Urban hierarchy in
the brazilian Amazon
Douglas Sathler*
Roberto L. Monte-Mór**
José Alberto Magno de Carvalho***
Alfredo Costa****
The Grade of Membership (GoM) model is used to outline profiles based on a
heterogeneous and multidimensional database, which allows identifying clusters
and describing the differences among them. In this study, GoM uses several
types of variables so as to improve the understanding of the greatness and power
of Amazonian cities. To accomplish this task, a model that takes into account a
variety of aspects, which exceed a purely economic or demographic analysis, is
proposed. Understanding the hierarchical organization of the cities in the Amazon
seems to be a very important exercise in order to understand the dynamics and
specific characteristics of regional urban nets. In this way, it is evident that policies
which stimulate the establishment of more structured urban nets in the Amazon
are needed. A more balanced population distribution throughout the territory could
bring a series of benefits, especially when it comes to the offer and access to all
different sorts of services.
Keywords: Amazon. Spatial distribution of population. Urban hierarchy. Grade
of Membership (GoM).
Introduction
In the Legal Amazon, the intensification
of natural resource exploration within
the territory through mining and mineral
extraction, organized and financed by large
companies, as well as intense deforestation
and land incorporation by agricultural
and livestock industries, along with the
colonization projects and the policies induced
and funded by the State, have promoted a
migratory outbreak with a demographical
growth that has launched new challenges for
the Region’s public policies (MONTE-MÓR,
1994, 2004; SATHLER, 2009).
The opening of major highways in the
frontier areas, after the 1960’s, stimulated
a differentiated occupation pattern in the
Legal Amazon, under the influence of the
intensification of flow between the main
focal points belonging to a great “archway”.
Encouraging this type of occupation has
* Geographer, Ph.D. in Demography (Center for Regional Development and Planning – Cedeplar/UFMG), associate professor
of the Vales do Jequitinhonha e Mucuri Federal University.
** Architect, Ph.D. in Urban Planning (UCLA), associate professor at Cedeplar – Center for Regional Development and Planning
of the Universidade Federal de Minas Gerais – UFMG.
*** Economist, Ph.D. in Demography (London School of Economics and Political Sciences), associate professor at Cedeplar –
Center for Regional Development and Planning of Universidade Federal de Minas Gerais – UFMG.
**** Undergraduate Student in Geography at IGC – Institute of Geosciences, da Universidade Federal de Minas Gerais – UFMG.
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Sathler, D. et al.
Urban hierarchy in the brazilian Amazon
provided several logistic and location
advantages, unlike what occurred around
the Region’s main fluvial paths.
Over the past decades, a true
urban explosion has been spotted in
the surroundings of the Region’s main
highways, in face of one of the most
formidable migratory movements ever
recorded (MATOS, 2005). Growth rates have
been higher than the national average, due
to the intense migratory flow, originating
mostly in the Northeastern and Southern
regions.
In this context of continuous transformation,
the theme of urban hierarchy in the Amazon
has been attracting specialists’ attention
in face of the specific and complex urban
nets in the Region. The search for better
comprehension of the questions related to
the Amazonian urbanization, urban nets and
hierarchical organization’s specifics seems
to be extremely important. This is due to the
fact that not only does most of the Amazonian
population live in cities, but it is also important
to take into account that, in the Amazon, many
people that live in areas that exceed the limits
of urban perimeters develop fundamentally
urban activities.
In balanced urban nets, the hierarchy
of cities, when properly planned and
respected, is capable of bringing a series
of economic and logistic benefits. The idea
of an urban net connects to the existence of
centers in a hierarchical distribution. Only
in a hypothetical situation is it possible to
imagine a region dominated by centers
that are equally “sized” (demographically,
functionally, among other aspects). In that
way, it is plausible to imagine that, where
there is a net, there is an urban hierarchy.
The theme is greatly relevant, since the
questions on urban hierarchy in the Region
are linked to a series of other relevant aspects
that go beyond the studies which consider
the influence radius of the organization of
cities, of systems of material and immaterial
flows and of urban agglomerations, as well
as other traditionally approached themes.
The urban hierarchy in the Amazon also
converses with questions referring to social
differences and poverty, deforestation, land
conflicts, and others.
252
The urban hierarchy in the Amazon with
unbalanced nets
Recent urban transformations in the
Amazon have generated interpretations
that often do not correspond to the regional
urban scenario, supported by the untruth that
Amazonian cities would not be organized
in a dendritical or monocentrical type,
simplified urban net model, which would
have been broken when new median cities
were introduced and with the growth spurt
of small regional municipalities. However,
even before the high growth rates of the
past decades, the Amazonian urban nets did
not present the same level of balance and
complexity found in the dynamic regions of
Brazil, or even in other developed regions
of the world. In the Amazon, the economicspatial integration promoted by globalization
was not enough to significantly reduce
distances between small cities and the
other hierarchical levels of the urban nets,
in face of a series of problems that reduce
or eliminate several types of flows. Thus,
deeper exploring of Amazonian specifics
in this transformational context is suitable.
The fragility of Amazonian urban
networks is related to the development of
barriers for the flows of people, goods and
services, such as: a) the long distances
that separate capitals from other towns
and hamlets; b) the lack of transportation
and communication infrastructure in large
areas of the Amazon territory; c) the large
proportion of the population without material
and educational resources, decisive to their
active participation in the many kinds of flows
(SATHLER, 2009).
In the Amazon, the great distances
between local centers, middle-sized cities
and the largest cities in the Region create
limitations to the flows of assets, people and
services between the several hierarchical
urban levels. The very distribution of the
urban centers in the Amazonian territory
occurs rather unequally, with a clear
concentration of cities in the surroundings
of an “archway” formed by the large federal
highways that involve and/or cut through
the Region, without, however, presenting
strong penetration and internal articulation
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Sathler, D. et al.
intensity with regional spaces. This creates
an obvious difficulty concerning the flows
between cities belonging to the “archway”
and the other centers within the territory.
The lack of infrastructure in the
communication and transportation sectors
seems to be evident in great portions of the
Amazonian territory. The low investments
in urban and regional infrastructure are
reflected in the creation of an environment
contrary to the one needed to accelerate
flows within the Region. Even in the presence
of some relatively large investments in the
current governmental resource distribution
chart, it is possible to notice that some of
them, such as the construction of large
power plants, prioritize generating wealth
and assets, most of which will not be
distributed within the Region.
