential densities of each of the spatial

units.

Distance Computation

 

To calculate the distance between each of the spatial
units and the central city, it is necessary to determine a
point in each district from which the distance to the cen-
tral city could be determined. To this end, the "center"
of each unit was derived by assuming the mid point of the
longest radial across the areal unit would serve as the "center
of gravity." As the study area as a whole is linear in form,
a cursory examination of the main road network suggested
that the road network did seem to have an effect on the shape
of the composite units. Thus, by using the mid points of the
longest radials as the reference points, the effects of trans-
portation on the urbanization and suburbanization process

is indirectly incorporated.

28

Generation of an Objective Surface

An inspection of each of the districts revealed that
the area of each of the units varies considerably [from 52
acres to 620 acresB]. As such, if the density at only one
point for each area were to be used, this would underestimate
the effect of the larger units and over estimate the smaller
units.

Robinson et al. and Latham and Yeates4 noted that apart
from the variation in the size and shapes of the spatial
units, there is also a data mix [i.e. the density of an area
is taken to be the density at a point within that area].
Thus, an objective surface was generated to serve the same
purpose as Robinson et al. and Latham and Yeates' hexagonal
grid. A hexagonal grid was not deemed to be appropriate in
this instance because of the linearity of the area - a pro-
duct of the relief of the area and reinforced by the trans-
portation network.

An objective density surface was generated using den—
sity isolines interpolated from the initial reference points.
It is possible to generate a density surface based on the
supposition that density is not a discrete but rather a
continuous phenomena over space.

The surface which was generated had to take account the
discontiguous portion of the map. [These discontinuities
also prevented the imposition of a hexagonal grid to achieve

an objective surface.] The "empty" areas were treated as

having zero population density on either side of the

29

intervening area could be represented. The exclusion of the
intervening areas from the enumeration districts also gives

a more accurate representation of the population density
pattern as the areas are not considered within the boundaries
of the defined urban area.

New surfaces were generated for 1960, 1970 and 1980.
Once this was accomplished, a stratified sample of points
was taken at 0.25 inch intervals on the density surface.
[1250 feet or 0.237 mile intervals on the ground.]. The
density at each of the 138 points which were generated from
this process, was interpolated from the imposed surface.

An examination of the original data in Appendix III re-
vealed that the pattern of population density distribution
around the central city is not symmetrical. This is parti-
cularly evident in the eastern portion of the study area.
The areas concerned are St. Augustine, Tunapuna, Trincity
and Arouca. These four areas were drOpped from the study
area as it was believed that the density patterns in these
areas reflected the presence of a university campus in
St. Augustine, the airport at Piarco and the third most im-
portant city in Trinidad; Arima.

The imposition of the unbiased density surface allowed
me to objectively increase the number of observation units
from 27 to 138. Had I considered only the original data
points, it is believed that the small number of observations
could have forced the acceptance of the null hypotheses in

the statistical analysis. [A small number of observations

30

would imply that the consequent F statistic would have to
be correspondingly larger, if the relationship being examined
is to be considered statistically significant.]

The distance of each of the 138 points [generated from
the stratified sampling process], from the center of the
central city was calculated as the straight line distance be-
tween the two points. Once this was done, this completed
the basic data set needed to begin the regression analysis,

using the Statistical Package for the Social Sciences.5

Limitations

It is expedient at this point to go through the limita-
tions of this study - given the methodology used. First,
the city of Port of Spain and its suburbs is smaller than the
metropolitan areas to which population density models have
been applied. This size factor may influence the amount of
variance in the distribution of population density captured
by the models. Typically, in a larger metropolitan area, the
larger sample of density points allows the existence of de-
viant cases to be averaged out. The influence of the

2 value be-

deviant areas in Port of Spain will lower the R
cause of their relative number and strength of their devia-
tion given the actual number of sample points.

Second, the distance measurements are straight line
distances, as opposed to the distance over the transporta-
tion network or travel time. Thus the distance measurements

do not take into account the effects of congestion which

would tend to increase the perceived distance from the city

31

center as.congestion increases. By increasing the perceived
distance to the center of the city, this could affect the
density gradient away from the center.

Third, this study does not take into account the effects
of the possible emergence of secondary centers in the suburbs
over time. Secondary centers could exert some influence on .
the population density around them, resulting in a layer-
ing of influence.6 However it is not the purpose of this
Thesis to identify such secondary centers, rather I am con-
cerned with identifying a transitional density pattern using

regression techniques.

