# Introduction

razil finds itself in an advanced phase of the process of demographic transition. The shrinking of the base of the aging pyramid and the growth of its vertex are already noticeable. This essay intends to compare the migration flow figures of two distinct periods: 1995/200 and 2005/2010, in order to ascertain what kind of migration flows is occurring in this period, that could eventually explain some of its migration behavior.(Figures 1-7)

A new phenomena that concern these migratory fluctuations has been taken to note and has been the studies of various research projects in the academic environment: a decline in net migration rate from traditionally underdeveloped regions (mainly the northeast) to more industrialized regions (primarily the southeast).

This decline in the net migration rate can be partly explained by return migration. Considering that fact, it is of fundamental importance to know migratory patterns of the population so as to foresee the spatial redistribution of the population in general that will eventually result in the reformulation of social policy to better regionally allocate national resources.

Spatial analysis and GIS are widely used in order to study such events (Bailey and Gatrell, 1996). Specifically in this case, Tobler's approach is used (Tobler, 1976) for mapping the flows and, for the identification of migration patterns.


# II.


# Tobler's Approach

If a potential migrant is taken at random in a population sample and is "thrown in the air", there will be a general migration tendency that this person will follow. Tobler calls this tendency a "wind" (Tobler, 1976). He has focused on the difficulties associated with the symmetry of the gravity model and tried to remove this problem introducing the "wind" in order to account for interaction in particular directions. The approach facilitates the description of large flow matrices by analyzing the asymmetric part of the from-to-tables.

It is interesting to see that the antecedents of the approach were motivated by the calculation of geographical locations from data on separations or on interaction. The inversion of models was used: for example, the social gravity model can be written as:


# And the inversion is

The problem was that the social gravity model is symmetric, i. e, D ij = D ji and M ij must be equal to M ij . In practice the data are different (M ij ? M ji ). This would imply that if the model is inverted, D ij ? D ji .

He stated that has "the consequence that the tri-lateration solution can result in more than one geometrical configuration or that the standard errors of the position determination are increased" (Tobler, 1976. p. 2).

To overcome this problem, a "wind" was introduced in order to facilitate interaction in some direction. This vector is estimated by the data. In its formal aspect, each location i, with coordinates (x, y), has associated with a vector with magnitude and direction:


# B

Volume XXI Issue III Version I 
( ) ij j i ij D f P P K M . . = ? ? ? ? ? ? ? ? = ? j i ij ij P KP M f D 1 ( )( ) [ ] ? = = ? ? + ? ? = n j i i j i j ij ji ij ji ij y x x x D m m m m n i 1 1 . 1 . 1 1 ?

# Where

. For the complete algebraic development, see Tobler (1979).
( ) ( ) 2 2 2 i j i j ij y y x x D ? + ? =
Sometimes we have an incomplete matrix for a set of data, so in order to overcome this situation a complete set of data is generated, using Baxter entropy program (Tobler, 1976). The program follows Wilson's derivations of the gravity model using entropymaximizing techniques. It has three variations and one can use a complete matrix or only the marginals as input. The program permits two variations with the gravity model or with the entropy model.

In the research described here we have used a 


# Results

In the comparison of the data migration between the periods of 1995/2000 and 2005/2010 for the Northern region, the States of Rondônia, Amazonas, Roraima, Amapá and Tocantins continued to receive immigrants, showing a positive balance for both periods, with the exception of the States of Acre and Pará that continued to show a negative balance, but with a significant decrease in the number of emigrants in the comparison between the two periods considered.

In the Northeast region it was observed a quite expressive negative balance for almost all States, especially for the States of Bahia and Maranhão, who contributed with significant numbers of emigrants by repeating the tendency observed in the 1995/2000 period, without major modifications. The States of Piauí, Ceará and Alagoas kept negative figures, but decreased their numbers in absolute values for both periods, perhaps showing some modification in their migratory pattern, which should be better measured in the future. Only the States of Sergipe and Rio Grande do Norte presented a positive migratory balance, perhaps due to new investments in the tourism sector, typical of these States.

In the Southeast region the negative highlights went to the State of Minas Gerais, which was the only one to make a considerable change in its demographic profile presenting, in the 1995/2000 period, an expressive number of immigrants, but in the period 2005/2010 presented a negative number in its migratory balance. The State of Espírito Santo showed a significant increase of immigrants, nearly doubling its values of the previous decade, probably due to the new investments in oil extraction and in agribusiness. The States of Rio de Janeiro and São Paulo also presented a positive migratory balance, but with much smaller values than the previous decade, perhaps explained by the so called return migration, which has been shown to be significant in Brazil in the past two decades.