In order to better comprehend the
dynamics of the Amazonian nets, it is not
possible to only look at the external aspects
of urban centers. It is essential to shed
light upon the internal characteristics of the
centers, a necessary exercise to understand
the intensity and direction of flows. Once
looking at the city from the inside, aiming to
better comprehend the intra-urban specifics,
it is easier to understand the way cities
interact and integrate with each other.
In this sense, one can note that the
diverse types of flows are also limited by
strictly socio-economic reasons. In the Legal
Amazon, as in other parts of the country,
it is evident that the larger portion of the
population does not have enough material
and educational assets in order to actively
participate in the regional and global flows,
whether of goods and services or those
related to social demands that are nowadays
considered essential, and also those
referring to more sophisticated demands,
that should be available in cities relatively
Urban hierarchy in the brazilian Amazon
close, in an urban net which functions
properly.
Even if some of the technological
novelties of the modern world stimulate the
emergence of differentiated patterns that, in
certain moments, are closer to what could
be seen as a mobile net,1 mainly in Belém
and Manaus, and that can now count almost
simultaneously on all the global innovations
that point towards flexibility and interactivity,
it is important to bear in mind that this pattern
of the world’s most dynamic urban nets, in
fact, is far from being solidly established in
the Region.
Apart from these specifics in the
functioning of Amazon’s urban nets, one
should also bear in mind the particularities
that come from the very formation of the
Region’s urban spaces. In the Legal Amazon,
the current conformation of the urban nets
was produced by an urbanization process
different from that in other regions of Brazil,
hugely influenced by state interventions that
have occurred since the 1960’s.
The development of the urban frontier,
which could be understood as the logistic
base for the Region’s quick occupation
project, was boosted by the great
entrepreneur incentive and by the migration
policy induced and financed by the State.
New centers were created, mainly in support
of mining, farming and colonization projects
(BECKER, 1990; 2001; 2005).
History shows that the emergence
and proliferation of cities are generally
directly related to the creation of surpluses
in rural areas. However, it should remain
clear that sometimes cities can spurt in
front of fields, such as large areas in the
Amazon, and the areas serve as logistic
bases for the reproduction of economic
activities developed around these centralities
(MONTE-MÓR, 2006).
1 The concept of a mobile net is suggested by Sathler (2009). Regarding the new forms of flexibility and interactivity which
appeared at the turn of the millennium, it is possible to notice that nets possess more and more points that seem to change
places at every moment, apart from flows that do not follow strict paths, or give off the impression of ever tracing a certain
path, coming and going instantaneously, or just “being”. People, companies and cities stimulate an unprecedented feeling
of omnipresence. In this perspective, nets are no longer geometric. They assume visible and invisible forms, impossible to
define or draw. Thus, the world gets to know not only the traditional dendritical and complex nets, counting now with vast
regions that present mobile nets. It is worth mentioning that, unlike previous concepts which prioritize the organization
form of the cities, the mobile net concept focuses on what is most essential in nets: the flow systems (SATHLER, 2009;
SATHLER; MONTE-MÓR, 2009).
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In many of the cases, Amazonian
cities respond to what happens in their
surroundings. In mining and deforestation
areas, and even in areas taken by mechanical
agriculture, the urban and industrial logic has
always been present. Thus, as in other parts
of the country, in vast regions of the Legal
Amazon, the urbanization that exceeds city
borders, favored by the development of
the technical-scientific and informational
environment and by the support of the strong
presence of urban-industrial production
relationships, could be comprehended
with the help of the extensive urbanization
concept. This term refers to the progress of
the urban tissue, which exceeds city limits,
generating new centralities, expressing a
broad economic-spatial process (MONTEMÓR, 1994; SATHLER, 2009).
Thus, the discussions about the urban
nature in the Amazon and the urban nets in
the region have raised important questions,
which consider the peculiarities related to
the urbanization process, spatial distribution
and the intensity of material and immaterial
flows. The studies on urban hierarchy have
incorporated yet other relevant aspects,
such as the correlations of size, power and
competitiveness of regional cities.
Throughout the 20th century, a series of
academic studies was produced, in which
the idea of a hierarchical organization of
cities appears implicitly or explicitly, basing
itself on a few essential questions that have
been leading theoretical and empirical
efforts: why do cities present different
population sizes? Is there any connection
between the size and the growth of cities?
How do economic activities respond to this
differentiation in the demographical size of
urban centers? How do economic activities
create this differentiation? Is there, in fact,
regularity in the population size distribution
between the cities of a certain region? And
if there is, why does this happen?
Overall, it is possible to state that the
literature was influenced by two schools of
thought. The first is supported by the Central
Place Theory, developed by Christaller (1933)
and improved by Lösch (1940). The second
was developed, based on the urban system
model, by Henderson (1974) and Krugman
(1996). The Central Place Theory takes into
account that different population sizes create
different conditions and opportunities for the
growth of economic and functional activities.
Later, Henderson (1974) established a model
in which the optimal size of a certain city
would be influenced, mostly, by the type of
economic activity.
There are other studies that are also
worth mentioning, such as Zipf’s in 1949,
which claims the existence of an impressive
empirical regularity in the distribution of
urban population sizes in several regions of
the world. Furthermore, the model of random
city growth developed by Simon (1955) also
deserves to be highlighted, since it has been
commonly quoted and discussed in past
decades.
More recently, the studies2 produced
within the school that is called the New
Economic Geography (NEG) continue
the debates, based on the idea that scale
refunds, relating to city population growth,
are not as constant as in Simon’s (1955)
model. The NEG takes into account that
the city population growth would be a result
of a combination between “centripetal”
and “centrifugal” forces that stimulate the
concentration of economic activities.
In Brazil, a study by IBGE (2008) fills a
gap that has existed over past years, related
to the detailed study of city influence areas
and the hierarchical organization of central
localities in the country. The IBGE then
established the primary hubs of Brazilian
urban nets in 2007 with the help of a great
number of secondary information, seeking
to identify the influence regions of these
centers, starting from the interaction nets
that connect cities.
Facing the complexity of the information
brought up and used by IBGE (2008), the
approach does not intend to develop a direct
outline of urban hierarchy with the help of
the Grade of Membership (GoM) model
that exceeds the one already carried out by
2 See Krugman (1996).
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IBGE. However, it focuses on supplying a
few new elements that help understanding
the organization of the Amazon’s urban nets.