Methodology

The SPSS package was used to determine the transfor-
mation of densities and distances for each of the "density
points." The regression equations which were considered are

as follows:

Clark Model

_ -bx
Dx - Doe

log of Density = log of Central Density -b.distance

[1n DX = 1n Do-bx]

32

Tanner and Sherratt Model

 

2
_ -bx
Dx-Doe

log of Density = log of Central Density -b.distance2

_. _2'
[ln DX — ln Do bx ]

Newling Model

 

2
_ bx-cx
Dx - Doe

log of Density = log of Central Density + b.distance -
c.distance2

_ _ 2
[ln Dx — ln Do+bx cx ]

7 in their appli-

Robert F. Latham and Maurice H. Yeates
cation of Newling's model, believe that it is the b parameter
which is especially useful, since it can take a negative,
zero or positive value, thus permitting the representation
of all possible changes in the density gradient at the center
of the city. They discovered that in time the model increas-
ingly approximates Clark's linear model and it is the b
parameter which is of greater importance, not the c. In
addition to this, an examination of the Tanner and Sherratt
model shows that to include this model as a separate model
would be redundant, since the Newling model incorporates the
exponent of their model. By setting b = o, the Newling

model is in effect transformed to the Tanner and Sherrat

Model. Similarly, by setting c = o, the Newling model is

33

transformed into the Clark model, given the flexibility of

the b parameter.

Regression Assumptions

Before the statistical analysis can be carried out cer-
tain assumptions as related to the transformation sof the
equations must be met.8 First, the model is an intrinsicly
linear, non-linear one which allows the transformationtbee
done. Second, the independent variables are independent of
each other, if not multicollinearity exists. Multicollinearty
can be eliminated by the inclusion of other variables or the
exclusion of variables. Third, the conditional distribution
of the residuals from the regression has a mean of zero and
is normally distributed. Fourth, the residuals are serially
independent of each other and their covariance is zero.
Fifth, it must be born in mind that when the original equa-
tion is log transformed, to return to the original form
when interpreting the results, the error term will be a multi-
plicative not an additive one. As designed this thesis satis-
fies the critical assumptions laid out above. Having satis-
fied the assumptions of the methodology used, it is possible
to proceed at this point to the formulation of the formal
hypotheses of this research and interpretation of the coef-
ficients of the equations used.
Interpretation of Coefficients and Formulation of
Hypotheses

The SPSS regression package will be used to provide

the coefficients of each of the equations for 1960, 1970 and

34

1980. [This programme also determines the significance of
both the equations and individual parameters.] Based on the
results produced using both the Clark and Newling models,
because of an inability to establish the superiority of either
one of the two models in terms of data conformance;9 I will
plot the density gradients which are significant at the 90%
and/or 95% confidence level. These graphs together with a
plot of the central density over time will be used in the
confirmation, rejection or modification of Clark's conclusion
concerning nations - that the rate of decrease in pOpulation
density with increased distance from the city center while
the central density has increased.

The formal hypotheses regarding the coefficients of

the equations are:

Clark Model

 

It is expected that b will be significantly less than zero
as this will be in keeping with a decline of density away

from the center. That is H1:b<o; Ho:b=o.

Newling Model
The hypotheses regarding the coefficients in this case will
be more complex, as the coefficients should differ depending
on whether they apply to western or non-western cities.
Thus, the hypotheses regarding the statistics in this in-
stance become a test of the western - non—western notion.

If the city is a non-western type of city the b para-

meter will be negative, while the c parameter will be either

35

zero or positive depending on the degree of curvative of

the density curve. Thus the resulting hypotheses are

H1: b<0, H0: b=o
H1: c>0, H0: c=0.

In the event that the city is a western type city the b

and c parameters will differ from that expected in a non-
western city. In this case the b parameter is expected to
be positive, indicating the presence of a density crater
around the city center. The c parameter should be negative
indicating the increasing curvative of the density surface'

away from the density crater. Thus the hypotheses are:

H1: b>0; H0: b=0
H1: c<0; H0: c=0
Residuals

 

To complete the argument for a transitional density form,
it is necessary to construct maps of the residuals or errors
from the equations calculation of the population densities
for the districts. An examination of the most deviant areas
will confirm the co-existence of features of both a "western"
and "non-western" type city, which in itself points to the

existence of the hypothesised transitional stage.

Summary of Techniques and Hypotheses
The regression technique used in this thesis has been
used to establish the existence of a transitional form of

urban population density distribution. To this end the

36

following hypotheses will be tested:

The rate of decrease of population density from the central
city outwards has decreased over time between 1960 and 1980.
If Port of Spain is in effect an example of a 'transitional
city,’ there should exist areas whose density is extremely
over or underestimated by the density functions. A discus-
sion of these deviant areas will be conducted with the aid
of maps of the residuals from the regressions. Based on the
findings of this research, a case for the transition from

a non-western to a western type density pattern will be put

forward.

1.

37

Footnotes

A list of the Sources of the data used in this study
is given in Appendix I.

Areal computation explained in Appendix II.
See Appendix III.