In the Southern region the Santa Catarina State occupies a prominent position showing an expressive positive migratory balance, almost tripling the number of immigrants in the last decade. The States of Paraná and Rio Grande do Sul have maintained the tendency of negative balances in the last two decades, but the State of Rio Grande do Sul, presented an even more expressive negative balance for the last evaluated period.

All This decrease is also well perceived in interregional migration. According to the 2000 Census, 3.3 million people had changed regions in the five previous years. The national survey samples (PNAD) of 2004 already shows a reduction to 2.8 million. Finally, the National Household Survey of 2009 shows that just over 2 million people had chosen another region to live.

In the South, the States of Paraná and Rio Grande do Sul perceived a considerable flow of return migration, while Santa Catarina is the southern State that attracts more new immigrants -its current migratory balance is 80 thousand immigrants. The same process can be observed in the Midwestern region, being the region that more retains its immigrants. According to the 2009 PNAD, in absolute terms, São Paulo remains as the State that receives more immigrants (535.000), followed by Minas Gerais (288.000), Goiás (264.000) Bahia and Paraná (both with 203.000 new immigrants). On the other hand, São Paulo is also the place that Migration Flows in Brazil: A Spatial Analysis using Tobler´S Approach generates more emigrants (588.000), followed by Bahia (312.000), Minas Gerais (276.000), Paraná (171.000) and Rio de Janeiro (165.000). (Figures 1-3). 


# Tables and Maps
![Author ?: Ph.D, (PUCMINAS-BRAZIL). e-mail: jofabreu@hotmail.com Author ?: (PUCMINAS-BRAZIL) Author ?: MSc. (Ph.D, Student)](image-2.png "")
![States of the Midwest region showed a positive balance regarding migration, especially the State of Goiás which presented an expressive number of immigrants for both periods. The State of Mato Grosso do Sul showed a profound modification in its migratory pattern, showing a positive balance for the period 2005/2010 compared to a negative number for the period 1995/2000. The States of Mato Grosso and the Federal District (Distrito Federal) both showed positive balances but with much lower immigration values for the period between 2005/2010. The number of Brazilians who have changed their State of residence is decreasing for the past 15 years, according to data from the Brazilian Institute of Geography and Statistics (IBGE). The survey shows that, between 1995 and 2000, about 5.2 million people have changed the State of residence. Between 2000 and 2004, the number went down to 4.6 million. The latest data indicates that between 2004 and 2009, just over 3.2 million people moved from their State of residence -there is an important decrease of 37% in the comparison between 2000 and 2009 data.](image-3.png "")
III.
11995/20002005/2010Federation UnitsImmigrants Emigrants Net Migration Immigrants Emigrants Net MigrationBRASIL5 196 0935 196 09304 643 754 '4 643 7540Rondônia83 32572 73510 59065 86453 64312 221Acre13 63416 070-2 43613 88214 746-865Amazonas89 62758 65730 97071 45151 30120 150Roraima47 75214 37933 37325 55611 20414 352Pará182 043234 239-52 195162 004201 834-39 830Amapá44 58215 11329 46937 02815 22821 800Tocantins95 43082 51512 91585 70677 0528 654Maranhão100 816274 469-173 653105 684270 664-164 980Piauí88 740140 815-52 07573 614144 037-70 423Ceará162 925186 710-23 785112 373181 221-68 849Rio G. do Norte77 91671 2876 63067 72854 01713 711Paraíba102 005163 485-61 48096 028125 521-29 493Pernambuco164 871280 290-115 419148 498223 584-75 086Alagoas55 966127 948-71 98253 589130 306-76 717Sergipe52 11156 928-4 81753 03945 1447 895Bahia250 571518 036-267 465229 224466 360-237 136Minas Gerais447 782408 65839 124376 520390 625-14 105Espírito Santo129 16995 16834 001130 82070 12060 700Rio de Janeiro319 749274 21345 536270 413247 30923 104São Paulo1 223 811883 885339 926991 314735 519255 796Paraná297 311336 998-39 687272 184293 693-21 509Santa Catarina199 653139 66759 986301 341128 888172 453Rio G. do Sul113 395152 890-39 495102 613177 263-74 650Mato G. do Sul97 709108 738-11 02998 97380 90818 065Mato Grosso166 299123 72442 575143 954121 58922 365Goiás372 702169 900202 802363 934156 107207 827Distrito Federal216 200188 57727 623190 422
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