As seen in the IBGE study, the model, when
applied, is based on the general idea that all
of these aspects are, direct players in the
hierarchical organization of cities, that is, that
the “greatness” of a city and its hierarchical
position in the net are not measured simply
by the number of people residing there.3
The Grade of Membership (GoM) model
The Grade of Membership (GoM)
model is used to outline profiles based on
a heterogeneous and multidimensional
database, which allows identifying clusters
and describing the differences among them
(WOODBURY et al., 1978; WOODBURY;
MANTON, 1989; MANTON et al., 1994;
CASSIDY et al., 2001).
In Brazil and abroad, the methodology
has been widely used to prepare analyses
connected to the study of epidemics and
health demographics.4 However, the method
is not restricted to these research fields,
since it is applicable to other studies with
several other purposes. In this text, GoM
will be used to broaden the possibilities
of studying urban hierarchy in the Legal
Amazon.
Apart from most of the cluster analysis
statistic methods, GoM does not consider
that people and objects are organized
in well-defined groups. In GoM, a same
individual (or observation) may have a
certain degree of pertinence to multiple
groups; hence it is also being called a fuzzy
set model (MACHADO, 1997). The GoM is
different from other multivariate analysis
models because of its capacity to provide
information on pertinence degrees towards
the outlined profiles, allowing deeper
analyses on the data’s nature. If applied to
this article’s problem, it seems to be fruitful to
build profiles in which municipalities possess
differentiated pertinence degrees instead of
Urban hierarchy in the brazilian Amazon
defined municipality groups, such as in the
cluster analysis model. Furthermore, GoM
has, among others, the quality of analyzing
categorical data with small samples with a
large number of variables.
According to Sawyer et al. (2002),
this methodology applied in delineating
profiles considers that: a) the unobserved
association among variable categories in the
model outlines two or more well-determined
profiles that are called extreme profiles; b)
these extreme profiles have all the properties
of classical closed sets; c) the pertinence
degree to the extreme profiles are attributed
to each individual. Thus, the individual that
has all the characteristics of one of the
extreme profiles will be 100% pertinent to
that profile and 0% to the rest. The more an
individual relates to an extreme profile, the
higher the pertinence degree to this level. It
is not unusual for them to be individuals that
are equally distant to all extreme profiles,
not having, therefore, characteristics that
relate them to the generated profiles. d)
the pertinence degrees of individuals form
a fuzzy set and the higher the number of
variables, the more defined is the set; e) in
GoM, as the elements in this set are individual
attributes, the variety issue, included and
badly handled in many statistical methods,
is not a problem; f) the method parameters
are estimated by iterative processes and,
therefore, the smaller the sample, the smaller
its convergence time (Sawyer et al., 2002).
According to Sawyer et al. (2002,
p. 759),
items (c) and (d) give the method, within
reasonable limits, the benefit of better results,
the smaller the size of the sample and the
higher the number of variables.
The authors still state that,
as the pertinence degree of each individual
is given by conjunction, in this individual, of
all the variable categories in the model, the
method shows, and in a very simple way, the
variety included in the sample (SAWYER et
al., 2002, p. 759).
3 It is important to note that the article does not work with the database available through the IBGE (2008), it only offers a
new methodological point of view with the intention of contributing towards the comprehension of the Amazonian urban
hierarchy.
4 See Sawyer et al. (2004); Alves et al. (2008); Maetzel et al. (2000); MacNamee (2004).
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Urban hierarchy in the brazilian Amazon
The method demands the estimation
of a pertinence degree score for each
individual, relative to the several sets, that
is, the fuzzy division of the individuals, in
order to obtain the extreme profiles. For each
element in a fuzzy set, there is a pertinence
degree score (g ik ) that represents the
level with which element “i” belongs to the
extreme profile k (Sawyer, 2000). These
scores vary from 0 to 1: 0 indicates that
the element does not belong to the set; 1
indicates that the element belongs entirely to
the set. The gik represents the proportion or
pertinence intensity to each extreme profile.
Therefore, there are the following restrictions
to the measure:
gik ≥ 0 for each i and j
for each i
In order to form the model and the
parameter estimate (scores), the following
biases are necessary, according to
Woodbury et al. (1978, p. 201):
a) the random variables represented by
Yijl, where “i” refers to the individual,
“j” to the question and “l” to the
answer category of each variable, are
independent for each “i”. That is, the
answers to different individuals are
independent;
b) the gik (k = 1, 2, …, k) are outcomes
of the random vector components
with a distribution function
. That is, GoM scores
are outcomes of random variables
when an individual is selected in the
population. The outcome sample
distribution (or scores in the sample)
gives estimates for the distribution
function H(x);
c) if the pertinence degree gik is known,
the “i” individual answers to the many
Yijl questions are independent for
each variable category;
d) the probability of answer “l” for the
jth question by an individual with the
kth extreme profile is λkjl. According
to the model assumption, there is
at least one individual that is a well
defined member of the kth profile. This
assumption gives the probability of
256
answer for this individual to the several
levels of this question. Then, one can
write this assumption as being:
for each k, j and l
for each k and j
e) the probability of a level “l” answer of
the jth question by the ith individual,
conditioned to the gik score will be
given by:
According to the assumptions above,
the probability model for the construction of
a maximum likelihood estimation procedure
is formulated. The probability model for
a random sample is the product of a
multinomial model by each cell probability,
given by:
where gik is, by assumption, known and
greater than or equal to zero.
Considering the assumptions above, the
maximum likelihood model can be written as:
The software chosen to run the model
is “GoM”, freeware version 3.3, developed
by Peter Charpentier, from the Epidemiology
and Public Health Department of Yale School
of Medicine, USA.
Applying GoM in the outline of urban
hierarchy on the Legal Amazon
GoM uses several types of variables
that aim to improve the understanding of
the greatness and the power of Amazonian
cities. To fulfill this task, a model that takes
into account a variety of aspects which
exceed the purely economic or demographic
analysis is proposed. Thus, the variables
which measure functionality and the ability
to offer basic and specialized services are
very valuable, as are indicators of access to
assets and those referring to equipment and
infrastructure in the city.