A.H. Robinson, J.B. Lindberg and L.W. Brinkman, "A
Correlation and Regression Analysis Applied to Rural
Farm Population Densities in the Great Plains,"
Annals of the Association of American Geographers,
51: , 1961, pp. 211-221. Robert F. Latham and
Maurice H. Yeates, "Population Density Growth in
Metropolitan Toronto," Geographical Analysis, 2,
1970, pp. 177-185.

henceforth refered to as SPSS.

Daniel A. Griffith, "Evaluating the Transformation from
a Monocentric to a Polycentric City," Professional
Geographer, 33:2, 1981, pp. 189-196.

Robert F. Latham and Maurice H. Yeates, 0p. cit., pp.
179.

Michael A. Poole and Patrick N. O'Farrell, "The Assump-
tions of the Linear Regression Model," Transactions of
the Institute of British Geographers, 52, 1971, pp. 145-
158.

 

Hideaki Ishikawa, 0p. cit., pp. 224.

CHAPTER IV

RESULTS OF THE STATISTICAL TESTS

The statistical tests performed were done with the in-
tension of assessing the performance of the two models -
Clark's and Newling‘s in capturing the changing form of the
urban density curves for Port of Spain and its suburbs.
Systematic departure from the densities predicted by the
models should indicate the reasons for the failure of the
models to fit the study area. The existence of deviant areas
may be attributed to factors relating to the transitional
stage of city is going through. The existence and explana-
tions for the deviant areas together with the form of the den-
sity curves predicted by the models will support the argu-
meat that there is a transition between the western and non-

western type of city as demonstrated by Port of Spain.

Raestatement of Hypotheses

The hypotheses which will be tested are:

i) H - The rate of decrease of pOpulation density from

1
the central city or City Proper outwards has de-

creased over time between 1960 and 1980.

38

39

ii) H1 - The pattern of urban population density in
Port of Spain is indicative of the city's
transition from a "non-western" type of city
to a "western" type, incorporating features

of both.

iii) H1 - Those areas whose pOpulation density is either
underestimated or overestimated by the density
functions can be explained by factors other
than the central density and distance from the

center.

An explanation of the more relevant factors influencing the
density levels in these areas will support the existence of
a hypothesised transition density pattern.

Figure 2 shows the change in the central density over
time for the central city. The decline in central density
noted here is atypical of the "non-western" city as des-
cribed by Berry, Simmons and Tennant. One can infer that
the central density had increased to some critical level of
crowding and that since 1960, the central density has been
declining.

The rate of decrease of the population from the CBD
outwards over time is best indicated by the slope parameter
of the Clark and Newling model. Table 1 shows the changing
value of b over time for both models. The comparison of
b's from the Clark and Newling models is done based on the

hypothesised similarity between these parameters in a

40

 

 

 

 

80 .
60 ‘
Central
Densfly
40 :
20 a
o I I T
1960 1970 1980
Year

 

Figure 2. Central Density Over Time in Port of Spain

 

41

"non-western" type city.

Table l - Rate of Decrease of POpulation from
the City Center Outwards 1960 - 1980

 

 

Clark Model Newling Model
Years b value b value
1960 -0.330 -1.475
1970 -0.l78 0.177*
1980 -0.096 0.241*

 

[* not significantly different from zero at the 90% or 95%
confidence level]

As can be seen from the values shown above, the rate of
decrease of the population has not remained constant over time
which is similar to the western type of city discussed by
Berry, Simmons and Tennant. The fact that b is positive in
1970 and 1980 using Newling's model is perhaps indicative of
the replacement of the residential population by commercial
activities. This together with the declining central den-
sity makes for the appearance of a "crater" in the density
surface. This is inkeeping with the increasing specializa-
tion of land use within the "western" type city as economic
development progresses. That is, competition for sites
at the city center by commercial users drives up the economic
rent of the sites beyond the means of the residential users -
hence forcing them to move out. "Competition for sites at
the city center ultimately causes a crater to form in the
population density surface, and this stage of development in

volves a positive b parameter."1

42

 

 

 

 

4 .-
3 . 1960
Log
Density 1980
2 - 1970
1 _,
I T I . l I
o 1 2 3* 4 5

Distance from CEO in miles

 

 

 

Figure 3 . The 1960, 1970 and 1980 Residential Density Curves
for Port of Spain and its Suburbs (Newling Model)

Using the Newling Model, the results for 1960 indicate
a population density pattern typical of "non-western" cities.
Figure 3 shows that the curve is concave to the origin with
a hypothetical central density of 132 persons per acre. The
central density is derived by taking the antilog of the inter-
cept term. The slope of the curve is —1.475 which indicates
a rapid decline in population density with distance. This
rapid decline from the center indicates that business and com-
merical activities have not yet replaced the residential popu-

lation.

43

The quadratic curve for 1970 indicates that the cen-
tral density has now fallen to a hypothetical 31 persons per
acre. At this time b = +0.12 and c = -0.06, indicating that
a density crater has formed around the central city and the
density curve is now convex to the origin. However, neither
the b or c parameter is significantly different from zero
at the 90% confidence level. The results of the quadratic
equation for 1980 using Newling's model are not significantly
different from zero at the 90% confidence level.

One of the problems with using Newling's model may be
the intercorrelation of the two independent variables [x and
x2]. As such an accurate representation of the individual
regression coefficients for each variable may not be possible.
This problem can be overcome by the inclusion of additional
data or variables may be excluded from the model. The omis-

sion of distance squared [x2] from the Newling model trans-

forms it to the Clark model.

Clark Model.

 

 

Table 2: Parameters of Equations
Clark Model Newling Model
Variables 1960 1970 1980 1960 1970 1980

 

Intercept (a) 3.096 3.753 3.656 4.119 3.489 3.355
(0.164)(0.134)(0.143) (0.267) (0.233) (0.248)

Distance (b) -0.330 -0.178 -0.096 -1.475 0.117* 0.241*
(0.058)(0.047)(0.050) (0.251) (0.219) (0.233)
Distance2(c) 0.233 -0.060* -0.068*

(0.050) (0.043) 0.046

*not significantly different from zero at the 90% confidence
level.
figures in parentheses are standard errors.

 

44

The regression using Clark's model produced a signifi-
cant equation for 1960 [at the 99% confidence level], with a
hypothetical central density of 124 persons per acre. A
slope of -0.33 indicates, as the Newling model did, a rapid
decline in population density with distance, as business
and commercial activities have not pre-empted the residential
population.

The density curve for 1970 exhibits a less steep de-
cline in density away from the CBD as the slope term has in-
creased to -0.178. This is inkeeping with a declining rate
of decrease of population density with distance. This equa-
tion'and the parameters are all significantly different from
zero. However the 1970 figures have indicated an increase
in the central density over the 1960 level which is not an
accurate representation of reality.

The 1980 curve exhibits a decline in the central den-
sity to 45 persons per acre. As in advanced western nations
the rate of decrease of density away from the central city
has slowed. This is associated with the increasing commer-
cial orientation of the city proper; along with increasing
population density in the surrounding area which was captured
by the Newling model.

As is typical of the results using Clark's model in
"western" type cities, Figure 4 shows that there is a pro-
gressive flattening of the curve over time as the density
gradient decreases over time. This is indicative of greater

relative growth at the center, implying that the center is

45

 

 

 

 

4 d

3 r . 1980
Log .

. 1970

Density

2 d

1 . 1960

o . 1 2 3 , 4 5

Distance from CEO in miles

 

 

Figure 4 . The 1960, 1970 and 1980 Gross Residential Density

Curves for Port of Spain and its Suburbs

approaching or has approached saturation level as far as
residential densities are concerned and the move to the
suburbs is increasingly the dominant trend in residential
development. This is inkeeping with the increased separa-
tion of place of work and residence [a common feature of
economically advanced nations]. Income growth associated
with economic development tend to flatten the density curve
if the demand for residential space is income elastic.
.Higher income allows households to spend more on travel.

When income and pOpulation change simultaneously [as in the

46

real world], the consequences for the urban spatial struc-
ture may be very complex. This will be seen to be the case

when the deviant areas are examined.

Explained Variance

 

Table 3 shows the F-test and R2 for both the Clark and

Newling models over time. The F-statistic is an indication
of the statistical significance of the relationship described

2 indicates the amount of

by the regression equation. The R
variance of the dependent variable [ln Dx] explained by all

of the independent variables.

 

 

 

 

 

Table 3: F-test and R2 for the Two Models

Clark Model Newling Model
Year F-test R2 F-test R2
1960 32.65566 19.248 29.74605 30.432
1970 14.32080 9.464 8.16268 10.717
1980 3.62916 2.581 2.92507 4.124

 

While the relationship described by the regression equa-
tion. is statistically significant, an examination of the
R2 over time, shows that the amount of variance in the resi-
dential densities explained by all the independent variables
falls off very quickly. This is inkeeping with the exis-
tence of complexities in the pattern of population densities.
Other researchers have usually found that the R2 value is

much higher, indicating a greater degree of explanation of

the density pattern using distance raised to some exponent.2

47

The lower-R2 values found in this case is inkeeping with the
existence of complexities in the population density patterns
as a result of the transition nature of the city's density

2 are also inpart, a function of the size

pattern. The low R
of the city. Other researchers using large metropolitan
cities have found that there is a density "generalization"
which occurs because of the sample size. This "generaliza-
tion" is not evident in Port of Spain.