To generate the analysis model for
the present study, only the municipalities
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Urban hierarchy in the brazilian Amazon
with a population higher than 20,000
inhabitants were taken into account. Even if
the municipalities with a population between
10,000 and 20,000 could take on a certain
degree of importance concerning centrality
in the Legal Amazon context, only those
over 20,000 were considered, focusing the
analysis on the spaces which hosted the
largest urban transformations in the region.
In this study, the scale chosen for the
analysis is the municipality. This is due to
the information available, mostly regarding
municipalities and not cities. Yet, there are
many issues in the legal definitions of city
and field in Brazil.5 Furthermore, the present
study considers that, in many parts of the
Amazon, the activities that are developed
beyond the urban perimeter of a city often
obey a logic far from being considered rural,
minimizing the problems that may appear in
this sort of approach.
Table 1 presents the list of variables
present in the model, separated into
six groups, according to the nature of
information, such as: spatial, demographic,
socioeconomic, infrastructure and services,
access to assets, functional.
Including spatial variables seems to be
of great importance, since urban hierarchy
is also defined under the influence of the city
TABLE 1
GoM model internal variable list
Variable nature
Variables
1 - Espacial
1.1. Centrality Indicator: variable that represents the number of times the city in
question was verified as being the closer urban center and with a bigger population
2- Demographic
2.1. Municipality urbanization degree
2.2. Municipality population in 2007
2.3. Municipality MCT (Management Commitment Term) between 2000 and 2007
2.3. Mesoregion MCT between 2000 and 2007
3- Socioeconomic
3.1. GNP (Gross National Product)
3.2. Value of Municipality Participation Fund
3.3. Proportion of poor people
3.4. Municipality HDI (Human Development Index)
4- Infrastructure and services
4.1. % of people with access to treated water service
4.2. % of people with access to electricity service
4.3. % of people with access to garbage collection service
4.4. Number of fundamental learning schools
4.5. Number of medium level learning schools
4.6. Number of fundamental learning enrolments
4.7. Number of medium level learning enrolments
4.8. Number of superior level learning enrolments
4.9. Hospitals
4.10. Hospital beds
4.11. Health stations
4.12. Health centers
5- Access to assets
5.1. Vehicle fleet
5.2. % of people with computer
5.3. % of people with television set
5.4. % of people with refrigerator
5.5. % of people with telephone
6- Functional
6.1. This variable is the result of a municipality functionality matrix in relation to total
(37) of functions with several levels of specialization.
Source: Elaborated by the author.
5 See Veiga (2000) and Matos (2005).
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Urban hierarchy in the brazilian Amazon
distribution in the net, with evident impacts
on how they interact and relate to each
other. Variable 1.1 represents the number
of times which a certain city was observed
to be the closest urban center and with the
largest population. Each time that a city is
seen as the largest and closest to any of
the 20,000-inhabitant centers (2007) in the
Legal Amazon, the city gains 1 point in the
so-called Centrality Indicator. Furthermore,
the Centrality Indicator also accumulates
points from the cities’ relations to centers
belonging up to the seventh order in the net,
with differentiated values (0.5 for the second
order, 0.25 for the third, 0.125 for the fourth
and so on).
In order to build the functionality indicator
(variable 6.1), the chosen functions (73)
sought to include from the simplest activities,
such as high schools and elementary
schools, to the most sophisticated ones,
such as higher education schools and the
availability of Masters’ courses rating 6 or 7
by CAPES.
The four profiles obtained were selected
based on ten results generated with a
random initial
, that is, ten models were
generated from four profiles. The constancy
observed in the final
obtained in the ten
models indicated that the global maximum
(mathematical criteria for optimization)
was duly achieved in all models. One out
of the ten models was chosen based on
the coherence of the results found for the
municipal population in 2007 which, without
the slightest doubt, is one of the main
variables regarding the apprehension of the
urban hierarchy.6 Thus, although GoM was
not exclusively developed for delineating
hierarchy patterns, this emerged naturally
from the information, revealing profiles that
matched expectations.
The profile description and denomination
were performed based on the ratio between
each expected probability (E) in the level (l)
of the variable (j) in the extreme profile (k),
, and the observed probability
that is,
(O) of the answer (l) of the variable (j) for
any municipality (marginal probabilities).
This ratio can be called, in a simplified
manner, as (E/O). A ratio E/O above 1.2 is an
indication that the profile has a “remarkable”
or “descriptive” characteristic; this criterion
is proposed by Sawyer et al. (2002).
The following profile description is made
according to the expected probability (E) of
each variable level relative to the observed
marginal probability (O). That is, profiles are
described based on the characteristics with
an E/O ratio equal to or above 1.2, as seen
before. It is important to point out that this
description refers to the pure types (gik =1)
of each profile.
Profile 1: 1) high urbanization degree
(2000), above 80%; 2) average to large
population (2007), greater than 50,000
inhabitants; 3) high municipal MCT (20002007), between 3 and 6% a year; 4) small/
average positive mesoregion MCT (20002007), between 0.5 and 1% a year and
between 1.5 and 2% a year; 5) average to
high GDP (2005), higher than R$500,000,000
up to the R$12,000,000,000 or more class;
6) average/high MPF (2005), higher than
R$8,000,000 up to the R$100,000,000 or
more class; 7) relatively small proportion of
poor people (2000) for the regional pattern,
less than 45%; 8) average and high HDI
(2000), between 0.71 and 0.80 or more;
9) average/high proportion of people with
access to treated water supply (2000), above
60%; 10) very high proportion of people with
access to electricity service (2000), above
90%; 11) high proportion of people living
in urban houses with garbage collection
service (2000), above 80%; 12) high number
of fundamental education schools (2006),
above 101 and including the class of
601 or more; 13) average/high number
of medium level schools (2006), above
8.11 and including class 61.07 or more;
14) average/high number of enrollments
in fundamental education (2006), above
20,001 and including class 250,001 or more;
15) average/high number of enrollments in
medium level education (2006), above 2,501;
16) average/high number of enrollments
in higher education (2007), above 1,001
6 It is important to note that this selection procedure of the most adequate model is explained by Manton et al. (1994).
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and including class 40,001 or more; 17)
high number of hospitals (2000), above 4
and 5 or more; 18) average/high number
of hospital beds (2000), higher than 101
and including the class 3,601 or more; 19)
average/high number of health stations
(2000), above 11 and including class 51 or
more; 20) average/high number of health
centers, above 3 and including class 33 or
more; 21) average/high vehicle fleet (2007),
above 15,001 and including class 250,001 or
more; 22) average/high proportion of people
living in houses with computer (2000) for the
regional patterns, above 3% and including
class 10.01% or more; 23) high proportion
of people living in houses with electricity
service and television (2000), above 80.01%;
24) high proportion of people living in houses
with electricity service and refrigerator
(2000), above 80.01%; 25) high proportion
of people living in houses with telephone
(2000) for the regional patterns, above
30%; 26) average/high/very high centrality
indicator, above 2.51 and including class
30.01 or more; 27) high/average functional
diversification, presenting more than 60.01%
of the functionalities.
Profile 2: 1) average to high urbanization
degree (2000), predominantly between
70 to 90%; 2) average size population
(2007), between 30,000 and 100,000, with
greater emphasis to the municipalities with
more than 50,000 inhabitants; 3) very high
municipal MCT (2000-2007), higher than 6%
a year, or negative, between -2.99 and -1.5%
a year; 4) high positive mesoregion MCT
(2000-2007), between 2.5 and 3% a year
and higher than 3% a year or small positive,
less than 0.5% a year; 5) average/small
GDP (2005), between R$500,000,000 and
R$1,500,000,000 and less than R$500,000;
6) average/small MPF (2005), between
R$8,000,000 and R$16,000,000 and less
than R$8,000,000; 7) average proportion of
poor people (2000) for the regional pattern,
between 27% and 58.51%; 8) average
HDI (2000), from 0.71 to 0.8; 9) average
proportion of people with access to treated
water supply (2000), between 40% and 80%;
10) high proportion of people with access
to electricity service (2000), above 80%; 11)
average proportion of people living in urban
Urban hierarchy in the brazilian Amazon
houses with garbage collection service
(2000), less than 60%; 12) small number
of fundamental education schools (2006),
less than 50; 13) small number of medium
level schools (2006), below 8.11; 14) small
number of enrollments in fundamental
education (2000), between 5,001 and
7,500; 15) average number of enrollments
in medium level education, between 1,001
and 5,000; 16) small/average number of
enrollments in higher education (2007),
between 1 and 1,000; 17) average number
of hospitals (2000), between 2 and 4; 18)
average number of hospital beds (2000),
between 101 and 400; 19) average number
of health stations (2000), between 6 and
10; 20) average number of health centers,
between 2 and 8 and between 17 and 32;
21) average vehicle fleet (2007), between
5,001 and 15,000; 22) average proportion of
people living in houses with computer (2000)
for the regional patterns, between 2% and
5%; 23) average/high proportion of people
living in houses with electricity service and
television (2000), between 60,01% and 90%;
24) high proportion of people living in houses
with electricity service and refrigerator
(2000), between 60,01 and 80%; 25) average
proportion of people living in houses with
telephone (2000) for the regional patterns,
between 10.01% and 30%; 26) small
centrality indicator, between 0.01 and
2.5; 27) average functional diversification,
presenting between 40.01% and 70.01% of
the functionalities.
Profile 3: 1) average urbanization
degree (2000), between 50 to 70%; 2)
average size population (2007), from 30,000
to 100,000, with greater emphasis to the
municipalities with a population of less than
50,000 inhabitants; 3) negative municipal
MCT (2000-2007), between -1.5 and 0%
a year; 4) moderate positive mesoregion
MCT (2000-2007), between 0.5 and 1% a
year and between 1% and 1.5% a year; 5)
small GDP (2005), less than R$500,000,000;
6) average/small MPF (2005), between
R$8,000,000 and R$16,000,000 and less
than R$8,000,000,000; 7) high proportion
of poor people (2000) for the regional
pattern, between 58.52% and 79.59%; 8)
small HDI (2000), from 0,61 to 7; 9) small
R. bras. Est. Pop., Rio de Janeiro, v. 27, n. 2, p. 251-268, jul./dez. 2010
259
Sathler, D. et al.
Urban hierarchy in the brazilian Amazon
proportion of people with access to treated
water supply (2000), between 20% and
40%; 10) average proportion of people
with access to electricity service (2000),
between 60% to 90%; 11) average/small
proportion of people living in urban houses
with garbage collection service (2000),
between 10% and 70%; 12) average/small
number of fundamental education schools
(2006), between 50 and 200; 13) small
number of medium level schools (2006),
inferior to 8.11; 14) average/small number
of enrollments in fundamental education
(2000), between 7,501 and 20,000; 15)
average number of enrollments in medium
level education, between 1,001 and 5,000;
16) small/average number of enrollments
in higher education (2007), between 1 and
1,000; 17) small/average number of hospitals
(2000), 1, 2 or 4; 18) average number of
hospital beds (2000), between 101 and 400;
19) average/high number of health stations
(2000), between 6 and 10 and above 31; 20)
average number of health centers, between
3 and 4; 21) small vehicle fleet (2007), equal
to or less than 5,000; 22) small proportion
of people living in houses with computer
(2000) for the regional patterns, between 1%
and 2%; 23) average proportion of people
living in houses with electricity service and
television (2000), between 50.01% and
70%; 24) average proportion of people
living in houses with electricity service
and refrigerator (2000), between 40.01
and 60%; 25) small proportion of people
living in houses with telephone (2000)
for the regional patterns, between 5.01%
and 10%; 26) average centrality indicator,
between 2.51 and 5; 27) small functional
diversification, presenting between 30.01%
and 50.01% of the functionalities.