The complexities refered to above stem from several fac-
tors - some of which have been mentioned previously: age
of city and mode of development, the form of the City in the
past and present. Traditional patterns continue to exist
along with newer patterns of development. For example, in
the city of Port of Spain, St. Clair and East Dry River are
approximately the same distance from the city center, yet
their socio-economic and density patterns are totally dif—
ferent - St. Clair being a traditional, elite residential
area while East Dry River is a destination area for the
poorer, rural-urban migrants.

The linear distortion of the city influences the shape
of the density curve. Areas which would normally be occupied
by certain levels of densities are not available. Thus,
residents who prefer these densities must move outwards to
the nearest available sites. This process is indicated by

the "leap frog" process by which the middle class suburbs

have developed.

48

The Government impacts on the pattern of residential
densities in the planning and location of housing schemes
[particularly low income housing schemes which are usually
associated with higher density levels.] The existing form
of the city limits the available areas for locating these
projects, hence as transportation has improved over time,
the need to locate these projects closer to the CBD has de-

creased.

Deviant Areas

It must not be forgotten that there are deviant areas
which are not explained by the model. The existence of these
deviant areas support the hypothesised co-existence of fea-
tures of both the "western" and "non-western" type of cities.
A comparison of the areas overestimated and underestimated
by the models will strenghten the contension that the form
of both the Clark and Newling models do not adequately de-
fine the population density in those areas.

Table 4 shows a great deal of similarity between both
models. An examination of the maps of the residuals from
the b regressions reveals that the models generally over-
estimate density to the west of the CBD and underestimates
it to the east. This reveals one of the problems associated
with the assumption of the Clark and Newling models - that
the density curve is symmetrical about the CBD. The over
and underestimation of density in this case indicates that

the actual curve is not symmetrical about the CBD.

49

 

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50

Traditional elite residential areas such as St. Clair,
persist today. This particular area is close to the edge of
the old city and developed particularly during the cocoa
boom of the late 19th century. Today it is the area in which
the heads of the Anglican and Roman Catholic churches,
government ministers and members of the diplomatic corps
reside. This in itself allows the perpetuation of this elite
residential area and acts as a magnet for similar deve10p-
ment around it.

Ellerslie Park and Federation Park are also areas of
elite residences, which exist in this case as a result of
government policy. Many of the homes in this area are owned
by the government and serve as residences for members of
Parliament, the judiciary and defense force.

The existence of areas such as Ellerslie Park, Federa-
tion Park and St. Clair are an indication of an inherited
Spanish tradition where the more affluent favour a residen-
tial location close to the center of the city but are also
repelled by the poorer east side. Less well off individuals
are delegated to the periphery of the city [at that point in
time]. However, Port of Spain has grown to the east by leap
frogging established low grade barriers [East Dry River and
Morvant] to the available land beyond.

In the tradition of a colonial city the elite residents
have also established themselves in the foothills of the
Northern Range in areas such as St.Anns, Cascade and Dieyo
Martin. The aesthetics of these areas [open spaces, fresh

air, varied landscape] are appealing to those who can afford

51

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57

to develop the lands for residential use. Diego Martin I

and Valsayn have developed particularly since the 1960's and
into the 1970's in the style of western type suburban deve10p-
ment. This development was particularly enhanced by the im—
provements in the highway network in the 1970's.

The areas immediately to the east of the CBD which are
underestimated co-incide with destination areas for rural-
urban migrants. As a result of the limited availability
of public transportation facilities, it is necessary for
these individuals to live in relatively close proximity to
the major employment center represented by the CBD. Mount
Lambert represents an area of great overcrowding because of
the prevalence of squatter settlements assocaited with the
fringe of a minor commercial center - San Juan. In addition,
Mount Lambert is an area in which there are several low in-
come government housing estates. These housing estates are
ultimately supposed to house the squatters. However, the
squatter settlement is growing faster than the government
can build adequate shelter for them.

Upper and lower Santa Cruz represents examples of local
detail. These areas are discontiguous regions which con-
stitute part of the suburbs of Port of Spain. Upper Santa
Cruz is in fact part of the rural landscape. The area be-
tween Upper and lower Santa Cruz is devoted to market gar-

dening to supply part of the food requirements of the city.