Profile 4: 1) average to high urbanization
degree (2000), between 10 to 50%; 2) small
size population (2007), from 20,000 to
30,000 inhabitants; 3) very high municipal
MCT (2000-2007), between 3 and 6% a
year and greater than 6% a year, or very
small MCT, less than -3% a year; 4) average
positive and moderately high mesoregion
MCT (2000-2007), between 1 and 1.5 % a
year and between 2% and 3% a year; 5)
small GDP (2005), less than R$500,000; 6)
260
small MPF (2005), less than R$8,000,000;
7) high proportion of poor people (2000)
for the regional pattern, between 64.92%
and 72.29% and very high, between 72.305
up to the class between 79.6% or more;
8) very small HDI (2000), less than 0.6; 9)
very small proportion of people with access
to treated water supply (2000), less than
20%; 10) average proportion of people with
access to electricity service (2000), less than
60%; 11) small proportion of people living
in urban houses with garbage collection
service (2000), less than 60%; 12) small
number of fundamental education schools
(2006), between 50-100; 13) small number of
medium level schools (2006), below 8.11; 14)
small number of enrollments in fundamental
education (2000), less than 10,000; 15) small
number of enrollments in medium level
education, less than or equal to 1,000; 16)
no enrollments in higher education (2007),
between 1 and 1,000; 17) small number of or
no hospitals (2000), equal to 1 or 0; 18) small
number of hospital beds (2000), less than
100; 19) small/average number of health
stations (2000), between 11 and 20 and less
than or equal to 5; 20) small number of health
centers, equal to or less than 1; 21) small
vehicle fleet (2007), equal to or less than
5,000; 22) very small proportion of people
living in houses with computer (2000) for
the regional patterns, less than or equal to
1%; 23) small proportion of people living in
houses with electricity service and television
(2000), less than 50%; 24) small proportion
of people living in houses with electricity
service and refrigerator (2000), less than
40.00%; 25) very small proportion of people
living in houses with telephone (2000) for
the regional patterns, less than 5.00%; 26)
centrality indicator equal to 0; 27) very small
functional diversification, presenting less
than 40% of the functionalities.
Complementary to these descriptions,
Table 2 presents the gik(s) distribution in
the four model profiles. The fact that, in
all the profiles, 138 municipalities (57%)
had a high degree of compatibility with
gik(s), above 0.75 (which is considered very
high), is another indication that validates
the profile numbers that were found and the
suitability of the model to the present study
R. bras. Est. Pop., Rio de Janeiro, v. 27, n. 2, p. 251-268, jul./dez. 2010
Sathler, D. et al.
Urban hierarchy in the brazilian Amazon
Ji-Paraná, Ariquemes, Porto Velho and
Rio Branco. One can also find some other
municipalities with a gik higher than 0.75
in the proximities of the Belém – Brasília
highway, for example: Gurupi, Palmas,
Araguaína, Imperatriz, Castanhal and
Ananindeua. Far from each other on the
map, some state capitals stand out, such
as Manaus, Macapá, São Luís and Boa
Vista. Out of this group of municipalities,
only Sinop, on highway 163, seems farther
and more out of line to the medium/large
agglomerations of the region. All state
capitals reached maximum compatibility with
profile 1, whereas seven intermediate-sized
municipalities also achieved this amount.7
Profiles 2 and 3, overall, present
characteristics seen as intermediate in
relation to the other profiles. It is worth
mentioning that Profiles 2 and 3 present
data (that is, the profiles “fit” appropriately
most of the municipalities). Furthermore, 97
municipalities (40%) had gik(s) between 0.51
and 0.75 (considered high). Thus, 97% of
the municipalities have gik(s) with amounts
higher than 0.50 in one of the profiles,
which is quite interesting, given almost all
the municipalities have a high compatibility
degree to some profile. It is worthy to point
out that a municipality with a minimum of
0.51 in one profile cannot have a pertinence
superior to 0.49 in any other profile.
According to Map 1, it is clear that the
municipalities with a high compatibility to
Profile 1 are distributed along the main
roads of the Legal Amazon, especially
those between Cuiabá and Rio Branco, in
the outskirts of the BR 364 and BR 070:
Cuiabá, Barra do Garças, Rondonópolis,
Várzea Grande, Tangará da Serra, Vilhena,
TABLE 2
gik(s) distributio
Profile 1
0 – 0.25
0.26 – 0.50
0.51 – 0.75
0.76 +
Total
Frequency
193
22
5
22
242
0 – 0.25
0.26 – 0.50
0.51 – 0.75
0.76 +
Total
Frequency
164
20
22
26
242
0 – 0.25
0.26 – 0.50
0.51 – 0.75
0.76 +
Total
Frequency
137
39
33
33
242
0 – 0.25
0.26 – 0.50
0.51 – 0.75
0.76 +
Total
Frequency
136
22
27
57
242
%
79.75
9.09
2.07
9.09
100.00
Accumulated %
79.75
88.84
90.91
100.00
%
67.77
8.26
13.22
10.74
100.00
Accumulated %
67.77
76.03
89.26
100.00
%
56.61
16.12
13.64
13.64
100.00
Accumulated %
56.61
72.73
86.36
100.00
%
56.20
9.09
11.16
23.55
100.00
Accumulated %
56.20
65.29
76.45
100.00
Profile 2
Profile 3
Profile 4
Source: Elaborated by the author.
7 Tangará da Serra, Rondonópolis, Barra do Garças, Imperatriz, Araguaína, Ananindeua, and Ji-Paraná.
R. bras. Est. Pop., Rio de Janeiro, v. 27, n. 2, p. 251-268, jul./dez. 2010
261
Sathler, D. et al.
Urban hierarchy in the brazilian Amazon
very distinct spatial patterns. When it comes
to municipalities with a gik higher than 0.75
in Profile 2, Map 2 makes it clear that these
are concentrated in the inner region of Mato
Grosso and in the eastern portion of the
Legal Amazon. As for the municipalities with
high compatibility rates to Profile 3, they are
located in the inner region of the states of
Amazonas, Acre, and in the western part of
the states of Pará and Maranhão.
The municipalities that belong to Profiles
2 and 3 are demographically medium-sized.
It is clear that Profile 2 municipalities, more
urbanized and more populated than Profile
3, are those placed by highways and roads.
Profile 3 municipalities are preferably located
along the margins of the main rivers that
cross the inner region. Maps 2 and 3 seem
to suggest that the influence of the highway
contributed, more than the traditional
transportation means in the region, to this
size differentiation, urbanization degree, and
functional diversity, among others.
Profile 4 municipalities with an elevated
gik(s) are concentrated in the inner regions
of Pará and Maranhão, and, on a smaller
scale, in the states of Amazonas, Acre and
Rondônia (Map 4). The municipalities with
a high compatibility with Profile 4 were the
ones with more pure types (30) in relation to
the other profiles.