58

New Regressions

 

The Results thus far have confirmed the expected find-
ings that Port of Spain and its suburbs are characterised
by a declining rate of decrease of the density gradient
over time. The central density has also fallen over time.
However, the low R2 values and lack of significance of the b
and c parameters for 1970 and 1980 using the Newling model
points to the existence of areas whose density levels can-
not be explained in terms of the general expected pattern.
In addition to this, the failure of both the Clark and Newling
models to explain the density levels in the same areas point
to the need to seek other reasons to explain the density
patterns of the most deviant areas. This would suggest that
by removing those areas whose estimated densities are be-
yond three standard deviations of the mean error term [the
errors should be normally distributed], the level of explained
variance in the density patterns should increase. Based on
this, the following areas were removed from the data set:
Mount Lambert, Upper Santa Cruz, Ellerslie Park, Federation
Park, part of St. Clair, part of Maraval and part of Diego
Martin. This reduced the data set from 139 to 123 observa-
tion points. The results using the Newling model are shown

on Table 5.

59

 

 

Table 5: Changing Values of the Parameters, F-test
and R2.
Year Log 00 b c F-test R2
1960 4.19 -1.46 0.2232 37.90 38.71
(0.25) (0.23) (0.0465)
1970 3.65 ‘ 0.13* -0.0790 30.68 33.83
(0.17) (0.16) (0.0314)
1980 3.47 0.13 -0.1088 16.26 21.32
(0.19) (0.18) (0.0367)

 

*not significantly different from zero
figures in parentheses are standard errors

A comparison of the results of this regression with the
findings shown on Table 3 show a marked improvement in the
explanation of variance of the dependent varible by the
independent variables, while preserving the trend previously
described. The density curves are shown below.

The results for 1980 in this instance are of particular
interest. Distance as an explanatory variable which was
significant only at the 58% confidence level for 1970 is
now signifiCant at the 90% confidence level. These results
are encouraging, as they suggest that over time, the Newling
model may give a good indication of the urban population
density patterns [with some special exceptions] in the
Port of Spain area.

The fact that it is the Newling model which gives the
best approximation of the density patterns in Port of Spain

and its suburbs is particularly interesting as it is this

60

 

 

 

 

4 -
3 —I
“’9 1960
Density
2 .—
1980
1 - 1970
i I I T i
o 1 2 3 ‘ 4 5

Distance from CBD in miles

 

Figure 5. Gross Residential Density Curves for Port of Spain and its
Suburbs: 1960, 1970, 1989m(123 Observations, Newling Model)

 

61

model which is able to capture the formation of a density
crater at the city center associated with the land use
specialization found in western type cities. In addition,
it has been shown that the central density has declined
over time as has the rate of decrease of the slope of the
density curves - also associated with western type cities.
However, there are some areas which did not conform with
the predicted density patterns, as they more closely re-
flect features of a "non-western" type city. The following
chapter will expand on these findings and attempt to anti-
cipate the future trends in Port of Spain based on these re-

sults.

62

Footnotes

 

Latham and Yeates, op. cit., pp. 180.

see for example, Latham and Yeates, 0p. cit., pp.
De Borger, op. cit., pp. 20; Brush, op. cit., pp.

184;

CHAPTER V

CONCLUSIONS

It was the objective of this research to identify a
transitional density pattern between western and non-western
type cities. Using Port of Spain as a case study the re-
sults presented in Chapter IV, does support the arguement
for a transitional density form rather than dicotimous
density patterns depending on Whether the city was western
or non-western. In general, population growth in cities may
be expected to result in increased density levels over time,
while the central density falls to make room for the in-
creased specialization of commercial land use in the city
center. This in turn causes a ridge of increased density
to form around the density crater associated with the city
center.

Income growth associated with economic development tends
to flatten the density curve, if the demand for space is
income elastic - a higher income allowing households to
spend more on travel. Such a trend has been seen in Port
of Spain as reflected in the changing distance decay para-
meters and the actual density curves for 1960 - 1980.

Where both income and population have changed simultaneously,

63

64

the consequences for urban spatial structure can be very
complex.

Berry, Simmons and Tennant believe that western and non-
western type cities differed in the way in which central
density and the rate of change in density over distance
changed through time. The contrast between western and non-
western type cities was said to be the result of different
patterns of residential location displayed by higher and
lower level socio-economic groups in the city. However, in
the case of Port of Spain, the preference patterns of the
wealthy and poorer groups have not remained static. Rather,
they have increasingly approximated the preference patterns
seen in western cities; while at the same time retaining
some of the features of a colonial city. For example, tra—
ditional wealthy residential areas close to the city center
[St. Clair] co-exist with suburban elite residential areas
such as Valsayn.

Port of Spain is characterised by high-values of 00'
or high levels of overall congestion, while having relatively
flat values of b [or a population which is widely distri-
buted around the CBD.] The suburbanization process which
has taken place in this city involves a great deal of de-
concentration [outward movement away from the CBD as indi-
cated by the density curves] and decongestion [decreases
in the central density levels]. Along with this western
type trend, in some areas such as St. Clair and East Dry

River which are approximately the same distance from the CBD,

65

very different density levels have persisted over time.
St. Clair has continued to exist as a wealthy residential
area partly because of the sentimental attachment of the
families to this area, and also as a result of the govern-
ment's desire to preserve the character of the area adja-
cent to the Queen's Park West as an area of historical and
architectural interest.1

The contrasting high density levels in East Dry River
is a reflection of the poverty of the area, haphazard sys-
tem of land tenure, large numbers of squatters and the area's
proximity to employment opportunities in keeping with their
economically disadvantaged position. Areas such as East
Dry River and Cocorite [both of which have similar socio-
economic status] have continued to exist to a large extent
because of the continued rural-urban migration process.
The majority of these migrants to urban areas are young
adults. As such the long term contribution of internal mi-
gration to urban population growth and density is actually
much greater than just the number of in-migrants. The des-
tination areas of these migrants have tended to remain the
same because of family ties in these areas and employment
opportunities in the informal economy which help the recent
migrant to adjust to a foreign urban environment and life-
style.2

Environmental stress generated by the encroachment of

commercial land use on residential areas such as New Town

and Woodbrook, over time has led to a net out migration of

66

residents as they are no longer able to compete with commer-
cial uses for sites in these areas. It is very probable that
the displaced residents from these areas are part of the
urban to suburban migration flow.

The co-existence of elite residential areas such as
St. Clair, Ellerslie Park and Federation Park close to the
CBD with western type suburban elite areas such as Valsayn
on the periphery of the urban area is an indication of a
dualistic urban structure which is different from both the_
Western and Non western types of structure suggested by
Berry, Simmons and Tennant.

While examples have been found of western cities with
non-western urban structures and.non-western cities with
western type urban structures,3 Port of Spain constitutes
an example of a city which displays features of both types
of structures. This dualistic urban structure is a reflec-
tion of first, the development history of Port of Spain.
Tradition dies slowly in Trinidad. This when considered
with the influence of colonial powers up to 1964 when the
country became independent has had a great impact on the ur-
ban structure of Port of Spain. The oil crisis of the early
1970's aided the development process in Trinidad as the
country benefited from its oil resources. The economic de-
velopment which has taken place has been accompanied by
changes over time in the urban structure of the major city -
Port of Spain.

Second, the growth of they city creates its form, but

the form also limits the future growth of the city. Once

67

a group has become entrenched in part of a city it is very
difficult to change the area. However, over time these
areas are subjected to increasing pressure from the surround-
ing areas, to conform to the general pattern. Thus areas
such as St. Clair would be threatened in the future if steps
are not taken to preserve the character of the area as it
exists today. The forces pushing towards westernization and
those maintaining traditional density forms will not re-
main in balance indefinitely. At present these forces in-
teract to produce a transitional density structure. Ulti-
mately, the modernization forces will dominate over the tra-
ditional forces in the interest of progress and develop-
ment if the city is not to stagnate.

The areas of high population density associated with
lower socio-economic groups may persist long into the future
as the march of peasants continues into the city into tra—
ditional destination areas as much of the suitable land has
already been settled. In addition to this, in the face of
the inadequacy of public transportation, the area which is
feasible as residential locations for these individuals

remain restricted.

Recommendations

It would appear that if the development history of
various countries along with the urban density patterns
are considered, it is likely that as the structure of
cities change to meet theIdemands of industrial develop—

ment, there is also a need for residential patterns to change.

68

As such different density gradient patterns should be iden-
tified which correspond to stages of economic develOpment
rather than attribute differences to socio-cultural factors.

The constant rate of growth of urban population density
over time suggested by previous researchers for "non-western"
type cities does not seem to be practically feasible. The
indefinite, continued increase in central density over time
would eventually reach a point beyond which further increases
would be impossible. At this point environmental stress
would dictate that densities decline as individuals move
to areas of less stress. Even without economic development,
the weight of sheer numbers would generate a change in the
pattern of urban population density.

Based on the findings of this study it would appear
that a western - non-western dicotomy of density patterns
is not valid. Rather, over time density gradient patterns
indicate changes in economic development. Port of Spain has
been put forward as an example of a transition between west-
ern and non western urban density patterns which displays
a dualistic pattern of urban structure.

If urban population density is viewed as a series of
stages of patterns, population density models could be used
by developing nations for analytical and predictive purposes
to their own benefit. This would be of particular value in
the planning process for underdeveloped countries.

Second, this study has focused only on one relatively
small city in a developing country. To confirm the gener-

ality of the findings of this study, it would be necessary

69

to examine the changes which have occured over time, in a
wide cross section of cities, in several countries at dif—
ferent stages of economic development. In this way the
validity of the western - non-western dicotomy could be test-
ed with greater confidence in the universality of a link
between economic development and urban density patterns.
Third, using several indices of economic development
over time, it would be possible to prove empirically, that
there is a link between changing urban density patterns
and economic development. The unavailability of sufficient
economic data for Port of Spain over time, has precluded
such an empirical examination. However, based on the im-
provements which have taken placein Trinidad and the views
of the government which support the fact that economic de-
velopment has taken place since 1960, I can argue that there
’is a link between the deve10pment process and changes in

the urban structure of Port of Spain.