Applying GoM seems to suggest that the
use of strictly demographic criteria would be
capable of delimitating, with a certain amount
of efficiency, urban hierarchical levels, given,
in the Legal Amazon, many of the variables
(socioeconomic, infrastructure and services
indicators, access to assets and functional
diversity) are positively correlated with the
population size of the municipalities. That is,
the less populated municipalities with high
compatibility to Profile 4 are also those with
the worst socioeconomic indicators and the
highest needs of basic services, as well as
low access to assets. The intermediate-sized
municipalities, with high compatibility rates
to Profiles 3 and 2, seem to be in a more
favorable situation than those in Profile 4.
The municipalities with a high compatibility to
Profile 1, with medium/large population sizes,
are those that offer the “best” socioeconomic
indicators in the Region.
262
However, the model showed some
interesting results that escape from this
general trend. In the case of Santarém,
the largest city in the inner region of the
Amazon (non-capital), the compatibility
to Profile 1 was relatively low (0.65 to
Profile 1), considering its demographic
size. Municipalities with less than half its
population, such as Ji-Paraná and Araguaína,
appear as pure Profile 1 types, amounts that
are well above Santarém’s. Marabá (0.57)
with almost 200,000 inhabitants, Itaituba
(0.25), Abaetuba (0.36), Parauapebas (0.43),
and Parintins (0.28), all with population sizes
above 100,000 inhabitants, also present low
compatibility to Profile 1, considering the
demographic size of these municipalities.
Some of the model variables caused
many medium-sized municipalities to be
included as pure Profile 1 types along with
large municipalities, such as São Luís, Belém
and Manaus. This seems to make sense in
some variables. In order to have a general
idea, the level of some medium-sized
municipal functional diversity is very close to
what was verified for the largest cities of the
region. Besides, the variables that measure
percentage, proportion and degree also
contribute to this result.
The results of the model suggest that the
position of a certain center in the Amazonian
urban nets is largely influenced by variables,
which relate to social differences, poverty,
and the municipalities’ capacity of providing
several kinds of services to the population.
Probably, the findings in this article
may not repeat themselves in the country’s
more dynamic nets, such as in the state of
São Paulo, in which the demographic size
may, in a balanced manner, be far more
well adjusted to the centralities’ functional
size, and the variables related to the social
differences and poverty will probably not be
as defining in the small and middle-sized
centers’ classification.
The study of urban hierarchy seems to
shed light on a number of issues referring
to the functioning of the Region’s urban
nets, providing support for the design of
public policies. For comparison purposes,
considering the Amazonian urban nets’
specifics, which were discussed in the
R. bras. Est. Pop., Rio de Janeiro, v. 27, n. 2, p. 251-268, jul./dez. 2010
Sathler, D. et al.
Urban hierarchy in the brazilian Amazon
MAP 1
The Legal Amazon: distribution of the g1 values of the municipalities
Source: IBGE. Censo Demográfico de 2000, Contagem da População de 2000, Atlas de Desenvolvimento Humano do Brasil
2000, Estatísticas de Saúde 2000, Perfil dos Municípios – Cultura 2006. Inep 2006. Banco Central 2004. Elaboration by the author.
MAP 2
The Legal Amazon: distribution of the g2 values of the municipalities
Source: IBGE. Censo Demográfico de 2000, Contagem da População de 2000, Atlas de Desenvolvimento Humano do Brasil
2000, Estatísticas de Saúde 2000, Perfil dos Municípios – Cultura 2006. Inep 2006. Banco Central 2004. Elaboration by the author.
previous topic, it is possible to notice some
of the localities which, on a national scale,
present an intermediate demographic
size and have the responsibility of being
R. bras. Est. Pop., Rio de Janeiro, v. 27, n. 2, p. 251-268, jul./dez. 2010
263
Sathler, D. et al.
Urban hierarchy in the brazilian Amazon
MAP 3
The Legal Amazon: distribution of the g3 values of the municipalities
Source: IBGE. Censo Demográfico de 2000, Contagem da População de 2000, Atlas de Desenvolvimento Humano do Brasil
2000, Estatísticas de Saúde 2000, Perfil dos Municípios – Cultura 2006. Inep 2006. Banco Central 2004. Elaboration by the author.
MAP 4
The Legal Amazon: distribution of the g4 values of the municipalities
Source: IBGE. Censo Demográfico de 2000, Contagem da População de 2000, Atlas de Desenvolvimento Humano do Brasil
2000, Estatísticas de Saúde 2000, Perfil dos Municípios – Cultura 2006. Inep 2006. Banco Central 2004. Elaboration by the author.
264
R. bras. Est. Pop., Rio de Janeiro, v. 27, n. 2, p. 251-268, jul./dez. 2010
Sathler, D. et al.
the final destination. This instability, that
is very difficult to solve, imposes on these
middle-sized centers a wider array of
social demands, unlike what happens in
centers of the same size in a balanced
urban net. Thus, managers and policy
designers should notice these spatial
peculiarities, when organizing the Region’s
public services availability, especially those
that are considered basic.
Conclusion
With regard to the organization of
the cities of the Amazon’s urban nets in
hierarchical levels, theoretical considerations
suggest that the centrality condition
attributed to a certain city is related to an
association of qualities and characteristics.
So, it is often the case that the studies
that sought to understand the hierarchical
organization of the cities were closely
linked to the demographical size and to the
way in which this variable influenced the
economic variables and the functions of
urban agglomerations or vice-versa. That
being the case, it is possible to state that
urban hierarchy is not adequately evaluated
if focusing merely on the demographical
size of the centers, or even on the way
the population size of a city is affected by
economic variables. Even when it comes to
the Legal Amazon, where, as seen before,
there generally is regularity in population
sizes with variables of different kinds in
the definition of hierarchical patterns, it is
noteworthy that some municipalities seem
to escape this trend.
The GoM model showed that a
municipality in the inner region, with a
high degree of compatibility with Profile 1,
that is, with a gik higher than 0.75, is more
likely to contain a centrality that plays a
functional role closer to what is understood
as a “medium city”, considering all the
conceptual complexity inlaid in the term.
Thus, 23 municipalities presented a high gik
in Profile 1. They include all the state capitals
of the Legal Amazon, which were qualified
as being pure Profile 1 types. Considering
that a state capital, even a demographically
middle-sized one, is generally on the top
Urban hierarchy in the brazilian Amazon
of the regional hierarchy and, therefore,
would not be qualified as a medium city,
it is noteworthy that, in this discussion
applied to the Amazon, the municipalities
of Ji-Paraná, Araguaína, Imperatriz, Barra
do Garças, Rondonópolis, Tangará da
Serra, Várzea Grande, Ariquemes, Sinop,
Gurupi, Castanhal, and Vilhena stand out
due to the high compatibility with Profile 1,
which is characterized by a medium/large
population size, high degree of urbanization,
high functional diversification, and medium/
high GDP (Gross Domestic Product).