70

Footnotes

 

1. Planning for Development: The Capital Region, Devel-
opment Planning Series NoTi/2/3, Town and Country Plan-
ning Division, Port of Spain, 1975, pp. 123.

2- 23. Angel and Stan Benjamin, "Seventeen Reasons why
Squatter Problems can't be Solved," Ekistics, 41:242,
1976, pp. 20-28.

3. Bruce E. Newling, 1964, op. cit., pp. 440-442.

APPENDICES

APPENDIX I

Data Sources

The Population Census for Trinidad and Tobago 1960;

Vol ii,£H;A, Central Statistical Office, Port of

 

Spain, Trinidad, 1963.

1980 Population and Housing Census, Bulletin No 1,
Central Statistical Office, Port of Spain, Trinidad,

1981.

Annual Statistical Digest, 1978,; No 25; Central Statis-

 

tical Office, Port of Spain, Trinidad, 1980.

 

71

 

 

 

APPENDIX II
Areal Computation using a Polar Planimeter

A starting point was selected on the boundary of each
enumeration district, such that the measuring wheel showed
the least amount of movement. Thus the effect of small
errors at the start or finish of the tracing could be mini-
mized. Once the first measurement was taken, the instrument
was not reset to zero. This was done to minimize subse-
quent measuring errors. As such the final reading after
completing the tracing of each area was subtracted from
the previous reading.

To compensate for human error in the tracing and small
instrument errors, the area of each district was measured
using the compensating feature of the planimeter. Two
tracings of each district were made and their readings taken.

The mean value of both readings was then used for the area

computation.
1.e. N = N1 : N2
where
N = final result
N1= initial reading
N2= second reading.

72

73

The compensating feature was applied in the following
manner: - the area of each district was measured first with
the tracer arm extended to the right of the pole arm. Then,
with the pole in the same position as before, the process
was repeated with the tracer arm extended to the left of
the pole arm.

Following this the actual planimeter operation was com-
pleted. The reading N is known to be the value of one ver-
nier unit [the units in which the length of the tracer arm
is given]. The value of one vernier unit was specified to
be 0.010 square inches, with the length of the tracer arm
set to 13. The area of each district could then be computed

using the formula

A = N x V
s
where
AS = Area
N = final reading
V = given scale value

V in this case is a product of the scale ratio and vernier

value

Sc2 x v

P
(D
<

ll

Sc = the scale ratio

v = vernier value [0.010]

Given that the scale of the map used was 1:60,000 [ie.e one

inch represents five thousand feet]

74

v 50002 x 0.010

v 250,000 ft.2

The tracer arm length of 13 was chosen as the shorter
tracer arm setting guarantees the highest degree of accuracy
since it has the smallest individual vernier scale. The
accuracy of the computed areas of each enumeration district
were checked at a later point with the areas computed by
the Town and Country Planning Division of the Ministry of

Finance, Port of Spain, Trinidad.

APPENDIX III

Data Base

 

Areal Unit Area Distance to Density Density Density
[Acres] City Center 1960 1970 1980
[mls]
Carenage 215 4.17 14 29 39
Point Cumana 52 3.73 24 45 50
Glencoe 92 3.31 10 25 44
La Puerta 161 3.20 4 22 31
Diego Martin 620
Diamond Vale 295 4.15 5 20 28
Petit Valley 482 3.29 2 18 18
Cocorite 156 1.72 4 22 32
St. James/
Long Circular 317 1.48 3 27 90
Ellerslie Pk/
Federation Pk 237 1.84 5 13
St. Clair 137 0.89 9 6 5
New Town 55 0.36 73 39 28
Woodbrook 286 0.77 36 26 21
Maraval 422 2.13 5 27 34
St. Anns 222 1.30 12 19 11
Cascade 201 1.84 18 17 19
Belmont 318 0.83 36 43 40
City Proper 241 -- 73 41 27
East Dry
River 336 0.71 28 68 72
Laventille 430 1.18 2 53 75
Morvant 232 1.07 17 64 ' 110
Barataria 424 2.07 26 35 35

75

76

(Appendix III (cont'd.).

Areal Unit Area Distance to Density Density Density

[Acres] City Center 1960 1970 1980
[mls]

San Juan 789 2.84 5 53 54

Lower

Santa Cruz 404 2.96 3 16 19

Upper

Santa Cruz 607 3.73 2 15 19

Mount Lambert 72 3.73 29 104 125

Valsayn 588 4.44 7 7 7

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