The GoM demonstrated that some
municipalities that contain cities of expressive
population contingent in the inner region of
the Amazon (not the capitals) do not present
a high compatibility with Profile 1, which is an
evidence of the existing needs in part of the
medium-sized municipalities in the region,
such as in Santarém—the largest city in
the inner region of the Amazon—,Marabá,
Itaituba, Parauapebas, Abaetetuba, and
Parintins.
The GoM also permits evaluating the
existence of differentiated patterns in the
location’s influence (highway – border
areas / rivers – countryside) regarding
model variables, since the description and
spatialization of the municipalities with a high
compatibility with Profiles 2 and 3 shows
this very clearly.
Profile 2, characterized by its medium
to high urbanization degree (between 70%
and 90%), by medium-sized population
(30,000 to 100,000) and low to medium GDP
(from R$ 500,000,000 to R$ 1,500,000,000),
encompasses a group of municipalities
found predominantly in the “archway” that
cuts through all the southern portion of
the region. Profile 3 is characterized by a
medium urbanization degree (from 50% to
70%), by a medium-sized population (30,000
to 100,000 people) and GDP lower than R$
500,000,000, and includes municipalities
located in a dispersed manner through the
forest, and, mainly, near the main rivers of the
region. It is noteworthy that, in this case, the
population, when analyzed alone, does not
help to differentiate Profile 2 from 3.
Thus, it seems evident that spatial and
functional variables exert an influence on
R. bras. Est. Pop., Rio de Janeiro, v. 27, n. 2, p. 251-268, jul./dez. 2010
265
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Urban hierarchy in the brazilian Amazon
the model’s final result. Understanding the
differences and particularities of the isolated
cities and the road arch cities seems to be
an interesting exercise, since the urban
hierarchy model suggests differences
that interact with the urban nature and the
regional urban net dynamics.
Profile 4 is characterized by small
municipalities that are little urbanized (from
10 to 50%), by a small-sized population
(between 20,000 and 30,000 inhabitants),
by a GDP lower than R$ 50,000,000 and
by high proportion of poor people in the
year 2000, between 64.92% and 79.6%.
These municipalities are not located along
the main roads of the region, but instead
they are found near rivers and secondary
roads, especially in the states of Pará and
Maranhão.
Furthermore, GoM used two variables
that aimed to make the model more reliable:
the Functionality Indicator and the Centrality
Indicator. With this methodological novelty,
the analysis of the hierarchical patterns
represented in the model by the 4 profiles
were closer to what could be understood as a
“methodological ideal”, difficult to be applied
empirically due to the complexity of the
subject, but included in studies theoretically
based. As for future studies, which will
seek to understand the hierarchical urban
organization of other regions of the country
and of the world, these indicators may be
incorporated if adapted to the regional
reality.
Understanding the hierarchical
organization of the cities in the Amazon
seems to be a very important exercise in
order to comprehend the dynamics and
specific characteristics of regional urban
nets. In this way, it is evident that policies
which stimulate the establishment of more
structured urban nets in the Amazon are
needed. A more balanced population
distribution throughout the territory could
bring a series of benefits, especially when it
comes to the offer and access to all different
sorts of services.
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Resumo
A hierarquia urbana na Amazônia
O modelo Grade of Membership (GoM) é utilizado para delinear perfis, com base em um
banco de dados heterogêneo e multidimensional, o que permite identificar grupos (clusters)
e descrever as diferenças entre os mesmos. Neste trabalho, o GoM utiliza diversos tipos de
variáveis, que objetivam uma maior compreensão da grandeza e da capacidade de influência
das cidades amazônicas. Para cumprir tal tarefa, propõe-se um modelo que considera uma
diversidade de aspectos que extrapolam as análises de ordem puramente econômica ou
demográfica. Entender a organização hierárquica das cidades na Amazônia parece ser um
exercício de grande importância para a compreensão do dinamismo e das especificidades
das redes urbanas na região. Nesse sentido, parece evidente a necessidade de políticas
que incentivem o estabelecimento de redes urbanas mais estruturadas na Amazônia. Uma
distribuição mais equilibrada da população ao longo do território amazônico poderia trazer
uma série de ganhos, sobretudo no que se refere à oferta e ao acesso a serviços de diversos
tipos e níveis de sofisticação.
Palavras-chave: Amazônia. Distribuição espacial da população. Hierarquia urbana. Grade of
Membership (GoM).
R. bras. Est. Pop., Rio de Janeiro, v. 27, n. 2, p. 251-268, jul./dez. 2010
267
Sathler, D. et al.
Urban hierarchy in the brazilian Amazon
Resumen
La jerarquía urbana en la Amazonia
El modelo Grade of Membership (GoM) se utiliza para trazar perfiles, en base a un banco de
datos heterogéneo y multidimensional, lo que permite identificar grupos (clusters) y describir
las diferencias entre los mismos. En este trabajo, el GoM utiliza diversos tipos de variables, que
tienen como objetivo una mayor comprensión de la grandeza y de la capacidad de influencia
de las ciudades amazónicas. Para cumplir tal tarea, se propone un modelo que considera
una diversidad de aspectos que extrapolan los análisis de orden puramente económico o
demográfico. Entender la organización jerárquica de las ciudades en la Amazonia parece ser
un ejercicio de gran importancia para la comprensión del dinamismo y de las especificidades
de las redes urbanas en la región. En este sentido, parece evidente la necesidad de políticas
que incentiven el establecimiento de redes urbanas más estructuradas en la Amazonia.
Una distribución más equilibrada de la población a lo largo del territorio amazónico podría
proporcionar una serie de beneficios, sobre todo en lo que se refiere a la oferta y acceso a
servicios de diversos tipos y niveles de sofisticación.
Palabras-clave: Amazonia. Distribución espacial de la población. Jerarquía urbana. Grade of
Membership (GoM).
Recebido para publicação em 01/12/2009
Aceito para publicação em 29/04/2010
268
R. bras. Est. Pop., Rio de Janeiro, v. 27, n. 2, p. 251-268, jul./dez. 2010